What Decides a CPU Tourney's WINNER?

[@Casual_PKBeats]

12:53: *Level 8, I would NEVER root for level 9 Also, at 10:42 I’m only just now seeing the red color on the tech ring, which means it COULD’VE been an untechable situation, but… I also don’t think that’s reliable, since there’s a red ring at 11:55 where level 9 still teched it. Honestly the mechanics of what is and isn’t techable has always been weird to me lol

[@kwisowofer9872]

About the red ring, it’s the outer ring that shows if it’s techable. When the red ring appears you can see the big blue/green ring around it. If that outer ring was red, then it would be untechable. Besides, that red ring only appears when a move does a lot of knockback, so considering that purple Mario was at 0%, then that up-b wouldn’t deal that much knockback

[@ayoraster2970]

I don't think it's untechable. Usually with untechables they have a red outer ring, and the threshold to get an untechable is really high. I don't think an up b at 0 could ever be untechable.

[@jefferydavidson5347]

I didn’t see any red ring at 11:55

[@beeftips1628]

It’s most likely what other ppl said but from what I’ve heard, it decides if it’s techable or not based on original knockback but hitting a wall can lower your speed just enough to allow it to be techable, allowing a techable red ring.

[@KainYusanagi]

Can confirm that it's the stats that matter with the spirit combos, with a high defense making a big difference. If you match the stats around the same values and then try again, the type matchup might actually factor, though.

[@LordPhilipJFry]

So basically, CPU matches are like quantum mechanics: observing them changes the outcome.

[@alejandrohernandesmartinez6211]

They just get nervous when you watch🥺

[@slavprinceuro]

@@alejandrohernandesmartinez6211 I love this comment

[@3twibles4sweetrevenge]

Hahaha good comment

[@gabegillespie8172]

KIMI NO SEI, KIMI NO SEI

[@MasutaMJ]

Quantum Tournaments. I'd watch that.

[@sparklyskittles6367]

sometimes when we are bored, my group of friends will run lvl 9 cpu tournaments, but once during a birthday party we accidentally set a luigi to lvl 6 instead he won the tournament

[@WeegeeDX]

only Luigi could pull off such a feat

[@bukenator0788]

he probably did nothing

[@MeesterTweester]

Melee Luigi CPU is cracked

[@Stoopid420]

I did this but it wasn't a single match with a level 7 luigi versus a level 9 ridley WITH SPIRITS and Luigi completely wrecked him to death it was very funny.

[@nickdavis27]

Did he win by doing nothing?

[@lamergamer8211]

I love using ways of doing things that are definitely objectively worse than alternatives, but are just more funny looking

[@MrPenguineo]

So true

[@neoxus30]

The beyblading of Iceack)

[@TheThirdPrice]

You should watch the video 'harder drives' it's all about that sort of thing. One of my favorite videos on KZbin

[@lamergamer8211]

@@TheThirdPrice I have. Its great

[@fernandobanda5734]

I think we can safely say that the skipped matches use a random outcome, with weighted bias towards higher CPU level and spirit power (and maybe character handicap?), but the devs couldn't bother to accurately calculate these odds. They programmed better things to be better, but not really reflecting a played out match.

[@palidopali]

Of course. I mean I wouldn't see anyone complaining at all if this algorithm was even way worse

[@hunterculpepper1973]

So basically any thing can happen

[@Pikana]

Yeah. The skip feature feels more like a thing that just exists because of the fringe cases it's useful to have. They figured everyone would just watch matches between CPUs as any serious use of the system would be for purely player vs player matches. Meaning anything with CPUs are likely there to watch CPUs beat each other up.

[@attackboss6]

Stage selection doesn't matter, you can make a custom stage that has no "end" and it still ends a cpu match with a winner if you skip

[@snivyboy168]

You gotta wonder though... what *did* happen in that skipped match?

[@ToaderTheToad]

@@snivyboy168 It's like Mario Kart 64, they used noclip while nobody was watching

[@LinearAztec]

There are a few factors I’m aware of. Once they’re sponsored, they’ll never win another tourney, and if Blood Falcon beats you in the dark realm you die for real

[@flogledragonspirit5391]

R.i.p. Audible Link and Skillshare Kirby

[@Starfloofle]

ah that goofy series was a trip

[@ballisticboo7808]

We will never forget Vincent, Falcon, and Dedede

[@athing8523]

I'm sad that series ended tbh

[@PlayerZeroStart]

I have to know what you're referencing

[@foxbra7258]

I love doing CPU tournaments, I have multiple Google sheets of data for them, so I absolutely love seeing this kind of content.

