Very difficult question. On busy weekend it's impossible to resize the bankroll after every game, so I resize my bankroll only after all games has been in that round.
Much has been written on these boards and on the Internet about money management and the Kelly Criterion. In theory it is very simple and precise, but in actual practice it requires a little remodeling and approximating. Money management is the answer to “how much should I bet so my bankroll grows the fastest and most safely”. Theory says our bankroll grows the fastest and safest when we bet the percentage advantage we have divided by the odds to the dollar payoff. In 11 to 10 sports waging where the payoff is .909 cents on the dollar and our goal is 57.5% winners (9.77% edge), theory says we should bet 9.77%/.909 = 10.75% of our bankroll on each bet. In reality there are several reason to reduce this percentage. First is the occurrence of betting multiple bets at one time. An example might be a Saturday of College Basketball bets that many times will exceed more than ten bets at one time. Not only would this be more than 100% of our bankroll, the money management theory itself is based on betting only one game at a time - so some remodeling is required.
Also, most handicappers tend to over estimate their winning pecentage. A winning percentage of 55.0% is about midway between our goal of 57.5% winners and 52.38% breakeven. At that reduced level we have 5.00%/ .909 = 5.5 % of the bankroll bet on each game. An additional reduction to 5.0% completes the remodeling and adds to the easiness of use. The money management plan then reduces down to a simple 5% of the bankroll bet on each game up to a maximum 35% of the total bankroll for multiple bets. Should you have more than seven bets at any one time, simply take 35 % of your bankroll and divided it among the total multiple bets you have.
Also, most handicappers tend to over estimate their winning pecentage. A winning percentage of 55.0% is about midway between our goal of 57.5% winners and 52.38% breakeven. At that reduced level we have 5.00%/ .909 = 5.5 % of the bankroll bet on each game. An additional reduction to 5.0% completes the remodeling and adds to the easiness of use. The money management plan then reduces down to a simple 5% of the bankroll bet on each game up to a maximum 35% of the total bankroll for multiple bets. Should you have more than seven bets at any one time, simply take 35 % of your bankroll and divided it among the total multiple bets you have.
<BLOCKQUOTE class="ip-ubbcode-quote"><font size="-1">quote:</font><HR> The money management plan then reduces down to a simple 5% of the bankroll bet on each game up to a maximum 35% of the total bankroll for multiple bets. <HR></BLOCKQUOTE>
Why maximum 35% ?
<BLOCKQUOTE class="ip-ubbcode-quote"><font size="-1">quote:</font><HR> Should you have more than seven bets at any one time, simply take 35 % of your bankroll and divided it among the total multiple bets you have. <HR></BLOCKQUOTE>
Should you involve 100% of your bankroll, then you have no choice but to do that, otherwise I don't see any reason to underbet.
Why maximum 35% ?
<BLOCKQUOTE class="ip-ubbcode-quote"><font size="-1">quote:</font><HR> Should you have more than seven bets at any one time, simply take 35 % of your bankroll and divided it among the total multiple bets you have. <HR></BLOCKQUOTE>
Should you involve 100% of your bankroll, then you have no choice but to do that, otherwise I don't see any reason to underbet.
That's a good question "Why limit your total bankroll action to a maximum of 35 %?".
The Kelly Criterion in its pure form requires that you wager one proposition at a time, and then you resize your next bet dependent on your current bankroll. The key result from doing this is that the order of wins and losses then make no difference on the final end bankroll.
When we start making multiple bets we sacrifice this control of the bankroll. An example might be 5-winners bet at the same time that do not increase our bankroll the same as if we had bet 5-winners one at a time with resizing up each time - we win less. The same problem arises from 5-losser - we lose too much. In the long run all should average out to approximate the "the one bet at a time" control, so this is really not the underlying problem of multiple betting of the Kelly Criterion.
