How to 'always' win at Battleship?

Battleship is a strategy type guessing game for two players. It is played on ruled grids on which each player's fleet of warships are marked. The locations of the fleets are concealed from the other player. Players alternate turns calling "shots" at the other player's ships, and the objective of the game is to destroy the opposing player's fleet. In this video you will learn the best strategy to win this game.
Chapters:
00:00 Rules
00:42 Strategy 1
01:11 Strategy 2
01:46 Strategy 3
02:22 Strategy 4

[@dodothebirb]

Me calculating the entire probability map of a 10x10 grid while my friend is wondering why I took an entire hour to fire one shot:

[@ukrop.4308]

fr, I'm not a calculator

[@supermakerraptorgamersgame285]

Good one ;)

[@doppelplusungutmensch1141]

... and it's a miss!

[@strategistaow3520]

Looks like it can be chess game

[@mapron1]

You can do a good approximation in your head. I actually did used Strategy 3 when played with my uncle 3 decades ago, and uncle won more often. So he teached me the last trick showned in video. You don't need to calculate it EXACT way, you can do it with computer couple times, well, then you will see it with your eyes (it's like chess, humans don't do billions of calculations)

[@Kallyn]

Another way to win is to move your ships around after each move and always claim the shot was a miss

[@lilneoman1]

NAVAL STRATEGISTS HATE THIS ONE SIMPLE TRICK

[@MikeB32280]

Only do this for the last 2 or so ships, that way the game feels normal until they start getting really unlucky at the end when you manage to pull out the win.

[@ttaibe]

Just do not place the frigate. In a normal game there is always a spot left where it will fit

[@gumpreeengthegumpreeeng]

But... But... that's cheating

[@sweetcellvids]

agreed, cheating will help you win

[@evanescentenquirer2684]

I think calculating the probability maps for each shot will take longer than actual naval conflicts

[@wontcreep]

TTRPG players on their way to spend 2 hours calculating rolls with all the modifier values on a combat that lasted 18 seconds in-game

[@felipevasconcelos6736]

I'm pretty sure people do calculate probability maps in actual naval conflicts

[@longinzaczek5857]

Yes but if you write a programm calculating propabilities, this will take only a second.

[@neurofiedyamato8763]

​​@@felipevasconcelos6736Nope. Closest to probability being used in combat is just a reference sheet that would had been pre-calculated such as CEP(center error probable) figures for munition accuracy. Traditionally, in naval combat, you are calculating stuff like ballistics for gunnery, triangulation for ranging, bearing, and navigation, and probably some basic physics like gas laws for steam engines etc. Even then, there were a lot of mechanical tool and even analog computers. You can't spend hours trying to get a shot off, your input data would be way out of date and you would have to start over. Nowadays, these calculations are all digitally done. Probability just don't have much application in actual (tactical level) naval combat.

[@felipevasconcelos6736]

@@neurofiedyamato8763 I didn't suggest they'd spend hours calculating the probability map of the position of enemy ships, of course that'd be done automatically within a fraction of a second. If you're triangulating an enemy ship, for example, wouldn't you get a probability map, since every instrument has an error? I assumed they wouldn't just take the mean and throw away important information about the distribution, but I don't actually know.

[@iwersonsch5131]

An important caveat is that, if your strategy is known, your opponent can be adversarial about their ship positions. So if your strategy isn't random enough, your strategy might only be as good as the worst possible score rather than the average.

[@skill_issuesmo7367]

omg iwer!!

[@captaingabi]

Exactly! If know the opponent use this strategy, I will position all my shipt on the edge, where the probability is the lowest, and thereofre it will be shoot latest.

[@EebstertheGreat]

Yes by the nature of battleship, every pure strategy is absolutely terrible. You need a mixed strategy. This one was sort of mixed in that it wasn't deterministic, but it's still easily beaten by positioning ships around the edge. The optimal strategy would presumably sometimes start with a guess at the edge, but it would be more likely to guess in the center.

[@btf_flotsam478]

This quickly becomes a straightforward case of game theory. Heck, it's even a zero-sum game (no matter if it's minimising turns or trying to beat your opponent), and it therefore has a Nash equilibrium.

[@Mr.Beauregarde]

Thank you @@btf_flotsam478 ppl be gaming like mercantilism is still cutting edge

[@PeterZaitcev]

Fun fact. In Russia, there's a different variant of the ruleset. The only but major differences are: 1. After you hit (wound or destroy a ship), you can fire again immediately 2. There are no 5-cell ships, but instead each player has 4x 1-cell ships, totalling up to 4x1, 3x2, 2x3, 1x4 3. Ships cannot occupy adjacent cells, _even diagonally_ This changes the game pattern drastically and adds a good level of mindgames during the deployment phase.

[@cha0t1c_g00d]

у вас вместо слова "корабль" получилось "говно" в первом пункте. О, уже исправлено.

[@ultearmilkojohn1145]

The first rule change literally nothing

[@PeterZaitcev]

@@ultearmilkojohn1145 That reduces TTK (time to kill) per ship. Instead of 3-6 turns for a submarine, it now takes 1-4 turns, with average of 2-3. During the late-game, this matters a lot.

[@NoNameAtAll2]

optimal deployment strategy becomes "convoy" where all large ships share "deadzone border" cells, while 1-cell boats are scattered in the rest of the field

[@lapidations]

@@ultearmilkojohn1145 Except it can change the whole outcome of the game. Even if you only have a destroyer with 1hp left, you can sink all of your oponent's armada in one turn with this rule.

[@PaulMurrayCanberra]

A still better strategy is not to shoot where the ship most likely is, but to shoot whichever square gives you the most *information* about where the ships are. Once you have 100% information, then you can take out the ships.

