Ultimate bankroll / bet size relationship

[Robert Fischer]

Originally Posted by Magister Ludi

You might consider using an exponentially weighted moving average. If your data has a limited "shelf life", it will keep it from getting stale by weighting recent observations more heavily than older ones.

this sounds useful

[SchagFactorToWin]

Originally Posted by DeltaLover

Concrete example:

I am using the followin strategy which presents a 1.03 ROI

************************************************** ******************************
back testing: Strategy1
final pnl: 5320.0
all races: 7561 found a bet in : 1688 races all winners: 261 win: 15.46% numberof horses bet: 1688
roi: 1.03151658768
************************************************** ******************************

I break the 1688 races to sessions of 10 and find the following:

************************************************** ******************************
CREATING SESSIONS OF 10 USINING AS UNIT BET 100.0
back testing: Strategy1
number of sessions: 168
mean PNL for session: 36.4285714286
stdev session: 795.008594624


This means that for each session of 10 races I expect to win $36 while my sigma will be $795

So, using formulas I get:

N= MLS = (3 * STD / 2 * EP)^2 = (3 * 795 / 2 * 36) ^ 2 = 961

So using (1):

TotalWonOrLost = EP * N - 3 * STD * SQRT(N) (1)

MinStageOfbankroll = 36 * 961 - 3 * 795 * SQRT(961) = 34596 - 73935 = -39339

So for this strategy which has 1.3 ROI and 795 stdev I need a bankroll of at least 39339 assuming $100 unit bets to assure that I will not go broke...

Thank you! I have been working on a bankroll measurement estimate by using brute force of randomization of past results, requiring a 5000 x 1000 row Excel worksheet. This makes things MUCH simpler.

[Robert Fischer]

"MLS"

Originally Posted by DeltaLover

...
So for this strategy which has 1.3 ROI and 795 stdev I need a bankroll of at least 39339 assuming $100 unit bets to assure that I will not go broke...

Kelly

Originally Posted by Magister Ludi

bankroll = BR = 39339
edge = 3.2%
odds = 5.47
edge/odds = f* = .00585
optimal bet = BRf* = .00585 * 39339 = $230
EV = eBRf* = $230 * 3.2% = $7.36

RF
bankroll size = $39,339
the max consecutive losses = 55 (10,000)
acceptable loss = 20% of bankroll for worst case (consecutive)losing streak
=($39,339*0.2)/55 = $143 bet size



Still getting comfortable with DeltaLover's bankroll formula.

Satisfied with what my more simplistic approach produced for this given probability range. Also learned more about where my approach stands in terms of risk within this type of scenario. $143 is slightly riskier than the $100 unit bets of DeltaLover's MLS bankroll example, and is more conservative than Magister Ludi's $230 optimal bet using Full Kelly.

Important to note that this was using a hit rate of 15.46%. I'll have to look at other odds ranges as well to see if my approach remains as useful.

[Capper Al]

Children in a candy shop. 99% of you lose money. A money management system isn't going to make you winners. I would say until you get into the top1!% and are winning keep it simple,keep it straight, and keep it flat. Flat betting might even help you understand your outcomes better paving the way into becoming a winner. I do appreciate the excitement of becoming a winner and the math models, but stick to first things first-- winning.

[DeltaLover]

Originally Posted by Capper Al

A money management system isn't going to make you winners.

This is among the sharpest quotes for year 2012, at least here at PA space... You have to be a genious to conceive it.. We learned something today.... Thx...

[raybo]

Originally Posted by Capper Al

Children in a candy shop. 99% of you lose money. A money management system isn't going to make you winners. I would say until you get into the top1!% and are winning keep it simple,keep it straight, and keep it flat. Flat betting might even help you understand your outcomes better paving the way into becoming a winner. I do appreciate the excitement of becoming a winner and the math models, but stick to first things first-- winning.

While I agree with you, this thread is about bet sizing, and Kelly. It is assumed you already have an edge, I believe. And if you already have an edge, proper bet sizing can, indeed, move you from negative to positive. Bad betting is the doom of many good handicappers.

