Surviving The Deadliest Game

published on July 9, 2020

Vsauce Kevin's here playing one of thedeadliest games ever created so deadlyin fact that I needed balloon Kevin toact as a proxy for me real Kevin I'mreal Kevin the game is Russian rouletteyou probably already know how Russianroulette is played traditionally a

Single round is put in a revolver thatholds six cartridges the cylinder isspun so that it's impossible to knowwhich chamber will be fired you pull thetrigger and there's a five out of sixchance that you are safe and a one out

Of six chance that it goes really badlyfor you I've inserted a single needleinto each dart so that in our version ofthis game it's gonna go very badly forpoor balloon Kevin and that's dangerousand unsafe this whole thing is dangerous

And unsafe and against the Terms ofService for every site on the Internetthankfully Russian roulette is mostlyused in movies as a dramatic device andI'm using it as a dramatic way toanalyze probability the important part

Is that you never do any of this everokay okay I want to figure out the bestway to survive this notoriously fatalgame so if balloon Kevin plays astandard game of Russian roulette he hasone in six odds of permanently deflating

His dome there's about an 83% chancethat my rubbery little clone wins and a17% chance he loses forever and that'sthat so here we go it's time to testyour luck balloon Kevinwait let's make this scenario a little

More complex let's say that there aretwo balloon bursting missiles inside sixchambers with two possible spherical airsacs splattering darts that have beenplaced next to each otheradjacent there's a two out of three

Chance that my air headed doppelgangersurvives on a random pull of the toy sodo you like your chances boy you thinkthat Sharpie moustache is better thanthe real deal well let's see if fate ison your side the two out of three

Survival chance comes through so it's onto the next roundmy gaseous twin has had a bit too easyof a chance up until now the survivalmath has been very very straightforwardhe's had no active role in deciding his

Own fate so let's give him something tothink about for round two I'm gonna givehim a choice and place the life odds andhis pipe cleaner hands the choice isthis now that he's managed to surviveone round of the game does he want to

Spin the cylinder before playing againor does he just play and hope for thebest the big question is is it betterfor him to randomize the cylinder orcontinue playing with its currentconfiguration well answer the question

Punk what's it gonna be a blue beingwearing balloon buffoon given that thereare two adjacent cartridges in there andthe toy has been fired once already doesit even matter mathematically whetherair Kevin spins or not

Let's find out the first option spinningit's the same scenario with the samemath you're basically recreating roundones odds which we know give you a twoout of three chance of survival so notreally a whole lot to consider there but

If you don't spin you know somethingelsethe toy has just been fired on one ofthe empty chambers which is how balloonKevin survived to get to round two and alittle logic reveals the math of whether

To spin or not spin think about thepositioning there are four possibleempty chambers and only one of them isdirectly before the two cartridges whichmeans there's a 75% chance that roundtwos trigger pull is on another empty

Chamber in just a 25% chance that thisballoon is about to go baboom by notspinning balloon Kevin has earnedhimself about eight more percentagepoints of survivability and it's such astraightforward probability calculation

Because we know that the darts areadjacent if they were just randomlyplaced in the chamber then things changehere's how there are 15 possiblepositions for two darts randomlyarranged in six chambers six of them are

Adjacent so darts would be in 1 & 2 2 &3 3 & 4 4 & 5 5 & 6 all the way to 6 & 1there are six more ways that there canbe a single space between the darts so 1& 3 2 & 6 1 & 5 4 & 6 3 & 5 2 & 4finally there are just 3 ways that darts

Can be opposite one another one in 4 3 &6 & 2 & 5if ba Leuven survives the first roundand he doesn't know whether the dartsare next to each other or spread outdoes he want his second shot with a spin

Or with no spin we know that we have a75% chance on surviving those sixadjacent positions for the cylindersthat have darts one space apart two ofthe four empty positions come before anempty and two of the four come before a

Dart so that's 50% and it's the same forthe opposite darts our overall safetyprobability here is a calculation ofthose weighted probabilities and it goesa little something like this6 over 15 times 3 over 4 plus 6 over 15

Times 2 over 4 plus 3 over 15 times 2over 4 3 over 10 plus 1 over 5 plus 1over 10 equals 3 over 5 by not spinninghere we have a 60% chance of survivalcompared to 6667% 2 over 3 when we dospin when we know the darts are adjacent

We can gain 8% survivability when weknow they're random we can avoid losingabout 7% it's not some magic solutionthat allows balloon Kevin to survivewhat's probably humanity's most deadlygame doing the math doesn't unveil a

Secret way to win 80% of the time itjust doesn't work that way it could getyou eight percent andeight percents pretty insignificantisn't it no it's not consider this 01%of DNA is responsible for all the

Differences you see amongst humans andonly one point three percent separate usfrom chimps 1984 was the last USpresidential election with more than an8% popular vote gap improving roadsafety by 8% would save 96 thousand

Lives per year a one thousand dollarinvestment growing at 8 percentcompounded annually doubles in just nineyears and ultimately if you're anincredibly attractive balloon with nicebig googly eyes a perfectly formed

Cotton ball nose and surprisinglymuscular pipe-cleaner arms that findsitself locked in a life-or-death game ofchance you'll take any advantage you canget to avoid being popped and as alwaysthanks for watching

Hey if you want to continue exploringRussian roulette probability foryourself and use your beautiful balloonhead to learn how to think brilliantorg has a challenge all about it too infact as part of their perplexing

Probability course brilliant is greatfor vsauce2 watchers like you becauseit's an entire platform based onlearning math and science by having funwith them they're interactive puzzlesallow you to expose misconceptions and

Help you learn to thinkby playing perplexing probability isjust one of these 60 plus courses onbrilliant that teach you by walking youthrough puzzles and guiding you andfiguring out the solutions if you

Haven't checked it out yet I highlyrecommend doing so just head on over tobrilliant org slash vsauce2 and sign upfor free and the first 200 people get20% off an annual premium subscriptionso that's a wonderful deal go check it

Out enjoy thinking I need a new balloonCap'nthanks for watching that worked reallywell oh my god

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