[@larryrobx]

Yep. Markov chain probabilities. You'd need a computer to calc those, of course. But, that'd optimize the expected # of moves to win. A good information theory observation here, Paul.

[@ItsAsparageese]

Reminds of how I play Wordle. I use each letter only once for the first 3 or 4 guesses usually, to rule out/in as many letters as possible, before solving it from what remains and/or gets identified along the way

[@wordsayer19]

Isn't that the same thing, though? The probability map calculates all the possible placements for ships, so shooting the most likely square rules out the maximum number of possible ship positions. In other words, it gives you the most information possible. Shooting for information is probably an easier way to visualize it, but unless I'm missing something, they're functionally the same method.

[@larryrobx]

@@wordsayer19If Battleship were a single move game, like tossing dice, then yes. But, it's a multiple move game. So, evaluating the decision tree more than a single step forward may reveal that other moves ultimately yield more info. This same concept applies to Wordle, Mastermind, and Minesweeper. But, unlike these 3 games, you also have an active opponent in Battleship, same as in Chess and Checkers -- hence, all the astute game theory commentary you'll find elsewhere in this thread. It's kind of amazing how profound such a seemingly simple game can be, once you dig deep into such strategy considerations. Enjoy.

[@Ridesdragons]

@@wordsayer19 I can give a specific example. let's say you know that someone still has a submarine left, and the only places left on the board are a T-junction made up of 10 cells (the intersection followed by 3 3-cell paths). the cell with the highest probability of containing the submarine is the intersection, as there are 4 placements that overlap the intersection, and every other cell only has 3 or fewer placements. however, if you shoot the intersection and are wrong, there are still 3 legal spots the submarine could be in. removing the intersection doesn't tell you anything about the paths out of the intersection. it takes at most 4 shots to find the ship. if you instead shoot _next_ to the intersection, the 3s, you eliminate that cell and the 2 following cells from the list of possibilities. it will now take you, at most, 3 shots to find their ship. the intersection in this case is the most likely position for the ship to be, but gives you very little information.

[@Electifried]

This video forgets a crucial part of the game: The part where you initially hide your ships. Where are the best and worst places to put the boats at? If you can work out the last place your opponent would think to guess, then you could have a huge advantage by sticking a boat there.

[@Mr.Beauregarde]

This could be rewritten as, play the man not the game. But the scope of the video is explicitly the game.

[@Jonas-Seiler]

@@Mr.Beauregarde you can absolutely still apply statistics and game theory and shit even if you assume the opponent used some strategy to place their ships instead of just placing them randomly

[@skinger9567]

Reverse the heat map would be a good starting point. All you ships scattered around the edges would presumably hinder this strategy.

[@wordforever117]

@@skinger9567 Not all ships. Once your strategy is discovered the rest of your ships will be sunk very quickly. Best hiding a 1x2 and a 1x3 at the edge. So at least if your larger ships are sunk quickly you can still catch up because of the two you have hidden

[@skinger9567]

@@wordforever117 so all the ships 1-2 rows in from the edge; that way once it's apparent what your strategy is, the opponent switches to the edge as a counter... but it was all a bluff, you were one step ahead of them.

[@Debbiebabe69]

The best strategy for battleships is to *not draw any ships on your side of the board* . That way, wherever your opponents shoots, he always misses. When you win the game, you simply screw up your paper so the opponent never knows. Except this one time, in the late 1980s. We were at school, it was a 'wet lunch' so everyone was inside doing various things. Battleships was a popular way to pass the time (many people spent longer drawing elaborate warships than actually playing). and a lot of kids were crowded around this particular boy and girl playing each other in an apparently long lasting game of over-the-table battleships. The boy thought he was unbeatable. He had drawn a grid to put ships on, but not actually drawn any warships. He was playing on a blank grid so could not lose. Except this time, his opponent was unbeatable too. The girl had drawn all sorts of things on her page, fish, seagulls, rainbows, stars, clouds..... but no ships. Obviously all the people around the table knew what was going on, but the players were oblivious - until the end of lunch bell rang and both players gave up and showed the other their 'fleet'..... Never heard the word 'miss' said so many times in one game......

[@kremenskiyjr]

you don't need to hunt ships that you hit. you may instead count all possibilities for what you may have hit and where to continue, and either hit another square where you are likely to find something, or hunt the ship by choosing the spot where you are the most likely to continue sinking the ship. that may slightly lower the average time to sink the whole fleet.

[@monad99]

it's the same thing, because doing that gives the four adjacent squares the highest probability

[@HoSza1]

not really the same because depending on the neigbourhood already targeted and the ship types already sunk, there might be differences in probabilities of the remaining directions, they are not neccessarily equal so need to be calculated precisely.

[@Alex.Johnsen]

@@monad99 But the four adjacent squares may not have equal probability.

[@namdoolb]

You hit a ship, it's always best to hunt it down & sink it. Lowers the number of variables you need to consider moving forward.

[@XaTrIxX2]

@@namdoolb What he means is, you also calculate probabilities based on what ships are left. If you only have the 5 squares long ship, that probably affects how you hunt it. The videos description did not take that into account yet.

[@calebklingerman7902]

The problem with this strategy is assuming your opponent will place randomly. An opponent who knows about this may choose to place their ships around the edge. Unless they know that you know that they know, in which case they will cluster in the middle. Best to build up an immunity to iocaine powder beforehand, just to be safe.

[@Josephkerr101]

I always lay out two clusters on either end of the map at two of the corners. Then the smallest ship goes near but not at the center. playing odds, confusing positions to buy time. (always funny when someone knows whats left but the hits don't cause a ship to sink) then when the rest are found they have nothing to go off of for the hardest to hit and find. this buys plenty of time for me to methodically sweep. when I get a hit I deploy strategy four, looking at probability.

