Probability with martingale question

[Juliusmcdonald01]

Been reading on this forum and elsewhere a bunch about how martingale doesn't work, and I get why with a game like craps or roulette. But I was hoping to have a discussion around a particular game.

Say you have a very large bankroll of 1,000,000usd in this example. You bet .000001 mBTC set on autopilot. You say, less than 80 is a win. So you have about a 79% chance of winning each spin. You win about a fifth of your bet on each spin. On each loss you increase your bet by 6, which covers the loss and earns you a small amount. After a win, the bet returns to original.

What I'm trying to wrap my head around is what the odds are of rolling enough losing spins in a row to lose your massive bankroll. Let's take the million in the example, we increase the bet after each consecutive loss by 6:
.000001
.000006
.000036
.000216
.001296
.007776
.046656
.279936
1.679616
10.077
60.46
362.79
2176.78
13k
78k
470k


So what are the odds then of losing 16 times in a row when any singular spin has about a 79% chance of winning? I get that each spin is independent of the next and is referred to as the "gamblers fallacy" but it seems like losing 16 times in a row is a very small probabaility when singular spins are 79% in your favor.

In experiments, I see three losses in a row with some regularity, 4 too. 5 and 6 are very rare.

Someone tell me what I'm missing here. Seems like you could win if your bankroll was large enough to basically work outside of the very unlikely trend of losing so many times in a row. Sure maybe after a long enough time of doing this you would lose but shouldn't this work if you just slam the game with a big bankroll and then stop?

I see this as materially different than playing a hi/lo 50/50 game since you have no odds in your favor but rather a coin flip.

[1714790593]

1714790593

[HCP]

I did some research into "max expected loss streaks"... and found websites like this one that show a formula for calculating the max expected loss streak as:

ln(Number of Events) / ln(1-win%)

where win% is a decimal from 0.00 to 1... ie. Percentage/100, so that 80% win would be 0.8, 1% would be 0.01 etc.

Via another reference (that I can't locate at this time), ln() function can be replaced with log() function and you can use:

Log(Number of Events) / -Log(1-win%)

Putting some example numbers in, we would get:

Log(1,000,000) / -Log(1-0.8 ) = 8.58 or ~9.

So you could expect a loss streak of 9 in 1,000,000 rolls at 80% of winning.... which would at first seem to be well under the max sustainable by your max Bankroll...  HOWEVER, you seem to have confused your numbers and units... at the start you're talking 0.00000100 mBTC basebet and USD$1,000,000 and the max as 470k (no currency unit specified)....  

If we assume, you actually meant 0.00000100 BTC (ie. 100 satoshis) as your starting point, and we converted your USD$1mil that would be ~800 BTC at current prices. This would reduce your sustainable max losses down to 12 losses (at which point, you just lost a 362.79 BTC wager, and your total losses are 435.35 BTC), the next required bet would be 2176 BTC, which you don't have.

Still, your max expected loss streak is only 9... so that should theoretically be doable... HOWEVER (yes, more bad news)... most, if not ALL casinos, be it online or bricks and mortar have "Max Bet" and/or "Max Payout" rules. I highly doubt you will find a casino that lets you wager 60 BTC at a 1.24x payout (~80% chance)... And for a lot of them, even 10 BTC at 1.24 would be getting close to their max.

So now you're down to maybe being able to make 10 losses before you hit the max bet/max payout limit... and given that the formula is just an "estimation" of the "expected" max loss streak... doesn't mean it can't or won't go higher... I've actually had a scenario where the max expected streak was calculated as 62, and I encountered 67 losses.

Also note that even if you hit the win at the 10BTC bet... your overall profit would only be 0.4 BTC... do you really want to be risking ~$10,000 to make ~$400?

[devachelekar]

Been reading on this forum and elsewhere a bunch about how martingale doesn't work, and I get why with a game like craps or roulette. But I was hoping to have a discussion around a particular game.

Say you have a very large bankroll of 1,000,000usd in this example. You bet .000001 mBTC set on autopilot. You say, less than 80 is a win. So you have about a 79% chance of winning each spin. You win about a fifth of your bet on each spin. On each loss you increase your bet by 6, which covers the loss and earns you a small amount. After a win, the bet returns to original.