The real problem is the total percent of our bankroll we put at risk at any one time. Risking 100 % of your bankroll is not compatible with being a serious professional gambler. A limit must be set. In the remolding of the Kelly Criterion that I presented above, I chose a reduction of the Golden Ratio (the Fibonnaci number 61.8%) by 50 %-11.8 % = 38.2 % and rounded to 35 %. You my wish to use limits of 12 multiple bets and 60 % maximum of the BR. But never go higher than that (or 100% !!).
If you have that winning edge and use the Kelly Criteron (pure or modified) eventaually you will reach a bet size that matches the "Comfort Zone" of either yourself or your outlets. So, don't throw caution to the wind and bet "outside the limits of your bankroll".. take the slower and more professional path.
The Kelly Criterion in its pure form requires that you wager one proposition at a time, and then you resize your next bet dependent on your current bankroll. The key result from doing this is that the order of wins and losses then make no difference on the final end bankroll.
When we start making multiple bets we sacrifice this control of the bankroll. An example might be 5-winners bet at the same time that do not increase our bankroll the same as if we had bet 5-winners one at a time with resizing up each time - we win less. The same problem arises from 5-losser - we lose too much. In the long run all should average out to approximate the "the one bet at a time" control, so this is really not the underlying problem of multiple betting of the Kelly Criterion.
The real problem is the total percent of our bankroll we put at risk at any one time. Risking 100 % of your bankroll is not compatible with being a serious professional gambler. A limit must be set. In the remolding of the Kelly Criterion that I presented above, I chose a reduction of the Golden Ratio (the Fibonnaci number 61.8%) by 50 %-11.8 % = 38.2 % and rounded to 35 %. You my wish to use limits of 12 multiple bets and 60 % maximum of the BR. But never go higher than that (or 100% !!).
If you have that winning edge and use the Kelly Criteron (pure or modified) eventaually you will reach a bet size that matches the "Comfort Zone" of either yourself or your outlets. So, don't throw caution to the wind and bet "outside the limits of your bankroll".. take the slower and more professional path.
The Kelly Criterion in its pure form requires that you wager one proposition at a time, and then you resize your next bet dependent on your current bankroll.
What about resizing taking into account the probability of success of the bet placed ? Then, When we start making multiple bets we sacrifice this control of the bankroll. we won't sacrifice it.
The real problem is the total percent of our bankroll we put at risk at any one time. Risking 100 % of your bankroll is not compatible with being a serious professional gambler.
The key here is the time frame. E.g. if you risk 100% of your bankroll over 2 weeks then what's wrong with risking it over 1 day ?
What about resizing taking into account the probability of success of the bet placed ? Then, When we start making multiple bets we sacrifice this control of the bankroll. we won't sacrifice it.
The real problem is the total percent of our bankroll we put at risk at any one time. Risking 100 % of your bankroll is not compatible with being a serious professional gambler.
The key here is the time frame. E.g. if you risk 100% of your bankroll over 2 weeks then what's wrong with risking it over 1 day ?
There's another way to scale bets down, other than using a cap with Kelly.
Assume you have 2 plays at 10%. When sizing, assume you lose them both. The first would be 10%, and the second would be 10% of your remaining 90% bank, or 9%. Ergo, on the two plays, you would risk 9.5% each.
Another example... You have 10 plays at 10%. If you lost 10% of your bankroll 10 consecutive times, you'd have have 35% left. Ergo, you split 65% up between the 10 bets, and risk exactly 6.5% on each play.
The whole theory of Kelly is no bad run will wipe you out. If you bet your whole bankroll on 10 plays and lost all of them, you're done. It won't happen very often - if you are hitting 57% winners at -110 (which roughly corresponds to a 10% optimal bet), it will happen 2 times in 10,000 times. If it happens once in your life, using proper kelly betting (which reduces bet size for multiple bets) keeps you in the game.
Assume you have 2 plays at 10%. When sizing, assume you lose them both. The first would be 10%, and the second would be 10% of your remaining 90% bank, or 9%. Ergo, on the two plays, you would risk 9.5% each.