[@richardvenables619]

I'm not left handed, either.

[@sabinrawr]

One important caveat about the "hit and hunt" strategy: ships can be placed next to each other (this is different from the version more common in Eastern Europe). If the opponent has done this, your hunt may take longer than expected. You could easily have a string of 5 hits and sink nothing. I'm not saying that hunting around a bit is a bad idea, but for completeness you may wish to account for this possibility when adding your probabilities.

[@sonicmeerkat]

Eh usually it's a bad idea to do that cause during hunting there's a good chance your opponent accidentally hits the other ship while trying to sink the adjacent ship

[@toddkes5890]

It also means you can't silently move the ships around on your board to give yourself another turn. That is why you plot not just your shots but also the enemy shots, so you know where it is still safe to cheat. ;)

[@cbot9302]

Yeah, I'm a big fan of the "put all of my ships in the bottom left corner right next to each other" strategy. It actually works way better than you might think. If you really want to mind game them, don't include your destroyer in the cluster and put it randomly elsewhere in the map, or like separated by 1 square from the cluster

[@mozvi1436]

If you hit multiple ships once it's still better for you. Sinking a ship in this ruleset makes no difference for your next move. Whereas knowing there are multiple ships in the same place gives you a great advantage since you know you won't have to search for another place.

[@sabinrawr]

@@mozvi1436 I agree that the strategy doesn't change much. I just added the caveat more as a reminder of this possibility, especially for our friends in Eastern Europe, who play by slightly different rules (different number of ships each size, ships may not touch orthogonally or diagonally). My friends and I sometimes play a harder version, where we don't announce that a ship was sunk. With this variation, it's impossible to tell the difference between a carrier versus aligned destroyer and battleship.

[@8wyj]

Your really underrated I thought I was watching someone with around 100000+ subs

[@Bigzthegreat]

ye, the algorithm has recently began to recommend vids from smaller creators

[@hugohogberg4014]

yea same!

[@aidenhastings6341]

You’re

[@ceremonious_houseplant]

That’s not possible. You can’t fit that many subs into a 10x10 grid. It will also be completely unfair to the other player.

[@dodo600]

Lol i just saw that sub now i thought like that too

[@GregMoress]

I discovered you could stack all the ships on top of one another. The beauty is two-fold: 1) It's much harder to find the 5 spots. 2) After the sink the top ship they don't fire again at the same spots to sink the one beneath it... I'd be incredibly honest and admit a HIT if they did.

[@dudegaming2862]

So true my opponent did that once XD.

[@obansrinathan]

I find you can only play that strategy once before your opponent quits/ beats you up

[@sarcasticguy4311]

@@obansrinathan Nah you'd have a good laugh for being clever and not use that strategy again for a couple months.

[@jeremybradford9959]

According to official Milton Bradely rules, you cannot stack ships. But, let's say you ignore the actual rules. I guess in that case, the specifcs don't matter since you're using made up rules anyway, and I guess you can use this strategy, but I think you still played it out incorrectly. (I know - It's hard to say something is wrong when you're using made up rules anyway, but I'd note:) A torpedo doesn't fire through the air, it fires through the water. So it destroys the bottom ship, and just like all the upper floors of a building collapsing when the bottom floor is taken out, taking out the bottom ship should also take out all ships stacked in that location. Again, it's made up rules anyway at that point, but if you're using the single-stack approach, that's how I'd rule it. P.S. 7 year old me definitely stacked the ships at some point :)

[@GregMoress]

@@jeremybradford9959I never considered that they were torpedoes... since I placed them from above... so 7 year old me considered them bombs. I'm a software developer, it's against our religion to read the documentation/rules.

[@aaronbredon2948]

I shoot in the 4 long pattern first - that gives a 50% chance of a destroyer hit, and 75% for the sub and cruiser. The 4 long pattern can be converted to the 2 long checkerboard after all found ships are sunk. Being aware of what patterns can be converted helps a lot.

[@Mr.Beauregarde]

Is 4 long pattern a half filled double sized checkerboard? B/c if so your incidental hit probabilities are off

[@aaronbredon2948]

​@@Mr.BeauregardeI generally start by filling out the board using long knight's moves (1×3). This quickly catches the carrier and battleship, plus generally at least one of the 3 long ships. Then I play moves on the base checkerboard pattern that are most likely to have 3 long ships. Once I am down to just the destroyer, I play the most likely squares to be part of it. Generally, I don't even get to the final filling out of the checkerboard. It really comes down to if you hit the destroyer during the 4-long and 3-long searches. If so, you are guaranteed not to need the long search. This play method is easier for the 7-shot variant (2 shots each for Carrier and Battleship, 1 shot for all other ships), as it kills off the Battleship and Carrier very quickly.

[@Mr.Beauregarde]

@@aaronbredon2948 I must confess. I've only ever played one shot per turn. I also have had a person get 4 hits in a row and wait for me to declare a ship sunk (they hadn't.. yet). I'm curious, do you proceed tail to tip until wrapping around at the edge, or finish a row then shift down?

[@aaronbredon2948]

@Mr.Beauregarde generally, I choose a starting point, go 3 to the right and down a row for each shot, then go 3 down and left a column from the first shot to do the next sequence, sinking shops when I find one. Once I have covered the board with that loose grid, I shift gears based on what is most open for ships. I once hit 4 in a row with misses at each end and no ships sunk - my opponent had tried to hide all his ships except the destroyer in one mass.