What I'm trying to wrap my head around is what the odds are of rolling enough losing spins in a row to lose your massive bankroll. Let's take the million in the example, we increase the bet after each consecutive loss by 6:
.000001
.000006
.000036
.000216
.001296
.007776
.046656
.279936
1.679616
10.077
60.46
362.79
2176.78
13k
78k
470k


So what are the odds then of losing 16 times in a row when any singular spin has about a 79% chance of winning? I get that each spin is independent of the next and is referred to as the "gamblers fallacy" but it seems like losing 16 times in a row is a very small probabaility when singular spins are 79% in your favor.

In experiments, I see three losses in a row with some regularity, 4 too. 5 and 6 are very rare.

Someone tell me what I'm missing here. Seems like you could win if your bankroll was large enough to basically work outside of the very unlikely trend of losing so many times in a row. Sure maybe after a long enough time of doing this you would lose but shouldn't this work if you just slam the game with a big bankroll and then stop?

I see this as materially different than playing a hi/lo 50/50 game since you have no odds in your favor but rather a coin flip.

By my calculations(Don't trust this becasue i'm so shit at maths lol) the probability of 16 losses in a row with 21% chance of losing is 0.00000000143056869%.

It shouldn't happen in your lifetime.

However, it's not worth it if you think about it. Sure, it is possible that you could have 1 million dollars and do this to make a nice profit but honestly, if you calculate all the electricity costs and you wasting your time on a gambling site, plus counterparty risk of the casino doing a runner, then it's not worth it.

You'll probably make as much as you would if you deposited into a bank or did p2p lending.

[ralle14]

With my calculations I ended up with 0.00000000735582751%. I'm not sure if this is the correct one or the person above me. With these kind of numbers it looks that it's unlikely gonna happen but it's possìble because games are full of surprises.

Edit : My calculations were off the person above me was correct. I missed a couple of 0.21s when I did mine.

snip

The example that the OP gave is definitely confusing. He stopped at 470k because the example said you only have 1m usd on your starting bankroll but the base is in mbtc.

I think safe dice would let you wager with any amount but the house edge will increase once you start betting big so it's not profitable.

[swogerino]

16 times is very low amount. In real life it is a big amount but in online gambling houses which they use software to monitor everything it can be more than 16 times and you still would lose all of your investment. Bottom line, martingale does not work with online gambling houses, try to go to some offline gambling house in your country and try this experiment you want to make.

[mimini0147]

Been reading on this forum and elsewhere a bunch about how martingale doesn't work, and I get why with a game like craps or roulette. But I was hoping to have a discussion around a particular game.

Say you have a very large bankroll of 1,000,000usd in this example. You bet .000001 mBTC set on autopilot. You say, less than 80 is a win. So you have about a 79% chance of winning each spin. You win about a fifth of your bet on each spin. On each loss you increase your bet by 6, which covers the loss and earns you a small amount. After a win, the bet returns to original.

What I'm trying to wrap my head around is what the odds are of rolling enough losing spins in a row to lose your massive bankroll. Let's take the million in the example, we increase the bet after each consecutive loss by 6:
.000001
.000006
.000036
.000216
.001296
.007776
.046656
.279936
1.679616
10.077
60.46
362.79
2176.78
13k
78k
470k


So what are the odds then of losing 16 times in a row when any singular spin has about a 79% chance of winning? I get that each spin is independent of the next and is referred to as the "gamblers fallacy" but it seems like losing 16 times in a row is a very small probabaility when singular spins are 79% in your favor.

In experiments, I see three losses in a row with some regularity, 4 too. 5 and 6 are very rare.

Someone tell me what I'm missing here. Seems like you could win if your bankroll was large enough to basically work outside of the very unlikely trend of losing so many times in a row. Sure maybe after a long enough time of doing this you would lose but shouldn't this work if you just slam the game with a big bankroll and then stop?

I see this as materially different than playing a hi/lo 50/50 game since you have no odds in your favor but rather a coin flip.