[@lol1013]

What's the appeal of watching cpu? They aren't even good; I can understand the appeal of watching bad players fighting it out, but cpu?

[@foxbra7258]

@@lol1013 what I mostly enjoy is the statistical side of it, I like finding out which CPUs do well in which scenarios or matchups, it's all just stuff I do for fun

[@Greenglower2012]

What r ur findings

[@diamondmemer9754]

Plot twist: When you skip a battle the game plays a very quick and texture-less sudden death between the two characters to see who wins

[@329link]

I could believe that actually happening tbh. When you take video rendering out of the equation, a computer can often simulate a game at an insane speed.

[@diamondmemer9754]

@@329link yep but the inaccuracies shown here tell us this isn't the case

[@nightmare3642]

@@diamondmemer9754 It simply immediately drops bob-ombs.

[@diamondmemer9754]

@@nightmare3642 that would be too randomic

[@Sabagegah]

19:51, 20:56 *I DID THE MATH!* (lol) Null hypothesis: both characters will have equal win rates (of .5). Alternative hypothesis: the win rates will differ. The two-tailed 95% confidence interval is bounded by 99/211±1.96*sqrt((99/211)(112/211)/211), which simplifies to a win rate between .4018 and .5365 for Isabelle. This includes the null hypothesis of .5, so we fail to reject the null. It is feasible that the true win rates are equal.

[@pgmonkeh2166]

For anyone that doubts this man, can confirm he did this right. This is known as hypothesis testing, something you learn during college (high school, to some of you) in statistics, or perhaps a bit earlier.

[@freddiesimmons1394]

What about a one tailed hypothesis, that kazuya will win more?

[@MesserTAMU]

Not all heros wear capes

[@Sabagegah]

@@MesserTAMU I should get a cape...

[@hurikain213]

"Mom can I get switch online to to use Spectate?" Mom: "we have Spectate at home." The spectate at home:

[@UnknownCleric2420]

4:05 Fun fact! This is also the odds of the Icon of Sin spawning an Archvile in Doom 2/Final Doom.

[@demi-femme4821]

Imagine that sequence happening several times in a row. Those are the odds needed to beat the Icon of Sin in Doom 2 without directly attacking it, and that's if you get the execution right. Yeah, there's a reason nobody has done this without tools.

[@UnknownCleric2420]

@@demi-femme4821 Or you could just get a Cyberdemon to shoot at a Lost Soul in Plutonia Map 30 :P

[@dabiskitt]

1:27 I would totally watch a full video of you cracking jokes and mentioning random smash facts over a CPU tournament!!

[@michaels.4527]

We used to drink to CPU tourneys when we were getting too drunk to play. Each person picks a character, yours dies, you take a drink. Your character loses take an extra drink after the drink for the lost stock... I've spent many hangovers cursing random smash characters. SDs are 2 drinks.

[@ashmyoshi3912]

I cant legally drink yet

[@SGEnjoyer]

@@ashmyoshi3912 just be older 5head

[@Amirrorofmirrors]

This must have been so tedious to set up. Thank you for doing the research so that we don’t have to

[@_vapor_3866]

19:50 Hello, statistics student here. I did the math on the Kazuya vs. Isabelle match-up and it turns out that the results were well within the realm of possibility for a 50/50 chance. Technically, I should say that "There isn't enough evidence to reject the claim that the odds are 50/50," but I can say with 99% confidence that the odds are even, if not extremely close to even. Great video btw, thanks for all the amazing content you put out.

[@Casual_PKBeats]

I appreciate your feedback, thank you for the info and for watching the video! :)

[@BainesMkII]

The chance of starting with seven red Mario wins is 1/128, but the chance of simply starting with seven consecutive wins of one color is 1/64. If you take away that "starting with" condition, the chance increases with the number of total matches. Probabilities are highly dependent on just how the scenario is defined, which is where a lot of people get tripped up in over or underestimating chances. Add into this the human tendency to look for (or outright create) patterns, and it arguably was likely that you'd find *something* that looked "suspicious" over multiple tournaments.

