Does martingale really works?

[CryForMeSky]

The point is that profit is profit regardless.  Dooglus's example is an extreme case highlighting how the amount you stand to profit or lose is a secondary factor that must be considered.  The greater the discrepancy of payout in relation to the odds, the greater this factor needs to be taken into account.  But, if your starting pot allows you to use the Martingale strategy such that your odds of losing everything is, for example, 2^16, it may very well be worth a few trials to some people.

Ah, I see.  I mean yes, technically profit is profit but I disagree with the "regardless" point.  Playing something with a lower house edge means more profit more often (although obviously still -ev overall).  Saying "I won money therefore it was a good bet" is faulty logic.

You're right, this is fairly obvious, but the answer to subject question should also be fairly obvious, and we're on page 45 already.

That is the nature of gambling and why fair sites can make hundreds and thousands of coins while ripoff sites will always be able to steal a few.  People are always looking for the quick "answer" that will lead to them winning large sums of money.  It's why every time someone makes a post about winning a large sum, there are ALWAYS a handful of people who post right after asking what his strategy was or how he did it.  People will always think that martingale is some sort of secret strat because they don't understand that they are really just wagering a huge amount in order to win a small amount, and giving the site a fortune in theoretic profit via the house edge.

[jeffhuys]

How this has 45 pages of replies is beyond me. Martingale only works when you have an infinite payroll. Seeing as this is not possible, martingale doesn't and will not ever work. It's really that simple.

[the joint]

The point is that profit is profit regardless.  Dooglus's example is an extreme case highlighting how the amount you stand to profit or lose is a secondary factor that must be considered.  The greater the discrepancy of payout in relation to the odds, the greater this factor needs to be taken into account.  But, if your starting pot allows you to use the Martingale strategy such that your odds of losing everything is, for example, 2^16, it may very well be worth a few trials to some people.

Ah, I see.  I mean yes, technically profit is profit but I disagree with the "regardless" point.  Playing something with a lower house edge means more profit more often (although obviously still -ev overall).  Saying "I won money therefore it was a good bet" is faulty logic.

You're right, this is fairly obvious, but the answer to subject question should also be fairly obvious, and we're on page 45 already.

That is the nature of gambling and why fair sites can make hundreds and thousands of coins while ripoff sites will always be able to steal a few.  People are always looking for the quick "answer" that will lead to them winning large sums of money.  It's why every time someone makes a post about winning a large sum, there are ALWAYS a handful of people who post right after asking what his strategy was or how he did it.  People will always think that martingale is some sort of secret strat because they don't understand that they are really just wagering a huge amount in order to win a small amount, and giving the site a fortune in theoretic profit via the house edge.

Yep.  I think people just have a hard time imagining that they could ever lose when those losing odds are 1:2^16 or something equally unimaginable, even if they bet thousands of times.  They think, "Well, every trial is independent of every other, so let it ride!"

I'm also guessing these are the same people that buy scratch-off tickets and have never won anything significant, and so they equate their odds of losing anything significant from multiple trials to their experience of never winning anything significant from multiple trials.

[deisik]

Prerolling doesn't work either.

That's where you roll tiny bets until you've seen 20 losses in a row, then start martingale betting from a larger base. The logic "since we just saw 20 losses in a row there probably isn't much of the losing streak left". That logic is faulty. The odds of seeing a streak of any given length in the next few bets are the same whether you've just rolled until you saw 20 losses in a row or not. Because all rolls are mutually independent.

This, exactly.   Because each roll is an independent event you never know if you're in the middle of a 100 loss streak.  However, some part of me thinks it also has to be true that rolling consecutive losses into infinity is also highly improbably and that longer and longer streaks of losses have to be more and more improbable.  So I always have a hard time rectifiying these two facts: the independence of each roll and the increasing unlikelyhood of increasingly large streaks.

I had been trying to say almost the same nearly a year ago (most likely even in this very thread), but I was unanimously laughed at. I argued that despite the fact that mathematically each roll is independent of all rolls before and after it, in reality they nevertheless should still be connected to each other somehow (something like the entanglement in quantum mechanics), at least previous rolls with the future ones...

Yeah, I know, this is what casinos owners would want us to universally believe!