Another example... You have 10 plays at 10%. If you lost 10% of your bankroll 10 consecutive times, you'd have have 35% left. Ergo, you split 65% up between the 10 bets, and risk exactly 6.5% on each play.
The whole theory of Kelly is no bad run will wipe you out. If you bet your whole bankroll on 10 plays and lost all of them, you're done. It won't happen very often - if you are hitting 57% winners at -110 (which roughly corresponds to a 10% optimal bet), it will happen 2 times in 10,000 times. If it happens once in your life, using proper kelly betting (which reduces bet size for multiple bets) keeps you in the game.
I've used these theorems for many years--: http://www.horsestreet.com/products/index.html#Manuscripts
you should get both...they're being put into software form too, as we speak....
you should get both...they're being put into software form too, as we speak....
Interesting calculations. I have seen other Kelly variants previously, but so far I have decided to stick with the original formula.
Flat bettor vs Kelly bettor favored Flat bettor in these examples, because probability stayed same all the time. If Kelly bettor should invest 10% of bankroll to odd 3.0 (Traditional 2/1) as in this examle, he has estimated that his chances to win bet is 38.62907815% all the time. Usually probabilites aren't same everytime.
Most of the variants also give you more profits when you are winning, but also more losses when you losing compared to original Kelly.
charleslanger, you said you have used these theories for years, so you are right man to tell.
1. I guess, the bet size with Schwartzs formulas depends on your own estimations, yes or no?
2. If yes, What will happen if your estimations are wrong or you have very unlucky season. Do you lose less with this vs Kelly?
1. I guess, the bet size with Schwartzs formulas depends on your own estimations, yes or no?
Yes. No. <g>. You can use his numbers and worksheets in robot-like fashion, and he also provides you with enough fodder should you wish to tweak things-- like risk ratios when investing in securities, for instance.
Now, if by estimations you are referring to your advantage(avg win %, avg payoff, etc.) being off-- then that would be a sign of either not enough longetivity with the particular betting mode, or not keeping enough detailed records.... For you would see that your season averages do not vary that much from year to year-- you would see that fluctuations(the expected losing / winning streaks), though sometimes wild, tend to average out / balance out by season's end. If by chance your numbers can't be used reliably, because say-- the different sports / games you bet have varying advantages-- you can always keep different bankrolls... it doesn't really take extra money, as they can be 'shy'.
What really helps here, imho-- is to keep copious records... and there's no such thing as writing down too much: such as a column stating why each bet is being made... tracking these 'reasons' is crucial....
Something a bit unrelated put forth by a long-ago author: when he had a big win he always looked for something he could've done differently to make even more money-- and conversely with a loss: he would try to find something right he did re the selection / bet-- in spite of the loss.
2. If yes, What will happen if your estimations are wrong or you have very unlucky season. Do you lose less with this vs Kelly?
Most definitely yes. This is addressed in many ways. He gives you a risk variance / bankroll ruin chart with the % occurrence of each size of losing streak for different bet-win percentages.
Most importantly, he tweaked the Kelly formula and added concepts used in securities investing, to come up with a very ingenious way to manage & grow your bankroll-- and he shows you with many bankroll examples how Kelly often hastens the road to ruin. Kelly's like Communism: works great on paper, but not in practice....If your win % & avg. payoff were always the same or better day in and day out, week in & out-- a practical impossibility-- then Kelly is the only answer. But he dissects Kelly and shows you how the largest wagers are always on the losing bets-- unavoidable, as one can't know when the loss that ends a win streak / or dip in win % is coming. He has come up with a way to totally reverse this phenomenon, and actually beat Kelly most of the time-- often even when incurring a slight negative expectation(flat bet loss), while to boot risking much less money!!!
