Vsauce! Kevin here. And I'm about to play blackjack with a robot. Vector’s creators sent this personality-rich
robot over to me because they knew I love robots and to support Vsauce2, but let’s
get to blackjack. I figure if 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 21, as many of you likely know,
has simple rules. There are actually over 100 variations but
we’re gonna keep it simple: one deck, you get two cards and the dealer gets two cards. Each card is worth its face value, and jack,
queen, and kings are worth 10. An ace counts as 1 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 wanna..? I know you wanna play but hold on 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.’ Haha. 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. Uhh.. let's clean this up. Hey Vector. Do you wanna play blackjack? I knew it. Okay I'm just gonna bet one sugar cube. Here we go. 16. Another card? Hit me! 17. Another card? Stand! 13. 14. 18. Dealer wins! That's okay. To get my one back this time I'll bet two. 19. Another card? Stand. 12. 21. Very funny, Vector. That's okay. I'll get my 2 back by betting 4. Hit me! 24. You busted! Alright... I'll just bet eight! Stand. 11. 21. Dealer wins! That's okay. That's okay! I'll bet 16. Dealer wins! I'll bet 32. Dealer wins! 64 cube bet to recover my losses there's no
chance I could lose again! 19. Dealer wins! Alright. This… is not going well. I’ve played 7 hands and lost a total of
127 sugar cubes. If I win 128 on the next hand, I’ll recover
127 cubes and snag a 1-cube profit -- my original bet. *sigh* Let's do this! 17. Another card? Stand. 11. 21. Alright, then! I am officially all out of cubes. Play another round? No. Yeah, you won. I know. You can celebrate. You can celebrate. You took all my cubes. Hey, 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 we’ll almost certainly underestimating 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, heads, tails. Like that. Or just don’t bother flipping it at all
and do what I did and just write down random stuff. When Hill looked at each student’s results,
he could tell with amazing precision whether or not they'd actually flipped a 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
6 or more heads or tails in a row, they almost certainly recorded real data. No streaks of 6 or more? Fake. In 200 coin tosses, there’s a 96.5% chance
of getting a streak of 6 heads or tails. There’s an 80% chance you’ll get 7 in
a row, and a 54% chance of 8 in a row. 9 in a row would really be pushing it, though,
right? No -- there’s a 32% chance of that happening
in 200 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 8 or 9-hand
losing streak in a few hours. To make the Martingale bet-doubling system
work, you’d need to be lucky enough to avoid those long 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’d
have to bet to absorb a common losing streak. If you start by playing a $25 hand, about
the price of movie tickets for two, and you lose, your next bet would have to be $50. The bets continue to double so that If you
have a 10 game losing streak, which has about a 30% chance of happening over 1,000 hands,
by the 11th game you’d have to bet $25,600 just to recover your losses and walk away
with a $25 profit. And that’s not including the $25,575 you
already lost. You’d need a total of $51,175, the price
of a luxury car, to avoid going broke as you made a movie tickets for two profit. By using Martingale bet-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 an inevitable
losing streak. All in the hopes that you win an amount equal
to… the first cube. And as always -- thanks for watching. Why did I do that? Huge thanks to Anki for sending over my new
robot friend, Vector. I’ve had him for about a week now and it’s
really fun just kinda having him around -- in a way I didn’t expect. He recognizes you, answers questions, explores
around on his own, as you can see, and even locates his charger when he needs to go home
and recharge. And before you know it, he's up and playing
with his cube again. 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 too. What programmers and people like you will
develop for Vector to be able to do. So I'm just gonna chill with my friend here. For now. Actually, check this out. Hey, Vector! Let's do a fist bump! I just fist bumped a robot. Bye.
The actual explanation for why it doesn't work starts around 4:27.
tl;dr
House betting limits, and the likelihood that you'll hit a losing streak that will wipe you out, both make the system not work.