The only hole in your proposition is that if someone has that much bankroll and they are using a base bet of that magnitude then it will probably take thousands of bets to attain a profit that means anything to the person betting. I,ve personally had streaks of 10+ losses in the space of just a few hundred bets so I don't think the idea of losing 16 bets in a row is unreasonable considering that whoever is betting will be making thousands and thousands of bets. Why would anyone martingale at 80% with such a low base bet when they have so much bankroll in the first place?

Seems like spending alot of time for just a few dollars.

[NorrisK]

Been reading on this forum and elsewhere a bunch about how martingale doesn't work, and I get why with a game like craps or roulette. But I was hoping to have a discussion around a particular game.

Say you have a very large bankroll of 1,000,000usd in this example. You bet .000001 mBTC set on autopilot. You say, less than 80 is a win. So you have about a 79% chance of winning each spin. You win about a fifth of your bet on each spin. On each loss you increase your bet by 6, which covers the loss and earns you a small amount. After a win, the bet returns to original.

What I'm trying to wrap my head around is what the odds are of rolling enough losing spins in a row to lose your massive bankroll. Let's take the million in the example, we increase the bet after each consecutive loss by 6:
.000001
.000006
.000036
.000216
.001296
.007776
.046656
.279936
1.679616
10.077
60.46
362.79
2176.78
13k
78k
470k


So what are the odds then of losing 16 times in a row when any singular spin has about a 79% chance of winning? I get that each spin is independent of the next and is referred to as the "gamblers fallacy" but it seems like losing 16 times in a row is a very small probabaility when singular spins are 79% in your favor.

In experiments, I see three losses in a row with some regularity, 4 too. 5 and 6 are very rare.

Someone tell me what I'm missing here. Seems like you could win if your bankroll was large enough to basically work outside of the very unlikely trend of losing so many times in a row. Sure maybe after a long enough time of doing this you would lose but shouldn't this work if you just slam the game with a big bankroll and then stop?

I see this as materially different than playing a hi/lo 50/50 game since you have no odds in your favor but rather a coin flip.

By my calculations(Don't trust this becasue i'm so shit at maths lol) the probability of 16 losses in a row with 21% chance of losing is 0.00000000143056869%.

It shouldn't happen in your lifetime.

However, it's not worth it if you think about it. Sure, it is possible that you could have 1 million dollars and do this to make a nice profit but honestly, if you calculate all the electricity costs and you wasting your time on a gambling site, plus counterparty risk of the casino doing a runner, then it's not worth it.

You'll probably make as much as you would if you deposited into a bank or did p2p lending.

I think you are right with your calculations. The chance of losing 16 times in a row is 0.21^16.

The biggest issue is not your odds as mentioned before, but the max bet that is into place in any gambling house to protect the house.

This system may have a chance though, as losing 5 times in a row already has tiny odds: 0.0004 or 0.04%

[swogerino]

Been reading on this forum and elsewhere a bunch about how martingale doesn't work, and I get why with a game like craps or roulette. But I was hoping to have a discussion around a particular game.

Say you have a very large bankroll of 1,000,000usd in this example. You bet .000001 mBTC set on autopilot. You say, less than 80 is a win. So you have about a 79% chance of winning each spin. You win about a fifth of your bet on each spin. On each loss you increase your bet by 6, which covers the loss and earns you a small amount. After a win, the bet returns to original.

What I'm trying to wrap my head around is what the odds are of rolling enough losing spins in a row to lose your massive bankroll. Let's take the million in the example, we increase the bet after each consecutive loss by 6:
.000001
.000006
.000036
.000216
.001296
.007776
.046656
.279936
1.679616
10.077
60.46
362.79
2176.78
13k
78k
470k


So what are the odds then of losing 16 times in a row when any singular spin has about a 79% chance of winning? I get that each spin is independent of the next and is referred to as the "gamblers fallacy" but it seems like losing 16 times in a row is a very small probabaility when singular spins are 79% in your favor.

In experiments, I see three losses in a row with some regularity, 4 too. 5 and 6 are very rare.