The only time Kelly beats his system(and only by a little bit at that) is when one's advantage stays the same or improves short-term-- and even then he demonstrates how Kelly risked / invested several times more money just to make a little more profit. And when the expected downturn comes, if it's fairly severe-- and this may be the gist of what you're alluding to-- Kelly may deplete the entire bankroll, while HMI(his system) shows a profit-- even sometimes during a negative expectancy...
For me, this has been the single most crucial product i have ever obtained... sure, the books & methods on coming up with winning selections are very important, however: without the proper bet strategy one can lose money in spite of having more winners than losers-- we've all been there. Conversely, one can be a hack with just a slight positive win %, who can make a living off gambling, by betting correctly. 'Cause flat betting just won't cut it as a sole income source....
I make no commission / have no financial interest or connection with the author-- other than total agreement and appreciation for his theorems-- like others such as Huey Mahl, John Patrick, the GameMaster, the Wizard of Odds, Robert Allen, etc.
Peace.
Yes. No. <g>. You can use his numbers and worksheets in robot-like fashion, and he also provides you with enough fodder should you wish to tweak things-- like risk ratios when investing in securities, for instance.
Now, if by estimations you are referring to your advantage(avg win %, avg payoff, etc.) being off-- then that would be a sign of either not enough longetivity with the particular betting mode, or not keeping enough detailed records.... For you would see that your season averages do not vary that much from year to year-- you would see that fluctuations(the expected losing / winning streaks), though sometimes wild, tend to average out / balance out by season's end. If by chance your numbers can't be used reliably, because say-- the different sports / games you bet have varying advantages-- you can always keep different bankrolls... it doesn't really take extra money, as they can be 'shy'.
What really helps here, imho-- is to keep copious records... and there's no such thing as writing down too much: such as a column stating why each bet is being made... tracking these 'reasons' is crucial....
Something a bit unrelated put forth by a long-ago author: when he had a big win he always looked for something he could've done differently to make even more money-- and conversely with a loss: he would try to find something right he did re the selection / bet-- in spite of the loss.
2. If yes, What will happen if your estimations are wrong or you have very unlucky season. Do you lose less with this vs Kelly?
Most definitely yes. This is addressed in many ways. He gives you a risk variance / bankroll ruin chart with the % occurrence of each size of losing streak for different bet-win percentages.
Most importantly, he tweaked the Kelly formula and added concepts used in securities investing, to come up with a very ingenious way to manage & grow your bankroll-- and he shows you with many bankroll examples how Kelly often hastens the road to ruin. Kelly's like Communism: works great on paper, but not in practice....If your win % & avg. payoff were always the same or better day in and day out, week in & out-- a practical impossibility-- then Kelly is the only answer. But he dissects Kelly and shows you how the largest wagers are always on the losing bets-- unavoidable, as one can't know when the loss that ends a win streak / or dip in win % is coming. He has come up with a way to totally reverse this phenomenon, and actually beat Kelly most of the time-- often even when incurring a slight negative expectation(flat bet loss), while to boot risking much less money!!!
The only time Kelly beats his system(and only by a little bit at that) is when one's advantage stays the same or improves short-term-- and even then he demonstrates how Kelly risked / invested several times more money just to make a little more profit. And when the expected downturn comes, if it's fairly severe-- and this may be the gist of what you're alluding to-- Kelly may deplete the entire bankroll, while HMI(his system) shows a profit-- even sometimes during a negative expectancy...
For me, this has been the single most crucial product i have ever obtained... sure, the books & methods on coming up with winning selections are very important, however: without the proper bet strategy one can lose money in spite of having more winners than losers-- we've all been there. Conversely, one can be a hack with just a slight positive win %, who can make a living off gambling, by betting correctly. 'Cause flat betting just won't cut it as a sole income source....
I make no commission / have no financial interest or connection with the author-- other than total agreement and appreciation for his theorems-- like others such as Huey Mahl, John Patrick, the GameMaster, the Wizard of Odds, Robert Allen, etc.
Peace.
