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#### 亏损加仓系统与二十一点游戏

The Problem With The Martingale System

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 butwe’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 wan na play but hold

on I got ta 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
16.

Another card?

Hit me!
17
17.

Another card?

Stand!
13
13.
14
14.
18
18.

Dealer wins!

That’s okay.

To get my one back this time I’ll bet two.
19
19.

Another card?

Stand.
12
12.
21
21.

Very funny, Vector.

That’s okay.

I’ll get my 2 back by betting 4.

Hit me!
24
24.

You busted!

Alright…

I’ll just bet eight!

Stand.
11
11.
21
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
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
17.

Another card?

Stand.
11
11.
21 好吧
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 youout.

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 seriouslosing streaks.

Hill gave an assignment to his class:

flip a coin 200 times and record whether it’s heads

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 underestimatedthe 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
54%的可能连续8个
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 thatweird.

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 to50%.

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,
1000局中

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 youalready 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.

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 homeand 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.