[@Skypatroller_BenCD]

15:48 there's an other problem you aren't using the strongest spirit from their categories (except for Akuma) cause the strongest spirit in the shield category is Galacta Knight and in the grab categories is Big Boss (also Galeem/Darkom are the strongest in neutral but sense their special effects are only usable in story mode so Soma Cruz is the strongest)

[@riley3087]

I thought the Akuma equivalent was the Absolutely Safe Capsule, considering the lack of spirit slots on both.

[@Skypatroller_BenCD]

@@riley3087 well no the top 4 are 1 Galeem/Darkom with 13640 of power for both 2 Galacta Knight with 13345 of power 3 Akuma with 13235 of power And 4 Big Boss with 12727 of power Soma is 12110 of power (with reminder that he is the second strongest neutral spirit in the game) and the Absolute safe capsule is only 10000 of power. For comparison he's weaker than Eggman (10118) and Protoman (10029) and both Protoman and ASC are the 28th and 29th strongest shields spirits (also all states are told with ALL spirits at level 99 so the max)

[@guymadeofbees8464]

@@Skypatroller_BenCD also you have to account for the fact that the ASC has all 10,000 in defense which gives it no damage

[@Skypatroller_BenCD]

@@guymadeofbees8464 defending wise he has the MOST defence of them all and the LEAST attack which is a reference to Earthbound 2 cause it is indestructible and can't attack you but still the ASC isn't that strong he only has the same power as Geno also the overall power are just an addition of their defencing and attacking states for example Super Sonic is 5537 in attack and 4009 in defense, 5537+4009=9927 which is Super Sonic overall power or Rayman is 3391 atk+3748 def=7567 power. And the ASC is only 10000 def+0 atk=10000 power unlike Geno who's 5250 atk+4750 def for the same result

[@leaffinite2001]

I use only james mccloud because he is fox with sunglasses

[@dazedheart9006]

Omg I loved to do “Tourney Roulettes” on SSBB. Everything was automatic and you couldn’t see the AI’s difficulty. A level 2 ICs somehow beat a level 7 Ganon I think once.

[@LaughingThesaurus]

I theorize that there's probably a behind the scenes Power formula that weighs CPU level and spirit power and possibly other factors like handicaps or starting stamina, maybe spirit abilities or individual stats but I sort of doubt it on that front. There has to be some math going on to calculate the odds, because I wouldn't believe a supercharged level 1 could possibly beat a level 9 in a match, without the match being purely about Math.

[@quantwomwhale5984]

20:50 I have never seen a Steve win a single battle in a CPU tournament in my entire life

[@alexv0714]

my brain works in a very statistical manner and this is something I've thought about for a long time due to Alpharad's old CPU tournaments. thank you for doing the testing for me, it was really fun and interesting!!

[@NinJaguar]

Cool experiments, I had known that tourney mode skips were RNG when it came to characters at the same level but never considered to what extent; interesting to see how CPU levels, stage/format selection and spirits come into play. Also glad you found your way to the level 9 CPU tier list, worth noting that the one labelled as being from 2021 is actually from 2022 (graphic was a typo that never got fixed) and still holds up largely!

[@LilyLambda]

I've been looking through the code a little bit, and I've found a list of parameters related to tournaments- Apparently the game uses a "score" system, where points are applied based on certain metrics, and the cpu with the higher score wins -10 points are added for every level after 1 -10 points are added for every 1500 team power for 1500-9000 (starting at 20 points for 1500), then 10,000 adds 80 points, and everything higher is 90 -amiibo use a similar system, where between 0 and 90 points are added based on level -10 points are randomly given (I'm not sure what the chance to give 10 points is) There's also three point systems I'm not sure about, as I couldn't find any code, only a list of numbers -"score_reversal" can either give 5 or 50 points -"score_unique" adds 25 -"score_attribute" adds 20

[@halt1931]

so a level 7 has 0 chance against a level 9, barring the last three unknown systems?