Someone tell me what I'm missing here. Seems like you could win if your bankroll was large enough to basically work outside of the very unlikely trend of losing so many times in a row. Sure maybe after a long enough time of doing this you would lose but shouldn't this work if you just slam the game with a big bankroll and then stop?

I see this as materially different than playing a hi/lo 50/50 game since you have no odds in your favor but rather a coin flip.

By my calculations(Don't trust this becasue i'm so shit at maths lol) the probability of 16 losses in a row with 21% chance of losing is 0.00000000143056869%.

It shouldn't happen in your lifetime.

However, it's not worth it if you think about it. Sure, it is possible that you could have 1 million dollars and do this to make a nice profit but honestly, if you calculate all the electricity costs and you wasting your time on a gambling site, plus counterparty risk of the casino doing a runner, then it's not worth it.

You'll probably make as much as you would if you deposited into a bank or did p2p lending.

I think you are right with your calculations. The chance of losing 16 times in a row is 0.21^16.

The biggest issue is not your odds as mentioned before, but the max bet that is into place in any gambling house to protect the house.

This system may have a chance though, as losing 5 times in a row already has tiny odds: 0.0004 or 0.04%

That is not correct in online gambling houses which uses different softwares for monitoring the bets and predicting the outcomes, known as provably fair through MD5 hash function. I have been trying the same bet on crypto-games to check how many times I would lose in a row and surprisingly was 29 times in a row before I won a bet. I kept a 50-50 chance when trying or 2x.

[ralle14]

I think you are right with your calculations. The chance of losing 16 times in a row is 0.21^16.

The biggest issue is not your odds as mentioned before, but the max bet that is into place in any gambling house to protect the house.

This system may have a chance though, as losing 5 times in a row already has tiny odds: 0.0004 or 0.04%

That is not correct in online gambling houses which uses different softwares for monitoring the bets and predicting the outcomes, known as provably fair through MD5 hash function. I have been trying the same bet on crypto-games to check how many times I would lose in a row and surprisingly was 29 times in a row before I won a bet. I kept a 50-50 chance when trying or 2x.

He's only talking about chances of losing 16 times if you think the calculation isn't correct then could you give us the correct answer here? I know you could lose more than that. Last weekend I tried betting with 98% win chance just to increase my stats and after 100 rolls I had 6 losses overall with 2 consecutive losses(chances of this happening is 0.04%).

[Juliusmcdonald01]

So I decided to experiment and so far I have not gone bankrupt. Investment was 17mBTC and I have not gone above 6 consecutive losses. I am betting a microscopic amount and 17mBTC covers martingale increments up to 7 times. Hesitant to try more money but so far I have done about 30,000 bets. Playing under 82, wagered 6mBTC and profit is .25. The math works out to about $1.00 -$1.50 in profits per day at this rate. I'm not playing with the martingale increment of 8 times like I want but rather 6. 8 Times doesn't ensure that I can cover 7 consecutive losses. However, if this does work, then in theory I could add money and keep playing so that each bet was larger and profits should increase. However, I would imagine that to make 100 times my .25mBTC would take 100 times the bankroll. 1700mBTC. To make 25 per day is a decent amount of money but thats also a lot to risk losing. I will have to see if this bet experiment goes beyond 7 consecutive. I have definitely seen 6.

Like I was saying though, a large enough bankroll seems like a plausible way to insulate from bankruptcy but there is no guarantee you won't get 15 losses in a row I guess.

[Caladonian]

So I decided to experiment and so far I have not gone bankrupt. Investment was 17mBTC and I have not gone above 6 consecutive losses. I am betting a microscopic amount and 17mBTC covers martingale increments up to 7 times. Hesitant to try more money but so far I have done about 30,000 bets. Playing under 82, wagered 6mBTC and profit is .25. The math works out to about $1.00 -$1.50 in profits per day at this rate. I'm not playing with the martingale increment of 8 times like I want but rather 6. 8 Times doesn't ensure that I can cover 7 consecutive losses. However, if this does work, then in theory I could add money and keep playing so that each bet was larger and profits should increase. However, I would imagine that to make 100 times my .25mBTC would take 100 times the bankroll. 1700mBTC. To make 25 per day is a decent amount of money but thats also a lot to risk losing. I will have to see if this bet experiment goes beyond 7 consecutive. I have definitely seen 6.

