Hypothetical Martingale

This topic is mostly hypothetical. I know you probably can't gain an edge using martingale (doubling your bets after each loss).

Obviously, if a player had an infinite bankroll with infinite table limits, martingale would work.

So, is there such thing as a high enough table limit that would allow a martingale system to win in the long-term? For example, say the table limits for even chance bets are between $1 and $1,000,000. How about $1 and $1,000,000,000? How about $1 and $1,000,000,000,000? You see where I am going with this.

For example, would a table limit between $100 and $99999999999999999999999999999999999999999999999999999999999999999999999999999999999 eventually crash and burn??? (would using martingale with these ridiculous betting limits still lose after many, many results?)

Quote: quickpick

Obviously, if a player had an infinite bankroll with infinite table limits, martingale would work.

So, is there such thing as a high enough table limit that would allow a martingale system to win in the long-term? )

I'll sort of disagree with your first point. If you have an infinite bankroll, and you win a bet, has your bankroll increased? Obviously not, as it is infinite before you make the bet.

The answer to the second question is no as well. If you are playing a negative expectation game, the sum of all your negative expectaion bets can statistically never be positive. If you ask the question this way.... I have $1,000,000 and want to win $1 using a martingale, what is the chance I'd be successful at pass line craps? The answer is CLOSE to 100%. But if you win 999,997 times out of 1,000,000 but fail 3 out of 1,000,000..........

Quote: quickpick

This topic is mostly hypothetical. I know you probably can't gain an edge using martingale (doubling your bets after each loss).

Obviously, if a player had an infinite bankroll with infinite table limits, martingale would work.

So, is there such thing as a high enough table limit that would allow a martingale system to win in the long-term? For example, say the table limits for even chance bets are between $1 and $1,000,000. How about $1 and $1,000,000,000? How about $1 and $1,000,000,000,000? You see where I am going with this.

For example, would a table limit between $100 and $99999999999999999999999999999999999999999999999999999999999999999999999999999999999 eventually crash and burn??? (would using martingale with these ridiculous betting limits still lose after many, many results?)

Martingale doesn't change the edge, but it is good at changing your probability of a winning session.... At the cost of making your losing sessions more crushing.
You should probably consider what meaningful increase in your wealth you want to achieve: If you have a million dollars in your hand, would an extra hundred change your life? If not, why bother?
If you were stuck in a war zone with $990 and the cost of a flight to safety was $1,000 then martying a coin toss would be a no-brainer, giving you a 99% of success.
OnceDear's rule of thumb might interest you

putting some commas in that, with
$99,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999 which unless I miscounted is $10^83 minus a dollar [I guess you tipped someone] , yeah, you could be pretty sure you'd never lose with a goal of winning $10^2. That is, not in your lifetime, assuming God will accept all your bets [no human has as much money as that, multibillionaires perhaps worth $10^11 neighborhood]. And if someone gave you $1 for each second after the universe began, you'd have a mere $4.32 × 10^17 however ... just to give you an idea there too

Pretty sure does not mean guaranteed

Without special arrangement, casinos will only accept bets in the range of 10^5, if 'pretty sure' is good enough for you; and you have to have started at a high limit table with a minimum bet more than $100 to start with, so you can see the house has pondered about this too. At your $100 table you could lose up to where your next bet would not be accepted and then go to a high limit area I guess, and that would be good as it would allow you time to quit shaking as you pulled that money out and go to the bar and chug down 3 or 4 doubles of liquor to keep from shaking when you did pull it out. Alas, if you won you probably won't remember it. 


But as has already been mentioned, if you are even a mere multimillionaire, $100 doesn't mean squat to you, the biggest problem of all.

Suppose you walk into a casino with an infinite bankroll, what would be a proper bet according to Kelly. Say you are there for the weekend and want to make sure you don't wipe out everything the day you got there. You divide your bankroll into three. Is each bankroll now 1/3rd of infinity or do you have three infinite bankrolls? If I take my Friday bankroll, which is one-third of my unlimited bankroll and double it, do I now have 4/3rds of an infinite bankroll.
On the other hand, how much do I need to lose before I no longer have an infinite bankroll. Do you lower your bet during a long losing streak since your infinite bankroll is now somehow smaller?
Why would I gamble when by simply dividing my original bankroll in half, I can create two infinite bankrolls.

If there is any maximum bet, no matter how high, then it is possible for a losing streak to last long enough so your Martingale losses would exceed it.

Remember that "eventually" is a very, very long time. I have some posts here dealing with a D'Alembert (start with a bet of 1; increase by 1 after each loss, and decrease by 1 after each win; when the bet reaches 0, you will have made a profit) on a 50/50 game where I did some simulations; "eventually," every streak got back to zero, but in some cases, it took something like hundreds of millions of bets.