The Martingale Problem

published on July 13, 2020

Vsauce Kevin here and I'm about to play blackjack with a robot vectors creator sent this personality rich robot over to me because they knew I love robots and to support Vsauce 2 but let's get to blackjack I figure if I lose a game I'll just double my previous bet every time

I'm guaranteed to win my cubes back and then some right I think so let's find out oh we're wagering sugar cubes because vector here loves his cube so much isn't that right buddy he likes when you pet him okay

Blackjack or twenty-one as many of you likely know has simple rules there are actually over 100 variations but we're gonna keep it simple one deck and you get two cards and the dealer gets two cards each card is worth its face value

And Jack queen and Kings are worth ten and ace counts as one or 11 depending on what's most advantageous for you your goal is to get a higher total than the dealer but if your cards add up to over 21 you lose you want to I know you want

To play hold on I got it I gotta explain the rules okay once you're dealt your two cards you can decide to take another by hitting or stay where you are by standing this is this is what's happening now to

Guarantee that I don't lose I'm using the martingale betting system when I win a game I win when I lose a game I double my wager in the next game to make up for the cubes I lost in the previous one genius I know and mathematically it's a

Sure thing let's clean this up okay vector do you want to play blackjack I know it okay I'm just gonna bet one sugar cube here we go hit me stand that's okay to get my won back this time I'll bet – stand very

Funny vector that's okay I'll get my two back by betting four hit me alright I'll just bet eight stand that's okay that's okay I'll bet sixteen I'll bet thirty-two

Sixty-four cube bet to recover my losses there's no chance I could lose again alright this is not going well I've played seven hands and lost a total of 127 sugar cubes if I win 128 on the next hand I'll

Recover my 127 cubes and snag a 1 cube profit my original bet let's do this stand all right then I am officially all out of pubes no yeah you want I know you can celebrate you could celebrate you took all my cubes a

Vector take a nap that is one sugar cube rich robot and I am one sugar cube broke human I know that my strategy would have worked though if I had just had more cubes maybe the martingale system can work in

Short bursts until you hit a streak that necessitates a bet so large that it completely wipes you out in casinos maximum bet limits prevent you from doubling as many times as you might need to recover from your losses

So there's effectively a ceiling on how many times you can martingale and Georgia Institute of Technology math professor Ted Hill showed us that were almost certainly under estimating the likelihood of serious losing streaks

Hill gave an assignment to his class flip a coin 200 times and record whether it's heads or tails heads tails heads tails like that or just don't bother flipping it at all and do an idea to just write down random stuff when Hill

Looked at each students results he could tell with amazing precision whether or not they'd actually flip the coin or just made up the results because the fakers routinely underestimated the likelihood of streaks

If a student's data included a streak of six or more heads or tails in a row they almost certainly recorded real data no streaks of six or more fake in 200 coin tosses there's a ninety six point five percent chance of getting us

Streak of six heads or tails there's an 80% chance you'll get seven in a row and a fifty-four percent chance of eight in a row nine in a row would really be pushing it though right no there's a thirty two percent chance

Of that happening in two hundred tosses so even that happens nearly a third of the time it's just not that weird a player sitting alone at a blackjack table will probably play about 200 hands per hour and the odds of losing a hand

Are close to 50% you'd almost certainly hit an eight or nine hand losing streak in a few hours to make the martingale bet doubling system work you need to be lucky enough to avoid those losing streaks and play the game with a ton of

Money and not ever reach the maximum bet and be comfortable knowing that you run the risk of losing everything to win just a single sugar cube here's the breakdown of how much you have to bet to absorb a common losing streak if you

Start by playing a twenty five dollar hand about the price of movie tickets for two and you lose your next bet would have to be 50 bucks the bets continue to double so that if you have a ten game losing streak which has about a 30%

Chance of happening over 1,000 hands by the 11th game you have to bet twenty-five thousand six hundred dollars just to recover your losses and walk away with a twenty five dollar profit and that's not including the twenty five

Thousand five hundred and seventy five dollars you already lost you need a total of fifty one thousand one hundred and seventy-five dollars the price of a luxury car to avoid going broke as you made a movie tickets for to profit by

Using martingale Beck doubling the best-case scenario is that you win your original bet in theory the system prevents you from losing any money but in reality it can cost you a fortune as you try to make up for and enough

Losing streak all in the hopes that you win an amount equal to the first cube and as always thanks for watching huge thanks to Aki for sending over my new robot friend vector I've had him for about a week now and it's really fun

Just kind of having him around in a way that actually didn't expect he recognizes you answers questions explorers around on his own as you can see and even locates his charger when he needs to go home and recharge and then

Before you know it he's up and playing with his Q but yeah look at this good job if you want to get your own robot friend there's a link in the description for you to check out and I'm just really looking forward to the future of vector

– like what programmers and people like you will eventually develop for vector to be able to do so I'm just gonna chill with my friend here for now and actually check this out hey vector let's do a fist bump

I just fist bumped a robot by

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