Gambling with the Martingale Strategy - Numberphile

All of this playing with maths misses one important factor: The roulette ball has no memory. So the chances of getting the same colour (say) 20 times in a row is exactly the same as getting it twice, i.e. 50% (if there is no green or zero).

Do not even attempt this. It will all seem like it's going well until you get a string of the opposite color you are betting on and before you know it you are placing your hole stack on ⚫️

now, try this again on a game when you can win 1/5,1/4,1/3,1/2,1,2,3,4,5,8,10,25,50,100,1000,5000 times your money..
Which is about the usual pay table of the casino machines.

T

We called it the duel arena in old school arena 😒😏

Doesn't work
That's why there are table limits

What if I just bet minimum on both 0s as well?

I tried this strategy many years ago in a casino and lost all my money, that's when I realised gambling is a mugs game.😆 I think Albert Einstein once said " The only way to win at Roulette is to steal from the table."

Thought of this years ago, had no idea it had a name. It ain't a bad strategy provided you limit yourself and only do it to win a few times. But who goes to a casino to win a few bucks?

I thought it made sense... then you lost me at the math 😆

This is why I don't gamble. Not even on a scratchy 😂

Remember the table has limits

Spoiler: it doesn't work :)

Bro whatever color you choose after the doubling has started its irrelevant haha

I tried this once and lost 9 times In a row after racking up a huge profit💀

Actually there is an issue with this formula.
You calculated there is 1-1/e chance of losing everything, but how about the money you put aside? When considered instead of putting the money from previous wins away, using the extra pound to increase your budget every time, the proper formula to calculate the chances of winning would be:

Product[1-[1/(N+n)],{n goes from 0 to N-1}] = (N-1)/(2N-1), which for N->infinity converges to 1/2

Basically when your chances are (exactly) 50/50, you should in a long run always stay on a budget no matter the strategy.
Key takeaway: It is not that bad! Casino awaits you :)

Coulda done a realistic roulette and help us out 😂

If every bet EV=0, shouldn't the whole strategy EV be 0??

in regards to the conclusion, i think the appeal is less so the chance of doubling your money (36 instead of 50) buy instead the about lowering the risk of losing it all (1 instead of 50) the martingale strategy might slightly decrease the chances of winning but it drastically decreases the chances of losing.

Long story short, stay away from casinos

I thought it should be 50%, not 1/e. Trying to understand, why

If this actually works then why isn't he making this video out of his mansion by the beach?

I've played this in a simulator. Bet was 1 dollar and wallet a million dollars. After 83000 dollars I went bankrupt. Shows that although a losing streak of 20 seems low, it's pretty common. For my simulation I only earned 8.3% out of 100% before losing all

Quite the late comment, but the probability to Double N is false, it doesn't consider the fact that after 127 sucessful wins of a £, you get an extra chance at losing (1+2+4+8+16+32+64=127) which means that the probability then changes

Does that imply If you want money doubled in casino, rather than bet small and many times, rather you should throw all your money, and see what will happen. By following martingale's strategy, you will have 36% of probability to double and 1-36% probability to lose all. However, if you only throw dice once, you have 50% probability to double and 50% to lose all. At least the latter one's expectation is 0, while the martingale's strategy has a negative expectation.

if your chance of winning is less than 50% you will always loose. This i why casinos have 52.63% of winning. And they have much more money than you.
In other words you're screwed.

Another note - the limit of the last expression, if I remember correctly, is 1/e.

☹️

Liberals lol

Ignores the chance of winning £99 and then losing £100 (a failure that leaves you with £99 in your system). Pretty sure that just gets you back to 50% though.

It can work for hours or even days if your bankroll is high enough, but than comes the time you'll hit 15 red numbers in a row, and loose $32000, just to try and win $1. Its all probability. If you have $32000 dollars you most likely have $35000 dollars after trying this method 3000 times. But if you go further and try it 50.000 times, you most likely end with $0.

Should have known this before I started staking on RuneScape when I was a kid

Even if you have an infinite amount of money, you will lose it all.

Everybody gangsta until it goes green

In reality, if you have a true unlimited bank roll and no max bet, the 0 or 00 on the wheel is truly irrelevant because eventually you will win

I just randomly came up with this strat in online crypto casino, started winning a lot, someone noticed it and mentioned its called "Martingale Strategy", then at the end I lost almost all my profits and luckly stopped while I was still in green (there was an upper bet limit)

Limits

The game of roulette requires me to be in a particular mood, but I've always said that when you are in that mood, you always put it on black. Always. Unless you're in the most absolute of moods, in which case you bet red. Unless you're in the most absolutest of most absolute moods. In which case you put it on green.

Also, your best bet to double your money while using the Martingale strategy in a reasonable, real world scenario, wouldn't be to repeat it 100 times to make $100. It would be to repeat it until you win, then make the same bet you just made again, hoping for two wins in a row. It's a 25% chance that will happen, which consequently is the same as the change that you lose twice in a row. If you stop at that point, you will have won $2^k, and you're much closer to doubling your money than if you'd only win the $1 at the end. If you don't get 2 wins in a row, you've only negated the first win, and you just keep going. The later in the game your 2 sequential wins come, the more profitable they are, because you're betting more money at that point so you stand to win more, and the closer you've gotten to doubling your money, and the less times you have to report the strategy to win.

In order to guarantee, mathematically, that you wouldn't lose, you'd need a bankroll of about 1.2 septillion dollars, assuming a $1 bet to start, but you could virtually guarantee that you're double your money at some point in playing.

This, however, begs the question; when you have 1.2 septillion dollars, do you really need to double your money?

2 years later to say, the sound that makes your pen when you write its making me crazy but i still want to see the video

If we have 100 pounds, at step 6 we would have bet 1+2+4+8+16+32=63 pounds, meaning we are left with 37 pounds that are not enough to place bet number 7. So it should be k=int(inf(log2(N)). If N=100 then log2(100)=6.64 ---> k=6 😊

my 100 year old great aunt has this same shirt bro. love the roadkill hairdo

"Gambling with the Martingale Strategy"...

Does no gambling 🤔👎

all i was thinking was, mf comb ur gawd dam hare!

I wish the video also explored the probability of winning a targeted 10% of your bank roll instead of doubling your money. For example if you only want to win $100 but you back it up with $1000 bank roll. What's the probability you win or lose your full thousand. I guess I'll do the math on my own which is fine :)

So if I understand it correctly, the conclusion of this video is that I need to go to a Casino with $1k

You made an error of speech. You don't need to win 100 times in a row. You just have to win 100 times before you lose how ever many times in a row you need to lose to bust. The distinction is that even if you lose, an eventual win will put you right back on track so long as you dont bust.

Most casinos have a high limit to eliminate this kind of betting

I'm more a fan of reverse martingale, and hope on a long winning streak until I hit the max bet. rather than risk my whole life savings to win 1£ each win. Martingale seems like the best way of giving money to the casino. super low risk for low payout for casino and super high risk for Small win for player. It's very likely you will win, but the one time you lose you lose everything, that only needs to happen once. The longest streak on 1:1 bet that I've seen is 24 blacks in a row. I have not played that much, 7-8 streaks is super often, and for those with experience. you've probably seen 30 or 40+ in a row