[@LilyLambda]

@@halt1931 with no spirits, yes

[@Liggliluff]

I was confused first when you said -10 points are added for each level. So for a random spirit-less match, their scores are 10*(LVL-1), and the random 10 points is given at a factor of like 10%, which results in: 10% chance that the level 8 CPU gets 10 extra points, but 1% out of that being when level 9 CPU also getting 10 extra points. So at 9%, only the level 8 CPU gets the extra point, making both have 80 points, and when they have the same points, the winner is randomly selected. Making it so level 8 CPU only wins 4,5% out of the games. It's a simple system, but it still makes me want to improve it. Step 1 is to determine the CPU skill of each character; Kazuya is at least 3 times better than Sheik, so taking the 13 step tier list, top tier would be 38 and bottom tier is 26. Multiply with the CPU level. So at level 9, Kazuya is 38*9=342, Isabelle is 35*9=315, Mario is 29*9=261, and Sheik is 26*9=234. Kazuya level 6 is 38*6=228 around the level of Sheik. Then add a random number from 0 to 100. Kazuya 9 vs Sheik 9 is 100 to 0. Kazya 9 vs Isabelle 9 is 73 to 27, Kazuya 6 vs Sheik 9 is 44 to 56. The strength of the tierlist and the strength of the CPU levels can further be adjusted. Then the spirits have to be added too.

[@Greenglower2012]

Wow

[@Liggliluff]

Considering how good the CPU can be in Ultimate compared to previous games, I get the feeling that they have made special AI code specifically for these characters. Because there's sometimes a huge difference between two level 9 of different characters. So terrible CPUs like Sheik, I think is because Sheik has the generic AI, while other characters got specially designed AIs.

[@byzantine5761]

cough kazuya being a level 12 CPU at level 7 or smth

[@SentientPulse]

And considering certain characters will just use random moves. I’ve had a Fox and a Mewtwo level 9 kill themselves with up b on stage>off stage. Like what option would mewtwo ever want to TP offstage into free fall lol. Could have been smash 4 though, but I also agree that there is most likely a general AI and something else for certain characters

[@Sabagegah]

Resisting the urge to calculate a confidence interval. Edit: I did not resist.

[@Pslamist]

12:44 - I love this effect-Smash is ALWAYS hype when the opponents are equal skill levels, even complete scrubs. Glad you enjoyed it.

[@EvelynFTTE]

About spirit numbers (around 16:00) It's possible that the result is due to scale. Grapple was half of Defense, whereas Defense was 2/3 of Attack. Even though the difference was 4000 points each time, the percentage is way different

[@whiz8569]

For why the Grappler spirit didn't do as well, it's possible the way the game determines which spirit is more powerful is based on a threshold system. So, for example, the game considers spirits to be level 8000 and higher to be in the same tier, so in that case, the defensive spirit is roughly equal to the offensive one, but in a higher tier than the grappler one.

[@THEDKA3]

Thanks for the video! Really interesting analysis to see how skipping battles affects the CPU tournament results based on different attributes. I am also glad you were able to reference the Level 9 CPU tier lists by the SmashCPU community at 18:58.

[@Greenglower2012]

Theres a community? Nice. Can you please explain why ganon is so much better in melee as a cpu?

[@THEDKA3]

@@Greenglower2012 Thanks for the question! So in Melee CPU vs. CPU matches, Level 9 Ganondorf poses as the most dominant character in the meta for many reasons. These reasons can all be traced back to how incredibly underdeveloped the game's AI were overall. (The AI programming was noticably poor until Brawl came out). In Melee, the CPUs had very slow movement and commonly relied on a few moves, mainly throwing out jabs when standing next to the opponent, neutral air when hit in the air (a direct counter to jabbing), and down air when the character is launched high enough and fall directly onto their opponent. Trying to approach Ganon as a CPU is an absolute nightmare. Since the CPUs could not dash unless they were using dash attack or dash grab, most characters could get destroyed at early percents by a raw forward smash, up tilt, or Warlock Punch. At close range, his jab is fast, did high damage, and has enough knockback to evade getting hit by a stray nair most of the time. Ganon's aerials are very strong, particularly down air which kills off the top very early with a large hitbox. His Up Special is his most infamous move, perhaps the best programmed move of all of the Melee AI's. It has absurd knockback and Ganon will abuse it as very simple edgeguarding tool, something that most other CPU characters lack. Combine that with Ganon's great survivability with his heavy weight, decent horizontal recovery, and SDs rarely, he destroys just about every Melee AI matchup. Whenever we run CPU tournaments for vanilla Melee we nerf Ganon to Level 7 to keep him balanced to most of the characters (along with Link and Luigi at Level 8), and yet he's still considered "top tier".