[@samsibbens8164]

Ok but this assumes a perfectly random placement of each ship

[@KirkWaiblinger]

Yeah, first of all there's the objection to assuming that the probability distribution of opponent's configuration should be uniform over the configuration space. But, then, on top of that, I'm not sure that this video even does compute that distribution, since it seems to be simply adding the possible arrangements of each ship individually, which doesn't account for the fact that they cannot overlap. We'd have to remove all those states where at least one overlap exists and then update the counts. Not that I expect this would make a noticeable difference to the expected time to win, but it's worth thinking about

[@niconeedsanap8130]

Me placing all of my ships on the top: ME ON TOP

[@alquinn8576]

if you have some reason to believe your opponent will diverge from random in a particular way, you could probably add weights to each ship position the counts done in the video to account for that

[@thierrypauwels]

The rules that I learned were a bit different. Each turn you had to announce 3 shots, and your opponent would only tell you the result of all three shots together, without saying which shot touched what. And the winner was not the one who sunk all the ships of the opponent, but the one who could locate all the ships of the opponent. A bit like mastermind.

[@captainct5ben504]

Sounds cool, never heard of this though

[@maximos905]

That's just a different variation of the game, there is also the 5 shot rule

[@therealbahamut]

@@maximos905 Ah, the good ol' "salvo" ruleset.

[@puppergump4117]

Sounds like every fight in Dragon Ball Z: Goku: KAMEHAMEHA!!! (x3) Enemy: explodes Everyone: Did we get him? Enemy: lol no

[@MoonLiteNite]

We called that version "salvo rules"

[@spartacus3111]

We played a version where you didn't announce when your opponent had sunk a ship. This led to sneaky tactics like placing the cruiser and submarine end to end, and your enemy would stop shooting after 5 hits thinking it was the carrier, when really you still had the tail end of the submarine alive XDXDXD Placing ships in a zig zag meant that they had no idea what was still alive to adjust their probability maps.

[@germsage6726]

My family also play that version of the game. Totally makes it a lot more fun. Hunting for that one last slot for the destroyer or the head and tail/end of a cruiser/submarine is usually the worst.

[@bugfacedog44]

I always just do the pattern where you search for any length-3 ships, and you have a 66% chance of hitting the little length-2 guy. Also there are times where I don't finish off ships after the first hit because you can waste shots finding direction, but would be clear exactly what direction it is if the grid is a little more filled out.

[@Mr.Beauregarde]

Starting where is the question

[@Clumbob]

No reason you can't look for the ship while still sticking to you grid pattern

[@yesyesyesyes1600]

Finishing off ships makes sense when the salvo fire rule is applied. 5 ships 5 shots 4 ships just 4 shots

[@yahnmahn9035]

I'm proud to say that I thought of the first three strategies all on my own while playing battleship. Unfortunately, I must be very unlucky, my sister always manages to beat me through random chance before I beat her.

[@CanyonF]

sounds like she thought of the first four all on her own

[@yahnmahn9035]

@@CanyonF lol, maybe

[@Mr.Beauregarde]

Have you considered the possibility she may be a witch?

[@sk31370n]

all you need is a strategically placed mirror @@Mr.Beauregarde

[@yurenchu]

Do you wear glasses?

[@Courtj3st3r33]

I played one game of battleship with my son, he tells me as we are playing that he has a winning strat. The next day I'm recommend this video. Thanks for spying on every conversation I have with my children.

[@musicalcharge]

Even if you don't calculate the exact probabilities every time, you can eyeball it all pretty quickly, which intuitively makes sense as well. Chances are higher in big open areas.

[@KarczekWieprzowy]

In my school we used to play with 1 4 squares long ship, 2 3 squares longs, 3 2 and 4 ships with only one square Now this is where my top strat comes in to play, put all bigger ships around the edge of the map, but then scatter the smallest four all over the middle Won every time someone didn't know how to counter it (we usually also applied a rule of "followup strike" meaning if you hit you could do another strike allowing you to take out entire ships in one turn)

[@IllarionYolgin]

Can you elaborate how to counter this strategy? I'm using it myself and want to know it's cons because I can see only pros.

[@KarczekWieprzowy]

@@IllarionYolgin Fuck if I know lol

[@Fadexpl]

ships with 1 square is ridiculous, reduces the game to a game of chance.

[@KarczekWieprzowy]

@@Fadexpl I mean... the whole game is a game of chance either way...

[@SONYUSR]

​@@Fadexplapparently that's a common russian variation

[@BrianStDenis-pj1tq]

I wrote this game and used a similar scoring strategy. My score was based on the largest ship available, not the sum of the best shot over all ships remaining. The result is almost always a set of squares with the same high score, so the algorithm picks one of those randomly to shoot. But, humans can beat it because humans don't place ships evenly spaced. Also, the computer player needs a strategy for placing ships. My game uses random placement, which humans can hit fairly easily. The game side needs good ship placement and good shooting algorithm to beat a human.

[@hvnterblack]

If "no touch" rule is apllied, it changes probabilty a lot.

[@The-Anathema]

Please explain.

[@Mati-zc2ym]

@@The-Anathema if rules are different, the strategy is different lmao

[@mac1991seth]

In some variants of the game, all ships have to be surrounded by empty space all around. You can't place two ships right next to each other in any combination. @@The-Anathema

[@The-Anathema]

@@Mati-zc2ym No shit. I was asking what the 'no touch' rule is, since I a cursory google search didn't reveal it. Now I *assume* it means the ships can't touch (adjacent or diagonal) but it's just that, an assumption.

[@The-Anathema]

@@mac1991seth Thank you.

[@boblybob]

It's only works if your enemy is picking the place at random the enemy could know what you're thinking and places it on the last square you're gonna pick using this strategy, and your opponent will probably also use that strategy so you could be the first one losing

[@Kyrelel]

I think you have misunderstood the strategy; there is no way for your opponent to defend against this strategy because he won't know where your first few random shots will land.