[CryForMeSky]

Prerolling doesn't work either.

That's where you roll tiny bets until you've seen 20 losses in a row, then start martingale betting from a larger base. The logic "since we just saw 20 losses in a row there probably isn't much of the losing streak left". That logic is faulty. The odds of seeing a streak of any given length in the next few bets are the same whether you've just rolled until you saw 20 losses in a row or not. Because all rolls are mutually independent.

This, exactly.   Because each roll is an independent event you never know if you're in the middle of a 100 loss streak.  However, some part of me thinks it also has to be true that rolling consecutive losses into infinity is also highly improbably and that longer and longer streaks of losses have to be more and more improbable.  So I always have a hard time rectifiying these two facts: the independence of each roll and the increasing unlikelyhood of increasingly large streaks.

I had been trying to say almost the same nearly a year ago (most likely even in this very thread), but I was unanimously laughed at. I argued that despite the fact that mathematically each roll is independent of all rolls before and after it, in reality they nevertheless should still be connected to each other somehow (something like the entanglement in quantum mechanics), at least previous rolls with the future ones...

Yeah, I know, this is what casinos owners would want us to universally believe!

It's still a laughable (although common) belief.  Every roll is completely independent.  To assume that previous rolls affect future rolls...in any way...is incorrect.

[dooglus]

You seem to have failed to read my previous posts carefully. I specifically mentioned that I had been assuming (erroneously) that the odds were set in such a way that a winning bet would recover all the previous losses plus win a profit equal to the losses accumulated in that sequence (not the original stake), since this is the way martingale is most often used (it makes no sense to win just the base bet)...

I guess you're referring to this:

You set your odds in such a way that each winning bet covers all the accumulated losses from the previous losing bets in a row plus gives you the same amount in profit (in the simplest case).

I thought by "the same amount" you mean "the same amount each sequence", ie. the base amount. But you meant "the same amount as the size of the last bet in the sequence".

That's not how martingale is most often used. It is probably most often used to bet on red or black on the roulette table where a winning bet doubles your money. On Just-Dice (where you can chose your own payout multiplier) martingale is by far most often used at 49.5% chance of winning, 2x payout. There are a few people who play with lower chances, higher payout multipliers, but they're in the minority.

This depends on what you mean by "the odds are in your favour". I offer you this bet:

5 times out of 6 you win. You're 5 times more likely to win than to lose. But when you win you only win $1, and when you lose you lose $100.

I would say that the odds are not in your favour.

Based upon a strict interpretation of my point, then yes, the odds are in my favor.

Again, it depends on what you mean by "odds in your favour".

If you mean "more likely to win than to lose" then yes.

If you mean "you are likely to succeed because the conditions are good and you have an advantage" then no. Your expectation is negative - it's a bad bet for you. You're more likely to win than to lose, but the amount you win is so small compared to the amount you risk that it's not in your favour. You don't have an advantage even though you win 5 out of 6 times.

It's hard to find a decent definition. All I find is Hunger Games junk. In that case the stake is life/death so it's hard to evaluate expected values.

My point is best demonstrated by imagining that a hypothetical secondary bet is placed on top of the original bet.

Using your example, let's say I had a 5:6 chance of winning $1 and a 1:6 of losing $100, and I guarantee a roll according to these odds.

Now imagine that you are a spectator who is asked to bet as to whether I will profit or if I will lose.   Someone says, "Hey, I'll bet $50 that he (i.e. me) loses."  You have a spare $50 in your pocket.  Do you take the bet?

Of course you would, so the point holds.  Though, as you point out, the odds of profiting alone might not be the only thing you want to take into account...

That 2nd bet is a good bet. I would take that one, because its odds ARE in my favour. You're paying even money for a 5-in-6 event. Just because the 2nd bet is a good one to take doesn't mean the 1st one is too.

This, exactly.   Because each roll is an independent event you never know if you're in the middle of a 100 loss streak.  However, some part of me thinks it also has to be true that rolling consecutive losses into infinity is also highly improbably and that longer and longer streaks of losses have to be more and more improbable.  So I always have a hard time rectifiying these two facts: the independence of each roll and the increasing unlikelyhood of increasingly large streaks.