[@supermaximglitchy1]

i once had a cpu tournament and I skipped a match between a level 1 vs level 8 and the level 1 won

[@tyler9425]

Lmao I was rewatching Alpharad’s cpu cs flr the millionth time when this video popped up

[@TaleOfTheToaster]

This is the video I’ve wanted since my school days watching Brawl CPU tournaments

[@TheAweDude1]

I think something like this would be great for a 24/7 livestream. That way you can have hundreds of matches, all automated, with automatic data recording, with a variety of different factors.

[@Shinigami-Cat]

Man I loved watching this- I was always curious about skipped tourney matches. I was quite shocked seeing only a 4% chance for a level 8 to win against a level 9. What I've personally seen would contradict that, but maybe I've just gotten lucky. Kinda curious what the difference of a level 4 and a level 5 might be, but I can't ask you to test everything. Thank you for making this, it was incredible to watch.

[@KazefuYousomo]

This was actually a really fun video! I mean I expected it to be interesting, but it was even more interesting than I thought it would be

[@Cooldudecrafter]

This is a question I've been waiting for an answer for years. Thank you PKBeats

[@FireflyMykah]

As a math/stat major with a bio background, I am now interested in creating a machine learning algorithm with the data to predict CPU fighting outcomes based on input parameters for the "skip battle" setting

[@therealohead]

My college has a casino night with poker, roulette, the works. They also have CPU betting. One huge tourney, and you bet on each CPU. Very fun stuff

[@haniyasu8236]

Ok, ngl, this would be a superb test-case for showing off some statistics tools. For having a math degree, I'm admittedly a little rusty at stats, but the binomial distribution, p-values, confidence intervals, and t-tests all seem to be pertinent here. It could make a pretty sick educational video actually to teach these concepts using the cpu tourneys as a launching off point.

[@laffypanda6822]

I have my theory on what happened when testing the types of spirits. The difference between attack is 4255 and the difference between grapple and defense is 3510. At first glance, this makes it seem like grapple is stronger compared to defense than defense was to offense. However what if instead of the difference of the two spirits, it uses the ratios. Doing so gives that defense is approximately 0.6785% as strong as attack and grapple is 0.6091% as strong as defense. This approach makes the difference between grapple and defense larger. Why do I think this may be the case? Because in video games, buffs such as a super effective type of stat boost are often applied in the form of a multiplier. If this potential multiplier was set at let’s say 1.5, then defense would manage to beat out attack but grapple would not manage to beat out defense. I can explain further if need be but tldr is that I think you may be underestimating the effect of the difference in spirit levels. I would very much like to see the results of spirits that are much closer in levels

[@TheShinyDude]

4:11 the moment I recognized gameplay from Chuggaaconroy's let’s play of Earthbound where he got the sword of kings on the first try, I instinctively prepped myself for his scream even if it didn’t play lol

[@truetitan1425]

At 16:11 when you theorize defense might be more important than offense, you're correct. Defense has a bigger multiplier than offensive for equal stats. I don't remember the exact numbers because it's been a few years since this has been relevant to me, but I learned this from the amiibo training community. In sm4sh, the primary meta was spirits, but the ult meta has shifted towards preferring vanilla (no spirits) tournaments, in part because, at launch, the optimal stats were just all defense (which is a pain to get). Funnily enough, this was later changed for amiibo such that offense and defense are now equal, but never changed for player/cpu spirits, meaning defense is still better than offense there.

[@solveforx314]

19:54 I'm a little rusty at AP Stats myself, but I remembered enough to figure out how to do a z-test on my calculator and got a p-value of about 0.37. What this means is that, assuming there is a 50/50 chance Isabelle wins, the chances of her winning 99 or less out of 211 are about 37%, which is not a statistically significant result. Usually, you need a p-value of less than 0.05 to say that your results are statistically significant. In summary, it's entirely plausible that Isabelle had a 50/50 chance at winning.

[@jonathon422]

I can't imagine all this research is much fun, but I can't help but be captivated by the the varied outcomes from seemingly random changes. I'd love to know more about how the CPUs function but if it's too agonizing getting all the data, then I'd rather you do something more enjoyable. 😅

[@femain1788]

I believe the best way to do this would be to use your clout (people that follow you, mostly discord) to run the test with you amplifying the number of possible test. That is of course if you wanted to do this. Adding the number of people would heavily increase your the number of test run giving a much hight confidence level to your test.