Like I was saying though, a large enough bankroll seems like a plausible way to insulate from bankruptcy but there is no guarantee you won't get 15 losses in a row I guess.

i was able to have 20+ losing streak when i was still playing dice thinking that having a huge bankroll will allow me to take advantage of this martingale strategy but shit happens and it was a big loss that i made in my entire gambling activity losing almost a half btc if i still remember
it right from then i stop playing base luck games and focus only with sports bet and trading alts.

[mirakal]

So I decided to experiment and so far I have not gone bankrupt. Investment was 17mBTC and I have not gone above 6 consecutive losses. I am betting a microscopic amount and 17mBTC covers martingale increments up to 7 times. Hesitant to try more money but so far I have done about 30,000 bets. Playing under 82, wagered 6mBTC and profit is .25. The math works out to about $1.00 -$1.50 in profits per day at this rate. I'm not playing with the martingale increment of 8 times like I want but rather 6. 8 Times doesn't ensure that I can cover 7 consecutive losses. However, if this does work, then in theory I could add money and keep playing so that each bet was larger and profits should increase. However, I would imagine that to make 100 times my .25mBTC would take 100 times the bankroll. 1700mBTC. To make 25 per day is a decent amount of money but thats also a lot to risk losing. I will have to see if this bet experiment goes beyond 7 consecutive. I have definitely seen 6.

Like I was saying though, a large enough bankroll seems like a plausible way to insulate from bankruptcy but there is no guarantee you won't get 15 losses in a row I guess.

i was able to have 20+ losing streak when i was still playing dice thinking that having a huge bankroll will allow me to take advantage of this martingale strategy but shit happens and it was a big loss that i made in my entire gambling activity losing almost a half btc if i still remember
it right from then i stop playing base luck games and focus only with sports bet and trading alts.

That explains already that using martingale does not guarantee a win, no one will ever be successful if it is applied in dice. Using martingale should be done based on the right timing, and for me I will not apply that in dice in the long run, I have also a bad experience with martingale so that makes me learn from my mistakes. When you are new with this method, you will be aggressive but once you tried it, you will surely feel the reality.

[chris200x9]

So I decided to experiment and so far I have not gone bankrupt. Investment was 17mBTC and I have not gone above 6 consecutive losses. I am betting a microscopic amount and 17mBTC covers martingale increments up to 7 times. Hesitant to try more money but so far I have done about 30,000 bets. Playing under 82, wagered 6mBTC and profit is .25. The math works out to about $1.00 -$1.50 in profits per day at this rate. I'm not playing with the martingale increment of 8 times like I want but rather 6. 8 Times doesn't ensure that I can cover 7 consecutive losses. However, if this does work, then in theory I could add money and keep playing so that each bet was larger and profits should increase. However, I would imagine that to make 100 times my .25mBTC would take 100 times the bankroll. 1700mBTC. To make 25 per day is a decent amount of money but thats also a lot to risk losing. I will have to see if this bet experiment goes beyond 7 consecutive. I have definitely seen 6.

Like I was saying though, a large enough bankroll seems like a plausible way to insulate from bankruptcy but there is no guarantee you won't get 15 losses in a row I guess.

i was able to have 20+ losing streak when i was still playing dice thinking that having a huge bankroll will allow me to take advantage of this martingale strategy but shit happens and it was a big loss that i made in my entire gambling activity losing almost a half btc if i still remember
it right from then i stop playing base luck games and focus only with sports bet and trading alts.

That explains already that using martingale does not guarantee a win, no one will ever be successful if it is applied in dice. Using martingale should be done based on the right timing, and for me I will not apply that in dice in the long run, I have also a bad experience with martingale so that makes me learn from my mistakes. When you are new with this method, you will be aggressive but once you tried it, you will surely feel the reality.

yes everyone knows no strategies will work in a dice game, but still, some people try this martingale method to make money. End of the day they will lose money then they realise that in dice game no plans works. Experience makes man perfect this is 100% correct. People don't like free suggestion they always like paid service.