I said that I’ve seen exact formulas only for even-money scenarios. The formula you see on Wikipedia is an estimate, not an exact calculation. Like all estimates, it will work very well for certain scenarios and be useless for others. Incidentally, you seem to think that one short Wikipedia article is the full bible on RoR. It isn’tQuote:Mental[]In fact, the wiki post gives a formula for a random walk where "at every iterative step, is moved by a normal distribution having mean μ and standard deviation σ and failure occurs if it reaches 0 or a negative value." So it works for more than just coin-flip PDFs.

Also, your conjecture cannot be applicable without specifying how many bets are intended to be made in session (barring busting out). The OP does not specify a session length and there is no canonical session length. What exactly is your conjecture? What do you mean by "works very well for me"? We cannot prove or disprove it without knowing what it is in detail.

link to original post

The description of the simple conjecture and the game I usually apply it to are listed in the last few pages of this threadQuote:Mental[

Also, your conjecture cannot be applicable without specifying how many bets are intended to be made in session (barring busting out). The OP does not specify a session length and there is no canonical session length. What exactly is your conjecture? What do you mean by "works very well for me"? We cannot prove or disprove it without knowing what it is in detail.

link to original post

Quote:Ace2I said that I’ve seen exact formulas only for even-money scenarios. The formula you see on Wikipedia is an estimate, not an exact calculation. Like all estimates, it will work very well for certain scenarios and be useless for others. Incidentally, you seem to think that one short Wikipedia article is the full bible on RoR. It isn’tQuote:Mental[]In fact, the wiki post gives a formula for a random walk where "at every iterative step, is moved by a normal distribution having mean μ and standard deviation σ and failure occurs if it reaches 0 or a negative value." So it works for more than just coin-flip PDFs.

Also, your conjecture cannot be applicable without specifying how many bets are intended to be made in session (barring busting out). The OP does not specify a session length and there is no canonical session length. What exactly is your conjecture? What do you mean by "works very well for me"? We cannot prove or disprove it without knowing what it is in detail.

link to original post

link to original post

Unless I’m missing something (which is very possible). there’s nothing about even money bets that makes an RoR calculation much more difficult than longer or shorter odds.

The concept gets applied in stock market investing through optimal portfolio growth theory. Kelly’s original paper, if my memory still serves, was a problem of information theory that is easiest to apply to a horse race (and which horses you should bet on when you have imperfect information but better than random information).

Yes, but that ideal 'betting system' is to raise you bet and hold it there. Flat betting at a higher level gets you the biggest increase in throughput with the smallest increase in variance and RoR. Any betting system which has this same average bet, but changes the bet up and down, is inferior in terms of risk. It will also be slower in many cases.Quote:Talldude90In general, wouldn't betting systems be a defined boon in a +EV situation as long as you are not raising your RoR significantly? Wouldn't you be getting a lot more coin-in against the +EV (as long as the system doesn't lower your EV), so your end profit should be bigger for a set amount of time gambling (say 4 hour session)?

link to original post

Quote:MentalYes, but that ideal 'betting system' is to raise you bet and hold it there. Flat betting at a higher level gets you the biggest increase in throughput with the smallest increase in variance and RoR. Any betting system which has this same average bet, but changes the bet up and down, is inferior in terms of risk. It will also be slower in many cases.Quote:Talldude90In general, wouldn't betting systems be a defined boon in a +EV situation as long as you are not raising your RoR significantly? Wouldn't you be getting a lot more coin-in against the +EV (as long as the system doesn't lower your EV), so your end profit should be bigger for a set amount of time gambling (say 4 hour session)?

link to original post

link to original post

Isn’t the “ideal” betting system to bet the Kelly fraction of your bankroll each bet, which would vary as your bankroll fluctuates.

How practical would that be to do on the fly while playing?Quote:unJonQuote:MentalYes, but that ideal 'betting system' is to raise you bet and hold it there. Flat betting at a higher level gets you the biggest increase in throughput with the smallest increase in variance and RoR. Any betting system which has this same average bet, but changes the bet up and down, is inferior in terms of risk. It will also be slower in many cases.Quote:Talldude90In general, wouldn't betting systems be a defined boon in a +EV situation as long as you are not raising your RoR significantly? Wouldn't you be getting a lot more coin-in against the +EV (as long as the system doesn't lower your EV), so your end profit should be bigger for a set amount of time gambling (say 4 hour session)?

link to original post

link to original post

Isn’t the “ideal” betting system to bet the Kelly fraction of your bankroll each bet, which would vary as your bankroll fluctuates.

link to original post

Quote:AxelWolfHow practical would that be to do on the fly while playing?Quote:unJonQuote:MentalQuote:Talldude90

link to original post

link to original post

Isn’t the “ideal” betting system to bet the Kelly fraction of your bankroll each bet, which would vary as your bankroll fluctuates.

link to original post

link to original post

What I've always been told about this was that it's not really wise to adjust your Kelly bet too often (on every single hand for example). I imagine you would base your flat bet on the formula and then play a pre-determined number of hands (a session?) and then recalculate from there.

But I don't know if that is actually something that is mathematically beneficial or if it's just recommended due to the sheer impracticability of recalculating and changing the bet that often.

Quote:DJGenius

What I've always been told about this was that it's not really wise to adjust your Kelly bet too often (on every single hand for example). I imagine you would base your flat bet on the formula and then play a pre-determined number of hands (a session?) and then recalculate from there.

But I don't know if that is actually something that is mathematically beneficial or if it's just recommended due to the sheer impracticability of recalculating and changing the bet that often.

link to original post

If I recall correctly, for a low variance game like Blackjack, Kelly says to wager a percentage of your bankroll equal to your percentage edge. But of course that edge fluctuates and you spread your wagers a lot. You are not going to sit placing bets of $101, $102, $103 $:o)

Just step up or down when your bankroll has changed significantly enough. E.g increased by 25%, maybe what was a $100 wager might be a $125 one.

Even with exact kelly betting, your bankroll chart would be all over the place and would not look very optimal.

Quote:AxelWolfHow practical would that be to do on the fly while playing?Quote:unJonQuote:MentalQuote:Talldude90

link to original post

link to original post

Isn’t the “ideal” betting system to bet the Kelly fraction of your bankroll each bet, which would vary as your bankroll fluctuates.

link to original post

link to original post

Not practical at all. I thought I was responding to a post about what was mathematically ideal in the abstract. But in the real world there are a bunch of practical considerations.