Well, look at it this way:

Streaks of length 20 are twice as common as streaks of length 21, which are twice as common as streaks of length 22, etc.

And streaks of length 20 are exactly as common as streaks of length 21 or more (assuming a 50/50 game).

To see that last point, suppose streaks of length exactly 20 occur with probability p. Streaks of length 21 will occur with half that probability (p/2), Length 22 with probability p/4, and so on. So the probability of a streak of length 21 or more is p/2 + p/4 + p/8 + ... = p(1/2 + 1/4 + 1/8 + ...) = p.

By pre-rolling until you hit 20 losses in a row, you've probably had to make a million or so rolls. And now you're wondering whether the streak will end at 20, or go on to be more than 20. Well as we've just seen, the probability of those two things is the same. probability p it will end at 20, and probability p*(1/2+1/4+1/8+...) = p that it goes to length 21 or more.

Back to the "does martingale works?" question - we had a guy playing on Just-Dice over the last day or so who has won huge amounts using something very like martingale betting.

Here's a chart of his profit over time:



and the site's profit over the last week:



So even though he's using a losing strategy, he's managed to get lucky and win.

[deisik]

That's not how martingale is most often used. It is probably most often used to bet on red or black on the roulette table where a winning bet doubles your money. On Just-Dice (where you can chose your own payout multiplier) martingale is by far most often used at 49.5% chance of winning, 2x payout. There are a few people who play with lower chances, higher payout multipliers, but they're in the minority.

I don't see much sense in such setup where you invariably win only minuscule amounts per streak but can lose big (though you can always lose big in any setup, but in my setup you can win handsomely too). Personally, I never used the setup we discussed, and that's why I misunderstood the post this discussion started with...

[jeffhuys]

So even though he's using a losing strategy, he's managed to get lucky and win.

Yes. That's the whole point about gambling: everyone has the same chances, some lose and some win. It all evens out in the end, though. If you REALLY want to make a lot of money, steal or work for it. Then HODL

[the joint]

...


Again, it depends on what you mean by "odds in your favour".

If you mean "more likely to win than to lose" then yes.

...

That was what I mean

I of course agree with you that the stakes must be considered.

The only reason I made the post was because it seemed to me as though people were treating "profit" and "doubling money" as equivalent.  I felt it wasn't totally irrelevant or meaningless to point out that one's goal when betting is an important consideration.

Practical scenario:  Rent is due tomorrow and you owe BTC1.01 and you have BTC1.00 only.  If you are late on your payment, you will face a 10% fee and will then owe BTC1.10.

To avoid the 10% fee, you could gamble your BTC1.00 with somewhere between a 98-99% chance of profiting/winning BTC0.01 so that you can pay on-time and in full.

Would you take that bet to make your rent payment on time?  I'm guessing there would be mixed opinions depending on who you ask.

In this case, the bettor's goal isn't to double his money.  His goal is to make a minute profit.

[the joint]

Here's an interesting question:

Based upon the number of car accidents resulting in death, we can calculate an estimated probability that a person will die while driving on his way to work.

"Winning" means driving to work successfully to earn a paycheck.

"Losing" means dying in a car accident (and thus rendering any past/future earnings valueless).

With infinite trials, you will die in a car accident.

Question:  Why do you go to work?

(Note: I know I'm leaving a lot of wiggle-room for interpretation and caveats, but I just thought I'd toss it out there as a point of discussion).

[CryForMeSky]

Here's an interesting question:

Based upon the number of car accidents resulting in death, we can calculate an estimated probability that a person will die while driving on his way to work.

"Winning" means driving to work successfully to earn a paycheck.

"Losing" means dying in a car accident (and thus rendering any past/future earnings valueless).

With infinite trials, you will die in a car accident.

Question:  Why do you go to work?

(Note: I know I'm leaving a lot of wiggle-room for interpretation and caveats, but I just thought I'd toss it out there as a point of discussion).

You could say that ("You could die doing it") about literally everything on earth.  Including drinking water.  People do things because that's what living life is.  It has zero bearing on making -ev bets.

[the joint]

Here's an interesting question:

Based upon the number of car accidents resulting in death, we can calculate an estimated probability that a person will die while driving on his way to work.

"Winning" means driving to work successfully to earn a paycheck.