[@boblybob]

@@Kyrelel he will probably know because in the middle is the place to start with this strategy so your enemy could've just pick the edge and the enemy also could've use this strategy too meaning you have a big chance to be losing kind of like rock paper scissors where one time people always use scissors because the enemy easiest move is to go paper but now the enemy could know your strategy and pick rock instead of paper

[@G0G0w0]

my favorite strategy at this game is either : put ur ships in all corners or just stack'em as one big pile, just note that stacking them can confuse ur enemy at first because, when they shoot around they might find that one of ur boat have a "+"shape instead of a "-", but once they realise u just glued them all, u basically lost. (also try playing shipwrecker with the wind waker noises, it makes it more fun, if u know what i mean)

[@ErshErshovich]

In my country the smallest ship is just one square in size, not 1x2. And it's prohibited to place ships right to each other or connect in any other way (i.e. a 2x1 ship occupies 3x4 area - the ship itself and "borders").

[@theother1s220]

What country are you from, if you don't mind me asking?

[@Mr.Beauregarde]

Certainly the former Soviet Union, probably in or neighboring Тверская Область.

[@JakubH]

@@theother1s220 we play it this exact way, I am from Czechia

[@My1xT]

​@@theother1s220not sure about 1 square ships but ship borders are a thing in Germany too

[@affegpus4195]

i wonder if placing ships next to the other is even a good strat to start with. when you get a hit, you then are gonna hit the surrounding area to find the rest of the ship. those shots have ~1/2 to 1/4 of being misses, by placing a ship next to the other all you doing is that you giving those scan shoots a chance to be hits depending where the first hit was. and there is really no way to mislead the opponent and make him miss shots by any confusion that might issue

[@omega4679]

So glad I just found this channel, you got so much highly underrated high quality content.

[@scfan7231]

Love this! Once in a while I ask myself this question and this sounds like a good answer. Enjoyed the vid a lot.

[@carsonrush3352]

As a shorter heuristic, (1) Map out the projected shots for finding the 3-length boats. (2) Start shooting at the projected locations near the center. (3) Don't aim for locations nearby your other shots (3+ away from other shots). (4) Once (3) can no longer easily be done, start expanding outwards towards the board edges and in between shots, always filling in the projected locations.

[@chaoticgood6439]

in poland you have 1 4 grid long ship, 2 3 grid long ships, 3 2grid long ships and 4 1grid long ships. so you cant just follow the checkerboard, or you would miss all the single grid "yachts" HOWEVER ships cannot touch at all, even on diagonal, so if you sink a ship you can just dot all the squares around it as empty

[@okroshka7]

That's battleship, and the video describes bullshit

[@krzemienpasiasty3371]

I am from Poland and i have never played with 1 grid ships.

[@Merione]

I always found it strange that you start with 5 ships, but you only get to shoot once per turn. I wonder how the strategy would change if you were allowed to shoot as many times as you have ships available (so 5 shots if you have all 5 ships, 4 shots if you have 4 ships, 3 shots if you have 3 ships, and so on).

[@Milktube]

The official rulebook that comes with the game even suggests this as an alternative style of play! They called it "Salvo" style or something to that effect. I think the strategy would depend on if you got feedback for the hits immediately, or had to commit to all 5 shots first and get all 5 feedback afterward. If the later, I feel like it would just become a luck/momentum game, whoever gets an early lead because of random chance gets an insurmountable lead that is impossible to overcome. If based on the former, then I think going first would be a huge advantage and I'm not sure how to balance that out.

[@T123456788]

@@Milktube I wonder if not getting feedback on each individual shot but rather "all 5 hit" vs "At least one of your 5 shots hit" and then the only other info you could get is "You sunk my X" would help to mitigate the luck/momentumness of the game without giving the absolute advantage that getting to take 5 shots with feedback after each shot to start the game would be.

[@EzEssence]

@@Milktube a suggestion that I would have is have both players announce their hit locations at the same time and then announce hits and missis at the same time.

[@dashyz3293]

sounds incredibly unfair. The guy going first already has a small advantage, and this snowballs that effect.

[@Grubnar]

The way I learned it (I live in Iceland) was that you have 10 ships. 1 Battleship, 4 squares. 2 Cruisers, 3 squares. 3 Destroyers, 2 squares. 4 Submarines, 1 square. You and your opponent then take turns guessing, 3 guesses each time.

[@austinbalon3124]

The true optimal strategy would assume your opponent has knowledge of the probability map during the placement phase. In this case you would use a weighted probability matrix where the weight is equivalent to the inverse of that squares pre-game probability value.

[@justusP9101]

I really thought this video had 580 000 views and not 580, i was surprised by the quality

[@MidnightWonko]

Neat. I once played a game of Battleship with my brother, and that mad lad placed all his ships horizontally in the bottom rows!

[@Andoriol]

Beautifully done video, very succinct ending. I think you could have easily done an 'example' game as well for demonstration purposes but I can't honestly criticize this methodology. Well done.

[@Trytytki]

That is a very cool video! Though i want to share one thing In my country we play battleships differently We still have 2 opposing players, each one has a 10x10 grid And there are changes Each player places the following ships on the grid: 4 one-tile ships 3 two-tile ships 2 three-tile ships And 1 four-tile ship The ships cannot touch each other and cannot touch diagonally and by that i mean by their corners Also the large ships can be adjusted freely and that means your eg. Four-tile ship can be a 4x1 line or a 2x2 square or even a (eg.) A1,B1,B2,C2 ship etc. So yeah these are the rules and if you play wisely it’s also pretty easy to exploit and „always” win I just thought it’s very interesting that basically the same game actually differs so much depending how’d you learnt to play, and hopefully you’d like to try this version too ;) Have a good one everybody!

