How Much Should I Bet?
One question many people wonder about is how much or what proportion of their betting pool to bet on something. Try our stake calculator below, and then go on to read all the theory behind it.
Probability of Winning
Some people argue that the amount should be based on your forecast likelihood of winning. This makes sense to some degree, in particular in so far as it would seem stupid to bet a huge amount of money on something that had a very low chance of winning, but surely value has to be considered too, as it would be foolish to bet a lot of your pool (or to bet at all) on something that while 95% likely to win, was only offering a return of 1%.
Value
Many learned mathematicians such as John Kelly advocate basing your stake on value. Value means how the odds compare to your view on the probability of the chance of winning. Obviously this is highly judgmental on your part, but that is what gambling is all about.
Lets look at an example which illustrates the relationship between odds and probabilities and introduces some of the basic maths (its hard to be a successful gambler unless you know some maths).
The answer is d)
Lets say you bet £100 on Moscow flyer at 6/4
If it really has a 40% chance of winning then your expected return is
40% chance of £150 profit
60% chance of £100 loss
Expected profit = 40% x 150 + 60% x -100 = 0
Hence if the expect profit is 0 with a 40% chance of winning then 6/4 must be the fair odds.
Value is created when bookmakers set odds that are greater than what you believe is a fair price for the selection to win. This will happen possibly because bookmakers take a different view to you on the chances of that selection winning, and more commonly because other punters are taking a different view, and consequently the weight of money is forcing the bookmakers to move the prices to balance their book. This sort of thing is particularly prevalent on patriotic type bets (England football team, Tim Henman etc.) where the weight of money make the odds far shorter than the true probability of the win.
Staking Based on Value
Kelly's formula basically says the better the value of a selection the larger the proportion of your betting pool you should put on. Value is defined as the ratio of your probability of winning versus the odds that are available
A = P - (1 - P )/(O - 1)
Where
A = Proportion of betting fund
P = Probability of winning (your opinion)
O = Decimal odds (including stake return)
The first thing to notice is that if P=1 (i.e. 100% chance of winning) then A=1 (meaning you put all your money on!). That makes sense if it really is 100% certain.
So lets look at our Moscow Flyer example again (still with a prediction of 40% chance of winning) but with some different odds to see how that impacts on how much you should stake.
1. FAIR BET (40% chance of winning & odds of 6/4 = 2.5 in decimal odds)
A = 0.4 - (0.6)/(1.5)
A=0
Conclusion: Don't bother there's no value there
2. GOOD VALUE (40% chance of winning & odds of 2/1 = 3 in decimal odds)
A= 0.4 - (0.6)/(2)
A=0.1
Conclusion: Bet 10% of your pool
3. BAD VALUE (40% chance of winning & odds of 1/1 = 2 in decimal odds)
A= 0.4 - (0.6)/(1)
A= -0.2
Conclusion: Negative - avoid
Example 3 is interesting as at the time Kelly wasn't considering Lay betting (Kelly's Criterion was developed in 1956) but whether this formula can be extended to laying (e.g. you lay to 20% of your pool) is uncertain as the formula seems to break down a bit in these circumstances as you can get numbers like -5 out of the formula if you put in very short odds, which doesn't make any sense.
Kelly's Criterion - Practical Use
Many people have criticised Kelly's formula for a number of reasons
1. Its very hard to come up with an accurate probability
This is true, but if you don't have a view of the real probability then you shouldn't be betting on it
2. If you get the probability too high this makes your stakes too high and is bad news
This is true and some now say that rather than use the result of the formula (A in the formula) as being the percentage of your stake, more use it as a general value indicator in comparing bets against each other.
3. If something is great value but very long odds then surely putting a lot on it is silly.
Kelly's criterion does reflect this fairly well in that your max % of your betting pool would always be capped at the probability of the selection winning. However it does tend to be a long term strategy rather than focusing on short term cash flow.
EG. If you think something has a 20% chance of winning (fair odds 5 decimal) but the odds are 20/1 then Kelly's formula says you should stake about 16% of your betting pool on it. This seems a lot given that you have an 80% chance of losing.
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