[lansdale]

Hi RF,

I admire many of your posts, and don't want to seem to be raining on anyone's theoretical parade, but average edge and flat-betting have nothing to do with Kelly. I went over this in a long exchange with blackjack guru Don Schlesinger who certainly understands the math of Kelly and gambling as well as anyone on the planet. In order to be making Kelly bets, you would have to be betting on the specific edge of a given horse in every race. I'm sure you've probably looked at Benter's well-known article, and this was exactly how he used Kelly - thus the exponential growth. The same is true of the other notables cited by ML - including Ed Thorp, who has made billions using it. Who is among Thorp's consultants? Don Schlesinger.

Cheers,

lansdale

Originally Posted by Robert Fischer

"MLS"


Kelly


RF
bankroll size = $39,339
the max consecutive losses = 55 (10,000)
acceptable loss = 20% of bankroll for worst case (consecutive)losing streak
=($39,339*0.2)/55 = $143 bet size



Still getting comfortable with DeltaLover's bankroll formula.

Satisfied with what my more simplistic approach produced for this given probability range. Also learned more about where my approach stands in terms of risk within this type of scenario. $143 is slightly riskier than the $100 unit bets of DeltaLover's MLS bankroll example, and is more conservative than Magister Ludi's $230 optimal bet using Full Kelly.

Important to note that this was using a hit rate of 15.46%. I'll have to look at other odds ranges as well to see if my approach remains as useful.

[Dave Schwartz]

I admire many of your posts, and don't want to seem to be raining on anyone's theoretical parade, but average edge and flat-betting have nothing to do with Kelly.

Now here is a position you and I can certainly agree upon.

In addition, one could easily argue that unless the true hit rate and payback are known at the time of the wager, Kelly is not appropriate.

Neither of these items is known to any parimutuel player, and often only the payoff (or odds) are known to the non-parimutuel gambler (i.e. sports bettor, etc.).

The best we can hope for is to be able to make a good estimate. Beyond that, it is all theoretical.

One's success (or failure) will be in direct proportion to the degree to which one's theory mimics reality.


Regards,
Dave Schwartz

[Robert Fischer]

Originally Posted by lansdale

Hi RF,

I admire many of your posts, and don't want to seem to be raining on anyone's theoretical parade, but average edge and flat-betting have nothing to do with Kelly. I went over this in a long exchange with blackjack guru Don Schlesinger who certainly understands the math of Kelly and gambling as well as anyone on the planet. In order to be making Kelly bets, you would have to be betting on the specific edge of a given horse in every race. I'm sure you've probably looked at Benter's well-known article, and this was exactly how he used Kelly - thus the exponential growth. The same is true of the other notables cited by ML - including Ed Thorp, who has made billions using it. Who is among Thorp's consultants? Don Schlesinger.

Cheers,

lansdale

I look for certain things in a race that give me an edge. Next I choose the best pool to attack. Now within that target-pool, my horse is going to have a specific edge. Generally for me, this specific edge, and target-pool is going to be a scenario that is similar to many others that I have played and will continue to find. I call these "wager types". These are, in effect, templates for conservative edge estimates. It's simply a convenience and a guide. Adjustments can be made. In most cases, current bankroll is the only necessary input (dynamic bet size).

This thread has gone a number of different directions. Different bet-sizing methods... bankroll sizing estimates... and we've been weighing the pros and cons of using Kelly, given the inconsistent nature of any specific edge estimate in horse racing - even when a long-term edge exists.

Personally, I am still considering fractional Kelly as a better way than my bet sizing method.

[overthehill]

this is a facinating thread and i have spent several hours grappling with this issue.

to me there there are two issues that need to be considered when factoring the kelly strategy.

1. we really dont know the actual final odds or edge, that is estimated

2. irrespective of 1. we have different threshold of how much pain from a losing streak we can tolerate without our affecting our handicapping.