[@simonetozzi7912]

Nice. I have been using a similar strategy, but here you analyze the position better. 👍

[@otter502]

3:11 small optimization is that you only need to update the squares around the missed shot and you can cache the probabilities of squares that arent affected

[@ohitsrusher842]

Very nice, i cannot wait to play this game and forget immediately lol

[@JG-jc8dm]

I am feeling quite proud that 6 or 7 year old me had figured out at least a little bit of this strategy and would likely account for why I always seemed to win.

[@Xeonomy]

Here in poland when I was a kid my mom taught me these rules: - there is one 4 square ship, two 3 squared ships, three 2 squared ships and four 1 squared ships. - each ships are called x-masted ships, where x is number of squares that the ship ocupies, so i.e a ship that ocupies 3 squares is called three-masted ship. - here is the most important change: the ships can bend. so four-masted ship can make an L shape, a square or just be straight. - the ships can't touch even if they are diagonal. so after the ship is sunk, you can instantly eliminate all squares around the ship.

[@r4_in_space]

What if, when you shoot around a hit square, you also apply the probability map, but not yet updated, and shoot the adjacent square with the highest probability?

[@talkysassis]

You can do that to sink the ship, but after that is better to update the map

[@danielyuan9862]

You can still use a probability map here, but only consider possibilities where one of the ships contains the hit square.

[@EndMaster0]

So I'm curious if weighting the smaller ships probability maps heavier on the last method would make it any faster? Cause other techniques are faster once you've already sunk the smallest ships and I'm wondering if the same thing applies.

[@levi1929]

A fun variant is to roll a d4 at the beginning of each turn to dictate how many shots you get. Each volley is shot in its entirety before Hits and Misses are announced.

[@kuwejtyt1680]

underrated, you deserve more subs

[@FoxRiverBridge]

This is hella cool and earned my sub

[@josephschubert6561]

I have a really specific strategy for a specific opponent. When my brother and played when I was younger, I always made my ships in the shape of a J. Of course, he figured this out pretty quick. At some point I switched to always placing along the edge, and somehow he never realized the change. There were a solid few months were my placement strategy gave me a big enough headstart that I could beat him.

[@madnessbydesign1415]

I would occasionally put all my bigger ships in one corner or along one edge, leaving the destroyer in open water. Drove them crazy... :)

[@musebaer]

Really great video keep up the HQ content

[@jackr2287]

I had always thought this was pretty simple. This formalizes it a bit more, but once you figure out the psychology you take to place vessels, and that it's worthless to clump shots too much... you can just start a walking pattern to figure out if you are anywhere nearby.

[@ris_kis]

Thanks for your guides

[@CatOnACell]

i like playing the faster burst ship mode. you target a point and say either (x) or (+). they tell you how many hits were in that cross or plus but NOT the squares hit and missed. if you lose a ship, you lose one edge of your burst. there is also scatter where you have one guess on your turn for each live ship remaining but that gets complicated really fast.

[@AS-mw6pw]

It would be interesting to know mathematically what the most effective ship placement is, if your opponent is using this strategy

[@CivilizedWasteland]

Probably bunching then all up in a corner and trying to place the larger ships towards the center so the guessing gets harder and harder. Of course a human could just see you bunches your ships together and switch tactics.

[@ShamanMcLamie]

​@@CivilizedWastelandI used to do that tactic, but once people figure it out it stops working and can guarantee a defeat pretty quickly. Putting them randomly on the edges of the map I find works a lot better, but that only works for so many games against the same player.

[@CazBun]

Saw this and had flashbacks to when i was 12 - used to win every game of battleships on binweevils with a slightly rudimentary version of this strat. 20 games a week, I WAS UNSTOPPABLE!

[@alpacaofthemountain8760]

Great video! Will think of this

[@SLiQ.]

opponent: "d4" me: "miss" opponent: "dang, your turn" me: "one sec"

[@cloudy_days2321]

To simplify the last approach, always choose a point in the middle of the largest open area.

[@lukejuras8024]

There's also a SALVO version included in the rulebook. You get to call out one shot for each ship you have remaining, and then the opponent tells you which shots hit after you call all of them. How does this change the formula, if you have to call 5 shots without knowing which one was a hit?

[@Mr.Beauregarde]

Obviously

[@amazonbass]

Wow... battleship in Brazil have completely different types of ships. For instance, the submarine is just one square, and there is the seaplane, which are 3 squares in diagonal, forming a "V" shape. Also, our grid is 15x15.

[@wyattstevens8574]

The PDF approach (last strategy) would still work!

[@rosiefay7283]

Fascinating. Now please may we have a video about the best way to deploy your fleet?

[@Kyrelel]

I can save you some time ... there isn't one.

[@itTchin]

Just easy counter strategy: put all big ships in one line on the border of map and put smallest ship randomly. For this you will have around 10+...50+ shoots advantage. When other player will have to make insane calculations hunts, etc.

[@igorzherebiatev5751]

And ships should never touch with each other.

[@wyattskinner697]

I don’t play by that rule cuz it’s lame.

[@bugfacedog44]

This is not a rule. They, very explicitly, can touch each other.

[@sabinrawr]

Battleship does not have this rule, at least in English-speaking countries. There is another version called Battle Boats that did have this rule, as does Polish Battleship.😊

[@waffler-yz3gw]

lol sounds dumb

[@vertonimal]

I do the exact opposite so I create "phantom battleships". Stips of hits about two to three in length. The amount of confusion as a person shoots my phantom and then caps either side without sinking anything is great. Of course this strategy backfires quickly because once they hit one the odds of them finding other ships by accident are very high. Especially if they "sink" the phantom.

