The Joy Of Hex

[@Etothe2iPi]

It's worth noting that, not only can there be no draw, but the first player must have a winning strategy. Good thing, that the strategy is not known for large grids.

[@jonathanbush6197]

On all the popular Hex servers, an opening protocol called the pie rule is used. Suppose black moves first against white. After black makes the first move, the second player has the option to swap sides. This is like when two people want to share the last of the pie. One person cuts the pie into two slices and the other chooses which slice to eat. This protocol makes the game much more interesting and fair. Now theoretically the second player can win, but the advantage is much smaller.

[@Noah-lj2sg]

swap rule prevents generally OP spots from being played first

[@mariquilla8891]

Actually, that's not true. Indeed, thanks to the pie rule, the second player has a slightly vantage

[@NickLoganbill]

This is awesome. I read a lot about the value of having a hex-based maps in games vs being square-based. Do you think you could do a video on the pros and cons of hex and square setups in turn based strategy games? Maybe that's too vague without selecting games, but I'd find it interesting if you ended up coming to a conclusion for which is better. Thanks again for the great content!

[@camdenwyatt69]

you probably dont give a damn but does anyone know of a way to get back into an Instagram account..? I somehow forgot the account password. I would love any assistance you can offer me.

[@alexzandernathaniel4451]

@Camden Wyatt instablaster :)

[@camdenwyatt69]

@Alexzander Nathaniel Thanks for your reply. I got to the site thru google and im waiting for the hacking stuff now. I see it takes a while so I will get back to you later when my account password hopefully is recovered.

[@NickLoganbill]

@@camdenwyatt69 this is the most obvious spam garbage I've ever seen. Both of you (aka same person who created two channels 3 months ago), delete your accounts.

[@camdenwyatt69]

@Alexzander Nathaniel it did the trick and I finally got access to my account again. I am so happy! Thanks so much, you saved my ass :D

[@guyinacage]

Someone should make the game of life with a hex board

[@alan2here]

"Golly" might have a hexagonal neighbourhood by now, even if not there are rule tables for simulating 2 state hexagonal CA's in 2 states on a square grid, everything ends up slanted but it seems surprising to me that it works at all. Conway's game of Life is life like 3/23 and this doesn't work identically as cells have 2 fewer neighbours, corners being part of the neighbourhood for Conway's life, but some Conway's life, life like variants exist for the hexagonal grid, as well as interestingly for the square grid with 4 neighbours instead of 8.

[@galva1083]

Beautiful presentation! One thing though that made me ponder is the very top left junction e.g. at 2:30 . That junction only has one marked edge which violates the rule of every junction having zero or two marked edges. I realize that you can resolve this problem by expanding the board outside by "virtual" circles and "virtual" edges such that the rule is fulfilled again.

[@ninja_sloth3906]

The rule you're referring to refers in turn to a junction in which 3 hexagons meet, as stated at 1:59. The very top left junction connects to only 1 hexagon, and so is exempt.

[@galva1083]

@@ninja_sloth3906 Thank you for your explanation!

[@marlonmerz9850]

3:20 this reminds me of civilisation 6 XD

[@Saul30119]

Hexagons are Bestagons

[@davidmunns135]

The Game ofHex was used as the matrix for the Tv Gameshow BLOCKBUSTERS which was hosted in the UK By the late Bob Holiness in 80s and well into the 90s as well (That’s when the show moved from I T V to SKY 1 ) The BLOCKBUSTERS board was made up of 25 lettered hexagons 5x4 the single player had two sides that were White and other two players played as Blue team and each game was played as a set of three

[@_inabox]

Very nice video. Keep it up!

[@nyb_ok]

Well explained. Thanks so much.

[@fawzibriedj4441]

Looking forward for a revival of the channel :D

[@realizeyourparadise]

Northernlion brought me here.

[@ionalien]

Pog brother

[@Hecatonicosachoron]

So does this work for any regular tiling where three faces meet at each vertex? In that case there should be a hyperbolic version! It would be most exciting!

[@woosix7735]

there is also the thing where the first player always has a wining stratgy

[@Sam-oz8pn]

Very interesting

[@columbus8myhw]

Someone should make a toroidal version of the game of hex, where draws are possible

[@ralph7349]

You are the GREATEST

[@pixelpastiche]

If only someone could send this video to NL.

[@ValkyRiver]

That looks like an isomorphic keyboard to me.

[@marcov4867]

First time I heard of this game I thought it would be the perfect game to play on a board I have. The board has hexagonal tiles and pieces. The only problem is that the board is hexagonal itself

[@HatterTobias]

You can make do by having a square board, but every rank is shifted half a square to the right from the rank before

[@MikhailMatrosov]

Your proof seems to be over-simplified. E.g. there might be border around "islands" of dots of the same color, which is not connected to two chains connecting corners. It is ok to leave such situations as an exercise to the reader, but I didn't notice that you explicitly said this.