"Losing" means dying in a car accident (and thus rendering any past/future earnings valueless).

With infinite trials, you will die in a car accident.

Question:  Why do you go to work?

(Note: I know I'm leaving a lot of wiggle-room for interpretation and caveats, but I just thought I'd toss it out there as a point of discussion).

You could say that ("You could die doing it") about literally everything on earth.  Including drinking water.  People do things because that's what living life is.  It has zero bearing on making -ev bets.

Well of course you can say that about anything, but that isn't the point.

The point is that, as I mentioned previously, there is a difference when the bettor's goal is to simply profit rather than double his money against the odds.

I would specifically argue that the reason we drive to work is because, although driving to work is essentially a -ev bet (life expectancy not withstanding), we do it because our goal is to make a profit, not to "beat the house."  Hence, I think that is more often why people gamble, i.e. to "profit," and that's it.
 

[dooglus]

Here's an interesting question:

Based upon the number of car accidents resulting in death, we can calculate an estimated probability that a person will die while driving on his way to work.

"Winning" means driving to work successfully to earn a paycheck.

"Losing" means dying in a car accident (and thus rendering any past/future earnings valueless).

With infinite trials, you will die in a car accident.

Question:  Why do you go to work?

(Note: I know I'm leaving a lot of wiggle-room for interpretation and caveats, but I just thought I'd toss it out there as a point of discussion).

With infinite trials, you will also die if you never go near a car.

So you are choosing between different ways of dying. Not dying isn't an option.

If you choose not to drive to work maybe you die of starvation or boredom.

If there's the option of just staying at home and living off handouts forcibly taken from those who do risk life and limb driving to work every day then isn't that the obvious +EV solution?

[CryForMeSky]

The point is that, as I mentioned previously, there is a difference when the bettor's goal is to simply profit rather than double his money against the odds.

 

I guess I don't understand the reason you are making the point.  You are saying that betting on a high-frequency low-payout bet will frequently result in a small win.  Yes.  That is very obvious.  I don't really follow the point you are making from this fact.  That betting is fun?  Absolutely.  That it is profitable?  Well, no, when you look from a theoretical point of view (in games with house edges).  Betting once @ 1.01x payout isn't a "good bet", it's a losing bet.  Even though you will frequently win the bet.

[deisik]

This, exactly.   Because each roll is an independent event you never know if you're in the middle of a 100 loss streak.  However, some part of me thinks it also has to be true that rolling consecutive losses into infinity is also highly improbably and that longer and longer streaks of losses have to be more and more improbable.  So I always have a hard time rectifiying these two facts: the independence of each roll and the increasing unlikelyhood of increasingly large streaks.

I had been trying to say almost the same nearly a year ago (most likely even in this very thread), but I was unanimously laughed at. I argued that despite the fact that mathematically each roll is independent of all rolls before and after it, in reality they nevertheless should still be connected to each other somehow (something like the entanglement in quantum mechanics), at least previous rolls with the future ones...

Yeah, I know, this is what casinos owners would want us to universally believe!

It's still a laughable (although common) belief.  Every roll is completely independent.  To assume that previous rolls affect future rolls...in any way...is incorrect.

Ok, I understand. Nevertheless, think about it a little deeper. You calculate the odds for a series of bets, which you say are independent of each other. But how can you calculate it if the outcomes are truly independent in the first place? If you can calculate a losing streak probability, then, properly speaking, the rolls are not that independent of each other in a sense. See my point?

[Bardman]

This, exactly.   Because each roll is an independent event you never know if you're in the middle of a 100 loss streak.  However, some part of me thinks it also has to be true that rolling consecutive losses into infinity is also highly improbably and that longer and longer streaks of losses have to be more and more improbable.  So I always have a hard time rectifiying these two facts: the independence of each roll and the increasing unlikelyhood of increasingly large streaks.

I had been trying to say almost the same nearly a year ago (most likely even in this very thread), but I was unanimously laughed at. I argued that despite the fact that mathematically each roll is independent of all rolls before and after it, in reality they nevertheless should still be connected to each other somehow (something like the entanglement in quantum mechanics), at least previous rolls with the future ones...

Yeah, I know, this is what casinos owners would want us to universally believe!