[@majkgmajkg2613]

Nice. In Poland, however, we have battleships with 10 ships. 1 with length 4, 2 with length 3, 3 with length 2 and 4 with length 1. That means that no matter how good your strategy is, everything comes to the luck of how quick you will be able to destroy all length 1 ships. :(

[@kuwejtyt1680]

this strategy can still be good though, and remember that sometimes your opponent will place all 1's in the corners to trick you, it happened to me before

[@kraageshmikosevaar794]

In this ruleset, ships cannot touch each other even diagonally. For ships of length 1, the probability of all cells will be equal to 1 at start. But if we sum up the probabilities for ships of all lengths, some cells will be more profitable to knock out at least something, and reduce the number of possible locations of ships with the length of one cell. So at least some optimizations can be made.

[@sabinrawr]

I have seen this version on Brain Bashers under the name Battle Boats.

[@jubbawubba]

Same in Russia

[@kevintrigg3707]

The psychological aspect can also be considered when you start needing to bring it out of the purely mathematical stage, I wonder how you would quantify the frequency of putting a ship in a corner/ along a wall. Cool Video!

[@feynthefallen]

I tried your strategy. My nephew got very upset when I told him I need an hour for my next move. I'm Currently picking game markers out of the cat bowl. I really can't say that your strategy is all that great when you consider the bigger picture.

[@viljosavolainen2286]

There was a commodore 64 battleship type game with bigger board. Each player got 20 shots with full fleet and number of shots was based on the ships at your disposal. So 2 square destroyer gives only 1 shot. First turn was all about finding biggest ships and second turn was making sure every found target was sunk if possible. Oh and not all ships were straight lines.

[@netizenkane]

I remember this 👍

[@fiftygrapes]

Whats expected number of shots given that opponent also knows you update shots based on probability maps and hence places adversarially, hence updating your probability map etc. In the limit where you get to an equilibrium

[@ianbelletti6241]

I usually quarter the board on the diagonals then fire in 4's, then 3's, then 2's. It's usually the most effective strategy.

[@elihufeustel3941]

It's refreshing to see this. Search and destroy is nice, but 4/5 of the time you don't find a DD. What happens to your approach if you wait until you find 2 or more ships to start destroying? Destroying ships represent wasted shots if you eventually find most ships, as you're more likely to know the found ship's alignment.

[@johnniezee7142]

I'm not from Chad to be able to recalculate the probability map after every shot:) But when playing this game at school I fugured that a viable strategy would be to hunt the biggest ships first, since this reqires minimal amount of cells to be checked and maximal amount of crossed out cells as a result. Plus yes, as someone mentioned, in Russia you get an extra shot if you hit a target, so finding something quick improves your chances even more.

[@Tommuli_Haudankaivaja]

I use a mixture of 2 and 3. I start from the middle shooting in a checkered pattern. If I hit a ship, I sink it and mark all adjacent squares. Wins me most of the time and doesn't take much time, unlike strategy 4. But I think that only works, because of the rules we play with. Adjacent ships are not allowed.

[@toddkes5890]

I tend to go with checkerboard, but randomly walk my shots around. Otherwise if people see that I start in the center they would put all their ships near the edge. By going everywhere but in the checkerboard they have no 'safe space'.

[@Tommuli_Haudankaivaja]

@@toddkes5890 Making a cross and then a plus on the board makes it almost certain that you hit a ship. Usually a big one, which allows for marking of way more squares. But usually, if your opponent isn't using a strategy, even just a checkerboard pattern is enough.

[@shalomamigos]

My strategy: 1) Think of the board as checkered, and only target one color of the grid (unless of course you hit something) 2) Hunt for the carrier and/or battleship first. They're easiest to find because they're so big. Minimize wasted shots for when you need to backtrack on searching an area. 3) Once you find the carrier (or whatever else you stumble upon), use that information to infer where the other ships might be. Sometimes people bunch up all their ships in one area. Sometimes they spread them evenly. Sometimes they bunch up 4 and put their destroyer far away.

[@pabloforchino4250]

I play with: one ship of 4 cubes, two ships of 3, 3 of 2 and 4 of 1. But is the same thing. Good video.

[@_Taiwan3842_]

Person 1: "Ok bro, your turn." Person 2: "Alright." *7 hours later* Person 2: "B7." Teacher: "Bro the bell rang 4 hours ago"

[@RobertPatrician]

That was awesome.

[@lordook5413]

We had a little bit different rules and ships but my strategy was something like strategy 3 but backwards (search for the biggest first - and hope to find small ones)

[@nema151]

I did something similar to this growing up but instead of a checker pattern i made a "x" first then a "+" it wasn't as good as this video but i also noticed that people avoided placing their ships in some areas. Using that bit of psychology, i was able to win most games.

[@alexfong780]

Thank you for the tip, I start calculating the probability map for 3 hours and my opponent resigned

[@Romanticoutlaw]

I usually rely on mind games. I know some people in my life are more likely to cluster them, some are more likely to put at least one touching a corner. But this will be great for the windwaker minigame

[@UmUs]

Awesome video!

[@jesroe5842]

Simple and concise. Brilliant animations. Someone give this guy an award.

[@Bobster536]

Thought the video would go into whether it's worth it or not to out ships on edge of the board, which used to be my strategy most of times

[@Fonzie530]

I love this would you consider doing something like this for another game?

[@PS-hv7on]

My strategy for battleship is to pile all the ships on top of each other, therefore creating a smaller, harder to locate target.

[@sinistertoady6712]

I played a version where each ship had different abilities, so the Aircraft carrier could send out 2 jets and then the jets could scout and shoot but only shoot once per game, they would also have different ways of searching with x and + patterns. The battleship shot a tomahawk missile which chunked out 9 squares and then you couldn't use it again. The submarine was the most powerful ship by being able to shoot 2 torpedoes which would keep going till contact or had reached the other side of the row or column, then after that it could scan and tell you if a ship was in the area or not, wouldn't give you exact coords. Then there was the light missile cruiser which could shoot 2 shots that would blow up three squares in a row or column. then there was the anti-aircraft missile which you could use to shoot jets with. so you had to both balance resources and find and destroy ships and then also not be wasteful with your moves. There was also a couple of different game mode such as classic, you have 1 turn, then its your opp's. then there was one where you could have as many turns as you had ships left so if you had all 5 you would take 5 shots, then the one my dad and I played which was target plus 1, if you hit you got another shot.