[@lumbajackthumbs7755]

But people can lie about data

[@femain1788]

@@lumbajackthumbs7755 assuming people are trying to actually help or he does it with only his most trusted discord users then the data should be reliable. As far as lying yeah people do, but if you go I. With the mindset that everyone cheats and lies nothing gets done

[@BabuBabu-ip6oh]

You are correct that the defense stat takes slightly more priority over the offense stat aiding in survivability. I tested this with a spirit that had equal attack and defense on two characters, and despite the attack stat being equal to its defense it was taking at least 1-3% less damage than normal than it would be without spirits on either character. The attack stat needs to be higher than the opponents defense stat to really make a sizable difference, even with type disadvantage you can tank some hits with high enough defense.

[@legosiw]

Cpu tier list is interesting. Im doing an amiibo tourney (currently paused for the lack of mythra/pyra and sora) and i wonder if the amiibo would follow roughly the same list. And before anyone asks, i cant sit and train each one so they all trained by fighting a cpu9 of themselves and have no boosted stats. Either way, its entertaining to watch

[@taboo4011]

fairly sure amiibos have the same ai as cpus

[@LilyLambda]

Fun fact! The only thing different between spirits and amiibo once you take away spirits is that cpus use moves at a determined probability, while amiibo can change probability based on a number of factors, so if you train amiibo with cpus, all you have is a cpu :)

[@roniemena]

It's funny how pkbeats says he isn't charismatic yet i still keep watching his videos because i find him likeable

[@justsans.]

Why have I never thought of this lmao this is actually really cool.

[@Rawls9805]

I’m curious if going with lvl 2s vs lvl 3s would change the result of skipped battles since you’d be pitting two “bad” AIs against each other rather than two “good” ones

[@darioschottlender]

Maybe it's based on power level, and the CPU level adds a power level modifier, so even though the lvl 9 CPU might have a great power level modifier, the spirit gives a much more important power boost and the lvl1 ends up having a superior power level

[@ripstick45]

I think it would have been interesting to test the difference between a level 1 and a level 2 as well. While the level 8 and 9 matchup was 4-96, that win rate doesn't explain if it was because of the level DIFFERENCE or the levels themselves. I think a comparison could be drawn to pokemon, where the importance of level difference decreases over time (think: lvl 5 vs lvl10 and lvl95 vs lvl100). I think in the case of Ultimate, it might be the inverse. also going to try and make a hard (and likely incorrect) callout here based on a hunch I have, the lvl1 vs lvl2 battles will be a 25%/75% split.

[@kenjib88]

you did a great job showing the statistics

[@andrewy.4845]

I have more than enough statistical knowledge to delve really deep into this and would be more than willing to help with a follow-up video!

[@pauldavison2856]

I recently discovered a kind of glitch or maybe just a weird mechanic thing that happened: if mii brawler does a flaming drop kick at a specific moment on piranha plant when a ptooie is just coming out, the mii will somehow take double damage from it. This happened when I was playing plant and I watched it back multiple times, and I couldn't figure out what happened.

[@DarkoGameplayer]

This was a really interesting video, I really liked this kind of "experimenting video"

[@momothemagecat]

This reminds me of one time where me and my brother had this drinking game where we got like 32 bots of random levels and we had to guess which bot won what match. Everytime we failed to guess, we took one shot of this absolutely devilish mix of alcohols I liked to call "The Bog Water".

[@amoura39]

THERE'S CPU TIER LISTS!?!?!?!?!?! THAT'S SO WILD LOL I think I looked into that before but couldn't find anything I really liked. I love how ordinary tiers don't necessarily apply in CPU things because the CPU's need good enough AI to properly play their characters lol

[@KiraSlith]

Gotta give Nintendo credit, a perfect coinflip ratio from a straight random number generator is very hard to do. There's usually a LOT more wander than 5% either direction in a 100 test pool.

