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BetAndWin: 4000 matches, 40 sports, live betting

Sports Arbitrage as a source of good bets.


Surebets are themselves a very good bettor tool. But they have an extra feature that is very useful one. Surebets are rather good source of positive EV (expected value) bets. Surebet includes one or more bets and at least one of them is a bet where you have an advantage, an edge over bookmaker.

When you look at a set of possible bets do you have much to say about what are good bets in this set? – I think almost nothing. But when we see bets which constitute 3-outcomes surebets we can definitely say that at least 33.3% of them are positive EV bets. And even more,  when we see bets which constitute 2-outcomes surebets we can definitely say that at least 50% of them are positive EV bets.

I can easily prove this statement. Suppose you have 3-outcomes surebet for 1-X-2 line, and thus 1/K1+1/KX+1/K2 < 1. Consider fair event probabilities: P1+PX+P2   = 1. Suppose that every coefficient of the 3-outcomes surebet has no positive EV, that is

K1 <=  1/P1

KX <=  1/PX

K2 <=  1/P2

Summarizing these three inequalities we get

1/K1+1/KX+1/K2   >= P1+PX+P2   = 1

It means that these three coefficients do not constitute a surebet. It contradicts to our first assumption. So, at least one of the three coefficients has to satisfy the following condition:

K >  1/P

Corresponding bet is, by definition, a bet with positive expected value (EV). That is, if you make the similar bets many times, you will get a profit in a long run. Now you understand that when considering 2-outcomes surebets we are to have at least 50% of positive EV bets. Not a bad start when seeking for a winning strategy.

There is a very simple and straightforward winning strategy, strategy giving a guaranteed profit in a long run. The strategy can be formulated as follows – make a bet on random outcome of a surebet. It has an easy though not absolutely strict proof. Let us consider two players. The first player is to make bets on random surebet outcome. Second player is to make bets on opposite outcome. It is rather clear that bets made by second player are also ‘random’. So, each player has the same expected value. Let it be W. Both players together have expected value 2W. But as you see these two players when considered as ‘one’ player make, in fact,  surebets each time they both make bets. So, 2W > 0, and W > 0. It means that ‘random surebet outcome’ strategy is a winning strategy.

We need to add some more details in order to make the strategy available for practical usage. Bet size is to be flat or random (being in some reasonable range). There is a large probability that bookmaker will be often cutting   wager limits for bets (in surebets) really having positive EV. If we do not take this issue into account we risk to have an asymmetry which makes the whole algorithm unusable. In order to correct the case we add the following rule to our winning strategy. Before we make a real selected bet we are to check if we are able to make both bets, of a size we defined before that. If wager limits for both (selected and skipped) bets are unchanged then we make selected bet.

When using this ‘random surebet outcome’ strategy you can estimate your edge, that is, expected value of your profit. Your bet edge is equal to an edge of a surebet, where you got selected bet from. In order to check this statement you need to use previous proof but take only surebets with a fixed profit. Thus, if we have an estimation of a bet edge then we can use Kelly criterion to increase our profit.

Further investigations are to be held in direction of additional surebets outcomes filtration. So that percentage of positive EV bets is increased. For example, it is often so that two (of three) bets that constitute surebet are to be made at the same bookmaker. To my mind it is more probable that bet with a positive EV is to be in opposite bookmaker, where you are to make only on bet. Of course, this hypothesis is to be tested statistically.

Also hypothesis that positive EV bet will be more often in case it is proposed only one bookmaker than several bookmakers is also reasonable to my mind. The hypothesis is also to be tested statistically. 

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