[@victorfinberg8595]

nice. here i am, thinking, oh, such a trivial game, i already know all that, and you managed to show me a new trick (approximate probability map)

[@Schregger]

I remember two versions that I played before. The first was dubbed "volley rules" (there might be a more proper name, but IDK). In that rule set, you each fire 5 shots a turn. You say each shot one at a time, and the opponent will say either hit or miss for each. After you do 5 shots, the opponent will call out 5 shots. This results in far quicker games, obviously. The second was one that I thought was a little weird. It went normally, until you either just miss a opponent's ship, or you hit a ship. If you hit, you get to fire a second shot. If you miss by a square (as if your called shot hits right next to a ship), the opponent gets to fire two shots in a return action.

[@keeganlafferty1395]

actually the 2 tile ship is the Patrol Boat in some/most depictions of the game while the Destroyer is one of the 3 tile ships instead of the Cruiser

[@HoSza1]

The task of calculating and/or updating that probability heat map is very likely to be too expensive in terms of computation resources. The interesting part is to find reasonable simplifications that can speed up the process at the cost of precision, for example allow overlapping and touching ships.

[@Mr.Beauregarde]

On an infinite board perhaps, or too infinite precision. But for 100 discrete tiles? That said, I agree with the claim "the interesting part is to find reasonable simplifications" When trying to convince a normie that math is awesome, I ask them how much bigger a 14" pizza is to a 12" [a-b][a+b]

[@HoSza1]

​@Mr.Beauregarde I don't know what you mean by infinite precision, but one method to find an accurate heat map is to enumerate all possible starting configurations of the whole set of ships and add one to the value of each occupied cells (they all start from zero). Once the enumeration is done, the cells' value are to be divided by the total number of starting configurations, so each cell shall contain a value between 0 and 1, that is the heat map values. Now a good mathematician (not me) may be able to find a very clever way to compute the same final heat map values without actually going over all the possible starting configuration, but the number of those is certainly very high: the carrier has 120 possibilities to be placed when placed alone, the battleship would have 140, the cruiser and submarine have 160 each and the destroyer would have 180. The product of these is about 7.74e10, though the real number of configurations is lower than this product (since no overlaps are permitted).

[@Mr.Beauregarde]

@@HoSza1 And a clever simplification would be pointing out how, by itself, of the carriers starting positions, only 20 are distinct. The rest being rotations and reflections of that set.

[@HoSza1]

@@Mr.Beauregarde That's a good start for sure, also each complete deployment of the whole 5 ships fleet can be rotated and mirrored which further reduces the search space.

[@yurenchu]

​@@Mr.Beauregarde Only 15 are distinct, not 20.

[@cactusdu67f]

Can we have detail about how you get the average shot for the four strategy please ? Its a great work !

[@andycole5957]

I like the strategy of starting wherever, but spacing out my shots by every 5th tile, like the stripe pattern he shows for the carrier. If I'm lucky, I get the smaller ships randomly within that; however, if I don't, I can shoot the middle open tiles to clear them of all the smaller ships without ever having to shoot two adjacent tiles. Of course, as the game goes on, the perfect checkerboard pattern gets shifted by what's open.

[@midcoregamer7625]

A1, B2, C3, D4, etc to make a diagonal line to cut the field in half (hunting if I find anything in the process), then make a diagonal the other way. This makes four quadrants, each of which I can diagonally hunt until every ship is identified and eliminated.

[@JohnnyNumber11]

In Germany, you can'r place ships next to each other (like shown at 4:02). So you will know, after sinking a ship, that all places connected to the ship (the diagonale onces also) aren't inhibited by an other ship.

[@c.s.s.1680]

something I always do, is that after you sunk a ship you can cross out the squares around the ship, because you are not allowed to overlap ships or place them next to each other.

[@Romanticoutlaw]

huh, I've never played with that rule. I basically always have ships touching to bamboozle my opponent

[@JustBCWi]

Without knowing the math, I was following this approach when I was 7. My preferred strategy is to have the player near something reflective so I can increase my statistical insight into where to place my next shot.

[@CC21200]

If you know your opponent will always use that strategy, what is the best placement to counter it?

[@finbar163]

Put your ships in unlikely positions, probably around the edges. But know that if they spot what you're doing they know where to look.

[@CC21200]

@@finbar163 My question was more about what to do against a computer that sticks to that specific algorithm, not against a human player who can spot things and change strategy.

[@Mr.Beauregarde]

@@CC21200 if you know its algorithm and it doesn't innovate you pick the last spots it would pick.

[@CC21200]

@@Mr.Beauregarde Of course. The question was what placement satisfies these last spots.

[@Kyrelel]

@@CC21200 Simple answer: There is no counter-strategy because you have no way of knowing where your opponent is going to place their first few shots.

[@iamaim2847]

My fave strategy is to hide ships in the corners and at sides. Many players know about probability in the middle higher, so they will start from there. And if you must keep 1 cell distance between ships, even if some ships a killed, the enemy gets less data about denied squares. It works against humans just once. But for one game it makes miracles.

[@Darth_Barnaby]

Reminds me of back when id play this in my Nintendo DS. I can still hear the angry captain yelling "Argh, you sunk my BATTLESHIP!"

[@DanielElicker]

"Can you just guess a square already" "hold on I gotta calculate the probability of all yours ships on each possible square first"