I think that really is the key question how much of your bankroll are you will to lose in one day or week and how many bets might you make in a day or week. that is much more relevent than the kelly IMHO

3. In my case i have observed that irrespective of i believe the liklihood of a horse winning a particular race. generally the the likelihood of the horse winning declines as their odds increase. thus a horse who is 12-1 ML but goes off at 9/2 is usually much a more likely winner than if the same horse goes off at 40-1. but the kelly criteria would have you betting more on such a horse.

4. I do think that if one focuses on the major tracks and on horses that are not one of the two morning line favorites there is less likelihood of a major odds shift in the last minute of betting. OTOH i have seen horses at major tracks that are one of the two favorites go from 5/2 to even money in that last minute of play which makes me very skeptical of using the kelly in such situations.

[Robert Goren]

I just want to make one think that is often overlooked when it comes to John Kelly, jr. His orginal paper had nothing to do with gambling. It was Ed Thrope and Claude Shannon who decided it had money management uses for gambling and investments. Those two were crazy smart. Kelly is very dangerous thing in the hands of the average bettor/investor who for the most part doesn't have clue how or when to use it.

[overthehill]

This is an awesome thread. My own thoughts as a non profesiona experienced horse player is that kelly is not relevent to horse players because we just dont know the edge, we just guess at it. I am ready to make certain assumptions about my own wagering at this point in time which is that on races where the odds are my horse on top under 6-1 I will cash about 20% of the time. and If i am not forced to reduced my bet size I will be profitable. the questions is how should i manage my money?

It would be appear that all things being equal the odds of losing 20 bets in a row is less that 1% but the odds of losing 10 bets in a row is about 8%. So i i were to approach this as a pro, it is very likely that i will lose 10 bets in a rows several times a year. In order no to become discourage when this happens I dont think I would be comfortable seenig more that 20% of my bankroll evaporate when this happens so that would cap my bets at 2%. Irrespective of what i think my edge is going in.

[pondman]

Originally Posted by Capper Al

Children in a candy shop. 99% of you lose money. A money management system isn't going to make you winners.

++++

There's a reason to avoid casino tables, and going straight to the race book. It doesn't take higher math to spot a 40%er. Just the will power to stay away from the game until the Net expectation is great enough.

It's an interesting arguement regarding Warren Buffet. Much of his success come through contacts, and knowing how much will be appropriated to his railroad by both houses before he buys a railroad. He has almost perfect knowledge, which you don't find in the majority of races. The probability of singling a horse rarely gets above 40% (at least that about my best confidence level.) And to get a Net expectation high enough there needs to be a high level of doubt spread among the crowd. Something must be noticeably negative in it's PP.

[Gallop58]

http://www.blackjackforumonline.com/content/horseracingbettingcheapclaimers.htm



"Horse Race Betting and Unknown Expectation

There are two types of games in which gamblers can potentially obtain an edge. First, we have situations like blackjack and video poker in which an edge can be obtained by using appropriate betting and playing strategies where the size of that edge can be calculated precisely.

You may have a very complicated way of playing blackjack, but we can, in theory, use a computer to evaluate your expectation. This is in direct contrast to gambling tournaments, playing poker, and betting on either sports or horses.

In gambling tournaments and poker, your edge is determined not only by the parameters of the game or tournament but also by the quality of your opposition. In betting horses, the key parameter is the savvy of the betting public. In sports betting, we have a combination of the intelligence of the bookmaker and that of the general public.

Betting serious money in situations where not only the size of your advantage is unknown, but also it is unclear whether or not you have an advantage, can be very disturbing to a blackjack player accustomed to knowing his expectation."

[badcompany]

I equate Money Management and Position Sizing to dieting. It's not particularly difficult to come up with a program which will make you lose weight. Sticking to it on a day in day out basis is what sinks almost all failed dieters.

A simple fixed percentage of bankroll system based on how much you're willing to risk per race/day/week is fine. Since people tend to overestimate their ability, err on the small side.