It's still a laughable (although common) belief.  Every roll is completely independent.  To assume that previous rolls affect future rolls...in any way...is incorrect.

Ok, I understand. Nevertheless, think about it a little deeper. You calculate the odds for a series of bets, which you say are independent of each other. But how can you calculate it if the outcomes are truly independent in the first place? If you can calculate a losing streak probability, then, properly speaking, the rolls are not that independent of each other in a sense. See my point?

Yes you can calculate the probability of that but here is one example, Lets say you bet on red and black, you get 30 REDS in a row (1 in 1 billion chance at 50%)
Now its true we calculated that BUT the chances of getting 30 REDS in a row are the same as getting 29 REDS in a row and 1 Black or 10 REDS 10 BLACKS 10 REDS or you name it, it does not matter.

[dooglus]

You calculate the odds for a series of bets, which you say are independent of each other. But how can you calculate it if the outcomes are truly independent in the first place? If you can calculate a losing streak probability, then, properly speaking, the rolls are not that independent of each other in a sense. See my point?

No, I don't.

Pick a playing card.

1/4 chance it's a heart.
1/13 chance it's a queen.

Those two are independent.

*Because* they are independent you can multiply the two chances to get the chance of both happening:

(1/4)*(1/13) = 1/52 it's the queen of hearts.

This doesn't work if the events aren't independent:

1/4 chance it's a heart.
1/2 chance it's red
so (1/4)*(1/2) = 1/8 chance it's a red heart?
No. Because 'it's a heart' and 'it's red' aren't independent.

[deisik]

You calculate the odds for a series of bets, which you say are independent of each other. But how can you calculate it if the outcomes are truly independent in the first place? If you can calculate a losing streak probability, then, properly speaking, the rolls are not that independent of each other in a sense. See my point?

No, I don't.

Pick a playing card.

1/4 chance it's a heart.
1/13 chance it's a queen.

Those two are independent.

*Because* they are independent you can multiply the two chances to get the chance of both happening:

It's a pity that you can't think outside the box. You multiply the two chances, so they are already related, being of the same kind, right? Therefore they are not truly independent of each other since each of them is still dependent on something else common for them. You can't multiply a number with something which is not a number. This is likely not a very good example, but still...

As to me, your example is not relevant to successive rolls

[dooglus]

You calculate the odds for a series of bets, which you say are independent of each other. But how can you calculate it if the outcomes are truly independent in the first place? If you can calculate a losing streak probability, then, properly speaking, the rolls are not that independent of each other in a sense. See my point?

No, I don't.

Pick a playing card.

1/4 chance it's a heart.
1/13 chance it's a queen.

Those two are independent.

*Because* they are independent you can multiply the two chances to get the chance of both happening:

It's a pity that you can't think outside the box. You multiply the two chances, so they are already related, being of the same kind, right? Therefore they are not truly independent of each other since each of them is still dependent on something else common for them. You can't multiply a number with something which is not a number. This is likely not a very good example, but still...

As to me, your example is not relevant to successive rolls

Pick one card from each of two decks then. It doesn't change anything. What's the chance you get a queen from the first and a heart from the 2nd?

Now, of course, the "heart, then red" events *are* independent, and so 1/8 is the chance of the first card being a heart and the 2nd being red.

Why do you think that multiplying the probabilities of two independent events causes the events to stop being independent?

[deisik]

It's a pity that you can't think outside the box. You multiply the two chances, so they are already related, being of the same kind, right? Therefore they are not truly independent of each other since each of them is still dependent on something else common for them. You can't multiply a number with something which is not a number. This is likely not a very good example, but still...

As to me, your example is not relevant to successive rolls

Pick one card from each of two decks then. It doesn't change anything. What's the chance you get a queen from the first and a heart from the 2nd?

Now, of course, the "heart, then red" events *are* independent, and so 1/8 is the chance of the first card being a heart and the 2nd being red.

Why do you think that multiplying the probabilities of two independent events causes the events to stop being independent?

I don't argue with your examples, I know what you say perfectly well myself. But you give examples which are not the same as successive rolls. If you pick a queen of hearts from a deck, will the probability of picking another queen of hearts from the same deck (provided there is only one queen of hearts in the deck) be of the same kind as the probability of picking next a king of spades?