Kelly criterion for EW bets

[slapdash]

If you are making simple win/lose bets and know the actual probability that each bet will win, then the Kelly criterion gives a simple formula, in terms of the odds and probability of winning, for the optimal proportion of your bank to stake on each bet, to make your bank grow as fast as possible in the long run. In a thread in At The Races Systems, akm asked for a similar formula for each-way bets. The answer is probably more on-topic here. There is a formula, but it's considerably more complicated. Let m be the profit you'd make on a 0.5 unit EW bet if the horse wins, and let n be the profit you'd make if it places (so, for example, if the odds are 10/1 and a place pays 1/5 the odds, then m = 6 and n = 0.5). Let p be the probability of the horse winning, and let q be the probability of it placing (but not winning). So 1-p-q is the probability that it is unplaced. Now let: A = mn B = (p+q)mn +pn +qm -m -n C = pm +qn -1 + p + q. Note that C is just your expected profit on a 0.5 unit EW bet. Then the optimal proportion of your bank to use as the unit stake (so the total stake is twice this) is [b + sqrt(B^2 + 4AC)]/4A sqrt means square root. Well, he did ask. :\ This also applies to other kinds of bet with two winning outcomes; e.g., an asian handicap bet with split handicap.

[DeepBlueDevilFish]

Re: Kelly criterion for EW bets Very interesting. Thanks. :clap

[bigs]

Re: Kelly criterion for EW bets Very nice indeed, It's actually a simple concept come to think of it! I might give it a try with a starting bank of my own to see where it ends! (I actually understood the mathematics ... well, I've been studying for something...) Slapdash I pose another question to you, that is not directly related to stakes, but to horse race analysis. If you'd consider a bayesian approach to a horse racing in order to pick a horse, what would be the top 5 factors to analyse as evidence?

[slapdash]

Re: Kelly criterion for EW bets

Slapdash I pose another question to you, that is not directly related to stakes, but to horse race analysis. If you'd consider a bayesian approach to a horse racing in order to pick a horse, what would be the top 5 factors to analyse as evidence?

I'm not sure if I know exactly what you mean by a bayesian approach. Do you just mean having a method of estimating the probability of a horse winning, conditional on various factors? I'm almost certainly not the right person to ask, in any case. Almost all my horse-racing bets are based purely on information from the betting markets. Having said that, if you're going to make an estimate of the probability based on a small number of factors, then I think that one factor that should definitely be included is the price available. Unless you have a very sophisticated way of using other factors to get a probability, then it's almost certain that there will be factors that you've missed, that the people setting the odds haven't. Suppose somebody estimates (without looking at the odds available) the winning chances of horses. Then if you look at the horses that they give a 50% chance, I'm sure it's true for virtually everybody that the ones that are odds-on will still do better in general than the ones that are odds-against, even though their estimate gives them the same chances.

[bigs]

Re: Kelly criterion for EW bets The thing is, bookmakers set a price, but the truth is that favorites win only 25% (+/-)... so the value should be anywhere else, because most of the times favorites get low odds. meaning that on the long run, either you chose the "Right" favorites or you'll end up losing money. But you're right when you say that bookmakers do the work for us, they have specialized people to analyze data and provide the odds they think best, and if they're winning money, it's because they're good at it ;)

[slapdash]

Re: Kelly criterion for EW bets

The thing is, bookmakers set a price, but the truth is that favorites win only 25% (+/-)... so the value should be anywhere else, because most of the times favorites get low odds. meaning that on the long run, either you chose the "Right" favorites or you'll end up losing money.

But that also goes for the longshots. In fact, even more so. You'll do better choosing random favourites than random 20/1 shots. But of course you'd lose money either way.

But you're right when you say that bookmakers do the work for us, they have specialized people to analyze data and provide the odds they think best, and if they're winning money, it's because they're good at it ;)

I'm not sure that's quite what I'm saying. Going back to the Kelly criterion, if you want to use it accurately then you need to know the "actual" odds you're getting and the "true" odds. Your first thought would be that what you ought to do is to estimate the true odds, then look at the odds on offer, calculate your edge, etc. But it seems to me that estimating the true odds accurately is hard. You both need to have very complete information, and you need to be able to convert that information into a probability. Otherwise your estimate will be wrong, and if there are apparently favourable odds on offer, then you won't be sure whether it means that there is value on offer or that you've missed something important in your estimate. It seems to me that it should be a lot easier to identify factors that correlate with the odds on offer being over-generous, without necessarily having a prior opinion of what the fair odds should be. This is why I don't fully agree with people who say that it's mad to bet without considering the price you're getting. Obviously, there are situations where it's clear from the price that it's far too skinny, or far too generous, but these are rare, I suspect. If you can identify factors that, in the long run, correlate with generous prices, then you don't need to know the "true" odds. On Punters Lounge, one of the most successful threads over many years has been Ralphie's Quick System. He has criteria for choosing horses that run again very soon after an easy win. He doesn't consider the odds at all (apart from excluding the long odds-on horses), yet he has made an impressive and consistent profit. If you asked me to estimate the true chances of one of his selections, then I wouldn't be able to give you a sensible answer without looking at the odds available. What I would do is to study his record to estimate the edge he has, look at the odds on offer, and combine them to estimate the "true" odds. Another example is TazaD. I believe that many of his NBA bets are based on identifying patterns in the recent record of the two teams that indicate that there is likely to be value in a bet. And as far as I know, he rarely then looks at the odds on offer and says "I'm not taking that." In a sense, it's the same with my own horse-racing bets. I try to identify EW bets where the place part of the bet is likely to give very good value. Not by directly estimating the chance of it placing and comparing that with the odds on offer, but by looking at the shape of the market and the place market on Betfair. I suppose what I'm saying is that there are three important numbers for any bet: (a) The odds you take. (b) The "true" odds. © The edge you have by taking the odds on offer. Any two of these numbers determine the third. Of course, you know (a). And what really matters is ©. I think it's sometimes easier to estimate © directly than it is to estimate (b) and then calculate © from (a) and (b).

[bigs]

Re: Kelly criterion for EW bets For now I just can say :clap I'll have to give it a bit of thought on your wise words, and see what gets out of that!