[@rubixtheslime]

I'm quite a bit into math, and honestly, this was very well done. I only really caught two issues and they were remarkably unimpactful. When collecting the results, including anything beyond the first 16 matches of given tourney _could_ lead to bias, as it means that anyone more likely to win is more likely to be sampled a second time. Of course in this case it's pretty reasonable to assume that the game doesn't pull a Mario kart and make some CPUs randomly better for the scope of a tourney. And even if it did I don't have to run any calculations, those results are definitive enough. For the case of everyone being equal, it's actually not a 1/128 chance that you'd get 7 in a row during the tourney. If there were exactly 7 matches it would be, but when you have more matches the odds go way up (because there's more opportunities for it to happen), and even more when you realize that 7 of the other side winning in a row would also raise the same alarm. I ran the numbers (brute force script), in the case of 16 matches, there's a 7.78% or 1/12.9 chance that the tourney will contain at least one instance of the same result 7 times in a row (4.29% or 1/23.3 if you're only looking at eg "left side" victories). The script (python3): sum(int(f'{x:b}'.find('1111111') != -1 or f'{x:b}'.find('0000000') != -1) for x in range(2**16))/2**16

[@rubixtheslime]

Please KZbin don't delete my comment just because i included the script

[@Casual_PKBeats]

These points make a ton of sense, and honestly I probably should've thought of them. Or at least, the point with the "1/128" chance. Though, in the context of the video, the 7-in-a-row being the FIRST 7 rounds was what especially stood out, but you're right that the odds for ANY 7-in-a-row to happen aren't quite that bizarre. I appreciate the extra information/expertise! Glad you enjoyed the video :)

[@rubixtheslime]

@@Casual_PKBeats yeah of course! Once again I want to stress that you did a very good job. I only really leave these sorts of comments when I can tell that the creator really cares about accuracy. I actually really liked the part where you just started doing coin flip simulations to get a feel for how much variance you might have, that was pretty smart!

[@manupm9161]

Quick question: are the odds of a level 7 to beat a level 8 also 4%?

[@randomguy6680]

Was wondering about level 1 and 2, but gesting this would be interesting.

[@SportsGaming-ll3ru]

I wish you included the dk guy screaming in the intro that’s my favorite :P

[@simplyfrozenwater]

[defense mario walks into a room where grapple mario and attack mario are fighting] defense mario: i have 8980 POWER-

[@sagacious03]

Neat analysis video! Thanks for uploading!

[@EmperorZ19]

4:03 The odds of getting the same coin flip result 7 times in a row are actually 1/64, not 1/128. The result of the first flip basically doesn't matter, it just determines whether the subsequent flips should be heads or tails. The chance of getting the same result once in a row is 100%, the chance of getting the same result twice in a row is 50%, and so on from there

[@Oretal]

When I ran cpu tourneys for my own entertainment I wondered if skipping then was just a coin flip. Knowing it still keeps a lot of things accounted is satisfying. Great video man!!!

[@ValToadstool]

I would guess there's some kind of formula that calculates a cpu's "strength" which when compared to other cpus gives the chance for each to win

[@deep_fried_cringe7962]

This video could have been a perfect introduction to a chi square test.

[@hampterland]

We need to use this method to figure out the true #1 character

[@Clemehl]

Do Characters have an affinity toward Offense, Defense, and Grapple in the code? Could Mario be a Defense character, therefore gaining "more" strength from Defense spirits? Would Luigi have different results as he might be considered as a Grapple character instead?

[@mrhalfsaid1389]

Power number on spirits are REALLY IMPORTANT, 1000 doesn't seem like much but it's very noticeable, so 4000 really does make a difference

[@TragicalLog]

Cheers on you for not deadnaming alpha's second channel

[@AgentQuacc]

What an interesting video! This sounds like torture to make though 😅

[@playinful]

The spirits thing combined with the alternate character thing makes me wonder what would happen if you made a very specialized spirit team (like one with a lot of sword attack buffs), put it on one character with several sword attacks and another character without any sword attacks, and made them battle

[@dvldgz6306]

CPU tournament is how I found my main back in brawl. Toon link is still my main. It's hard to explain to people when they ask why I won't switch to young link

[@cms_bb8817]

Pkbeats will be like “someone sent me this new glitch where toon links down taunt will move him into the left platform of battlefield. So anyway I taped the down taunt button down for 38 years and…”

[@kyokoro_p]

One thing that could've been done to further prove the Lv.9's odds to win vs Lv.8's was to put a tourney of ONLY Lv.8 and one Lv.9 (or two, on different sides of the bracket).