[@TippingPointMath]

You are correct that the islands may be there, but they would not change the argument that a corner must connect to a corner. Thanks for your observation.

[@0EEVV0]

Mikhail Matrosov to the reader lol

[@davidmunns135]

Nash won The Nobel Prize for mathematics for his work on Game Theory I can’t remember in which year he won And later after suffering a nervous breakdown wrote the autobiography A Beautiful Mind which was turned into a movie Starring Russel Crow as Nash and directed also co scripted By Ron Howard

[@livedandletdie]

Label the tiles A B C D E F G H I J K and associate them each with a number 1-11. Then associate each tile with 3 colors. C for Clear, R for Red, and B for Blue. You can even introduce randomness to the game by selecting 2 tiles at random and switching their colors. Or play the 3 player variant, it's however it can result in a tie.

[@dirtyrainbowsaltwater8490]

I pressed on the link but it doesn’t work 🙁 help

[@koohoo4500]

Nice!

[@alan2here]

Aww, video ended after just 4 mins.

[@kyleli1188]

Is it possible to argue for this logic? the only way for one side, say red, to stop blue from connecting to the other side of the board is to create a wall of pieces directly across the board, which would lead to victory for red and vise versa. As long as there is a hole in the wall, the other side can slip through for victory. The only other possibility is that you close the hole and win.

[@TippingPointMath]

It's not clear that a wall all the way across is needed to stop your opponent. The square grid pattern shows both players being blocked. So the geometry of the cells makes a difference. This information must be used in any proof.

[@trejkaz]

I see what you did there.

[@sasha-2574]

the proof presented is quite simple and elegant

[@DynestiGTI]

So is the 11 by 11 grid the smallest it can be and is a hexagon grid the lowest sided shape to use that still works?

[@TippingPointMath]

You can go smaller than 11x11. Are there shapes other than the hexagon that work? Keep in mind that tiling the plane with only one type of tile is tricky.

[@jamesonthomas9583]

+Tipping Point Math Triangles maybe

[@jonathanbush6197]

Tipping Point, you might be interested in the game of Pex: www.boardgamegeek.com/boardgame/39288/pex

[@drag0vien289]

If player 1 plays perfect, can they always win? For different board sizes can player 2 always win?

[@MrEdwardCollins]

Player 1, if they play perfectly, will always win no matter what the board size. From Wikipedia: There is a reductio ad absurdum existence proof attributed to John Nash c. 1949 that the first player in Hex on a board of any size has a winning strategy. Such a proof gives no indication of a correct strategy for play. The proof is common to a number of games including Hex, and has come to be called the "strategy-stealing" argument. Here is a highly condensed informal statement of the proof: 1. Either the first or second player must win, therefore there must be a winning strategy for either the first or second player. 2. Let us assume that the second player has a winning strategy. 3. The first player can now adopt the following defense. He makes an arbitrary move. Thereafter he plays the winning second player strategy assumed above. If in playing this strategy, he is required to play on the cell where an arbitrary move was made, he makes another arbitrary move. In this way he plays the winning strategy with one extra piece always on the board. 4. This extra piece cannot interfere with the first player's imitation of the winning strategy, for an extra piece is always an asset and never a handicap. Therefore the first player can win. 5. Because we have now contradicted our assumption that there is a winning strategy for the second player, we are forced to drop this assumption. 6. Consequently, there must be a winning strategy for the first player.

[@chunkyVo]

This game seems particularly vulnerable to 'first turn advantage'. Does the person who plays second spend the entire game on defense or are there any opportunities to out maneuver a skilled player?

[@TippingPointMath]

There is an argument that the first player has a winning strategy, although we don't know that strategy for sufficiently large boards. To counter the bias towards the first player, one can play with the "pie rule". This says that if Player 2 would prefer to be Player 1 after seeing Player 1's first move, then they switch.

[@PedroTricking]

They switch and what? The previously player two plays twice?

[@jonathanbush6197]

Suppose Alan is playing Bob. Say Alan moves first as black, and Bob swaps. Then Alan will be white, and it will be Alan's move. Does that make sense?

[@PedroTricking]

Oh, so I as Bob, get the piece played by Alan then? Thank you.

[@jonathanbush6197]

Yes, when you swap, the first token played becomes yours. It's called the pie rule because it's like when two people share the last of the pie. One cuts the pie into two slices and the other chooses which slice to eat.

[@davidmunns135]

i play on a 10 x 10 board

[@Przemek20a]

I use 13x13 board

[@davidmunns135]

ausome

[@Przemek20a]

Do u think that made from me professional player?

[@suntzu6122]

But is this a good game?

[@BartvandenDonk]

The land puzzle is not the same as the Hex Game which is 2 dimensional and there could be a 3 dimensional bridge involved on the map Puzzle.

[@abdelrahmanmohamed7007]

مصر ام الدنيا Egy

[@4franz4]

first

[@EugeneVDebs-mo6dh]

This is rigged

[@pabloo410]

first