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Say you have a hot tip for the weekend. Your favourite team are being offered at odds of 3.0 to win a game and you think they have at least a 50% chance of winning the match. You have what is known as 'value'. What this means is that if you bet on this game, then 50% of the time you'll win (getting back 3.0 each time) and 50% you'll lose (losing your stake of 1 unit). Overall you'll be in profit because 50%*(3.0-1.0) + 50%*(0-1.0)=0.50

That is to say, that on average you'll make 0.5 times your stake every time you make this bet. That is the definition of value - that you make profit, ON THE AVERAGE, when you take on this bet.

Now imagine that instead of 3.0 you were being offered 1.80. Now if you placed this bet, you'd lose, ON THE AVERAGE, 0.1 times your stake every time you bet. Of course sometimes you'll still win the bet and get 1.80 times your stake but the times you lose, AVERAGED with the times you win will see you lose ON THEN AVERAGE. You have no value.

This is a fundamental tenet of successful betting. If you don't have value, you lose money when you bet. If you do have value, you make money - provided you employ proper money management strategies!

So what does that mean?

Well, lets take an example. Lets say some foolish bookie does indeed offer us 3.0 for a 50% chance (another way of saying the 'fair odds' should be 2.0). We have value and we know that means we should bet. So maybe we take our life savings of £10,000 and bet it all on the match (we'll assume our friendly bookie is happy to take such a big bet!). We have value, so we, on the average, win every time we bet. We even know how much profit to expect. In this case 0.5 times our stake. Excellent! We're going to turn our £10K into £15K. Unfortunately it isn't that simple. Remember that a 50% shot is still going to lose 50% of the time and our life savings are gone! Clearly staking our full 'betting bank' on a game isn't the correct strategy. At the other extreme if we only put a minimum stake (say £1) on the game, we're missing an opportunity to make money.

So what is the answer?

Well clearly somewhere in between is a figure where we're maximising the amount we gain when we win, and yet leaving ourselves sufficient comfort that on those times we lose we can still continue without undue pain. Sound vague? Unfortunately it is. Ultimately what we are looking to do is to balance our upside (when we win) with our downside (what we can are risking). Some of us will be quite aggressive and may be prepared to accept a larger risk of losing a given amount (or even all!) of our money to be compensated by more profit, ON AVERAGE. Others among us may be much more cautious and seek just to maximise our profit subject to keeping risk below a certain level. Each of us has our own risk-reward balance.

So how can we progress?

Well, lets for the moment assume that we have an idea of what our risk-reward balance is, what kind of things do we need to bear in mind? Well a simple list might be:

1. Do we have value?
2. How much value do we have?
3. What are the odds at which we are betting?

(1) determines whether we bet, while (2) and (3) determine how much we should bet - in conjunction with our risk/reward balance noted above. Simply put, the more value we have the more we should bet. However we also need to consider the odds at which we're betting. Having 10% value on a bet at odds of 1.25 is very different than having 10% value on a bet at odds of 10.0. In the former case we expect to win 88% of the time, while in the latter case we expect to win only 11% of the time. Because of that, despite having the same amount of value in each case, we need to keep our stakes smaller when the odds are bigger.

It can be proven theoretically*, that the optimal stake size is given by the formula (Edge)/(Odds-1) where edge is simply the amount of value you have.

*NB. this is a slight simplication of the orginal work by Kelly, but close enough for almost all practical purposes. Optimal here means in the sense of maximising the growth of your bank.

So how do we know how much value we have?

This is a very difficult question, and beyond the scope of a short article. However, we can say the following. In a situation like sports betting where in any practical sense it is impossible to give an exact figure for the probability of a particular outcome (unlike say a lottery or casino game); all we can do is form an estimate. That is we estimate what the 'fair odds' are and use that to estimate whether or not we have value in any particular situation. If over time, we are correct, on average, in determining value, then we will make a profit. The inverse of this - i.e. if we've made a profit in a series of past bets, how confident can we be that this will continue - i.e. that we are actually good at estimating value, is far more difficult, and again beyond the scope of this article. Suffice to say we can use various statistical tools to determine how good we are.

Ok, so we're not sure exactly how much value is there, so what?

Well, we have seen that the stakes used (for our comfort level of bankruptcy) should vary according to the amount of value we have, and the odds on offer. The real question is what is the effect of a) underestimating the amount of value we have and b)overestimating the amount of value we have.

Well underestimating the value isn't too bad actually, it just means we make a little less profit than we could. However, overestimating the amount of value we have can HUGELY increase the risk of going broke.

So how can we use all this information?

Well ideally, you should be able to get from tipster the sort of information you need about risk - i.e. what level of confidence can you have in his results, and what risk/probability do you have about making various levels of profit and loss over given sequences of bets, and under various levels of staking. You then choose a level of risk that is comfortable for you, and stake accordingly.

Failing that, be conservative! Cutting your stakes in half will halve your potential profit, but it may make a gigantic difference to the amount of risk - sometimes cutting it by a factor of 20 or more!

We thank www.punters-paradise.com/forums/ for this article.