[@Ithaca-vv5dy]

God dammit! You just HAD to bring up the 1/128 item drops in earth bound! I’m trying to get one from ghost of star man right now and I wanna cry

[@mrwhite2203]

19:00 LOOK GARY THERE I AM

[@Jjaeger_H]

Glad to hear I'm not the only one that leaves Lady Luck to make my decisions for me lmao, I'm way too undecisive by myself. Though I personally like using wheel decide when it comes to multiple options

[@zacharyerickson9846]

I would love to see you try to figure out which CPU is objectively the strongest at level 9

[@DarkWizardFoxo]

these are very interesting videos like these are such helpful statistics that would help somebody like me who randomly rolls like a d20 for a lot of his decisions in life Have a way more interesting way to have random chance give me a good time, also this does bring up the curiosity of since you did the level one with a spirit versus a level nine what if you gave the level 9 the weakness to the level 1, and gave the level 9 like the weakest version of that spirit I'm curious to see how much that would change the entire match up

[@MyNamesYuyu]

I feel like streaming watching lvl 8 vs 9 would be really fun on twitch where people could bet channel points and get underdog bonuses if they gambled on lvl 8 and won

[@playbtdbattles2409]

For 4:03 the chances of getting heads tails alternating or any order is still the same chance so it doesnt really change much

[@ShurikanBlade]

So from this video alone and no research on my behalf what determines a victory goes in this order. Whether you skip or watch > Level difference > spirit or no spirit > spirit kind > character, items, stage, final smash (minimal to no effect)

[@vara202]

One thing I really want to see is if a level 1 CPU has a better chance against a level 2 CPU than a lvl 8 does against a lvl 9. Is the 4% consistent all the way up the levels or does the power difference increase?

[@ethanhutchins4769]

Did you know that mii brawler's helicopter kick up special has a weird interaction with air attack spirits equipped, specifically when on the ground

[@ktviewing]

I looked at this video and thought "Maybe someone can explain these chances to me." You did what you could, you put the time in with multiple variants, I'll give that to you. This fascinates me cause Ultimate has its way of calculating such things by itself. The only thing that makes me sad is that I will never get the best possible guess to why and how a lv 1 Luigi managed to beat every lv 9 they fought in a tourney to find me at the finals in Melee when I was in middle school. I even skipped their fights and they kept taking home gold till I took the tourney win from them. That was the strangest, most mind-boggling outlying experience that will never be solved in my experience with this series 😂 Or maybe it's just a Melee thing. God knows 🤣

[@djcooler333]

I did a test years ago (in brawl) testing to see what cpu level is the smartest, using Mario as a base. I was able to conclude that level 6 cpu is the smartest with the cpu only becoming more aggressive with a level increase.

[@joey5745]

Smash 64 cpu matches are actually pretty wild! I definitely recommend

[@TheRealBatabii]

I wasn't sure if "skip" just still did the match, but didn't have to render anything, and as a result, all the calculations were done super-fast behind the scenes. Probably a silly way to do it though.

[@benhuang2773]

After seeing the Spirits section, I'm wondering what would happen if both CPUs were the same level, but one had the weakest possible spirit (while the other had no spirit at all)

[@TightSweaters4]

Level 8 Mario is now my favorite character in gaming.

[@deancarver2093]

So excited for this year's Super (Smash) Bowl!

[@whereisspacebar2991]

God I love CPU tournaments. I get so attached to random bits of code.

[@quinton1236]

Great video as always, one thing I feel you could of tested was if final smash meter had any effects on the outcome of matches.

[@Casual_PKBeats]

Technically I did! The section at 13:17 has me turn it on :)

[@phancanedoo013]

Now i'd like to see how CPUs behave in teams, because, as someone without friends, i consistently get teamed on by enemy CPUs, even when i have my own teammates, which leaves me to wonder: Do CPUs have biases against the players?

[@Liggliluff]

(2:20) Melee introduced tournaments with 64 players Brawl reduced it to 32 3DS/Wii U removed it from local play Ultimate brought it back with 32 Due to Ultimate having more than 64 fighters, it really should have been 128 at max.

[@MinMin4theWinWin]

I'd love to see which is smarter: an amiibo trained by a lvl 1 cpu vs an amiibo trained by an untrained amiibo