The Multi Matchers and EV
Multis promos offer another great opportunity to profit from bookies. To help you maximise your expected returns from these bets, we built the multi-matcher - but how does it work?
Maximising EV
The multi-matcher finds potential combinations of legs to maximise the expected value (EV) of your multi, within your risk tolerance. The ‘expected value’ here does not guarantee profit. You can lose on these bets. However, if you placed this multi an infinite number of times, the expected value is how much profit you would make on average. By continually taking positions with +EV we can guarantee long-term profits, but there will be some ups & downs along the way. This is what we talk about when referring to variance.
Naturally, we want to maximise the expected value in our betting. In this case, our value or ‘edge’ on the bookmaker is derived from our stake being returned as a bonus when one leg of our multi loses. This means that we want to maximise the probability of exactly this scenario playing out.
This is somewhat counter-intuitive, although not dissimilar from racing, (we all know the value is in the promotion!) If exactly one leg loses, we will lose money since if we have an 80% bonus retention, we effectively lose 20% of our original stake. However, this is a lot better than losing 100% of our stake, as would normally be the case. And the more probable it is that exactly one leg loses, the higher the payout will be when it doesn’t happen, so the outcomes balance out.
Based on this logic, one may assume that EV is maximised by choosing one bet with higher odds, and the rest with as low as possible. We have now confirmed this assumption with a simulation analysis, testing tens of thousands of odds combinations and finding the optimal strategy for an n-fold multi to be:
- Non-maximum odds: minimise the n-1 lowest odds
- Maximum odds: maximise the highest odds
This means that if you have a three leg multi with minimal allowed odds of 1.1, the optimal odds would be 1.1, 1.1, 999.
Although this multi maximises EV, it’s not practical. You would expect to have to place a multi at these odds 1.1 x 1.1 x 999 = 1208 times before you win one, which would require a gigantic bankroll and a lot of patience… Additionally, as matched-bettors, we only have a limited lifespan for taking promos before we get gubbed, so it’s optimal to extract expected value sooner rather than later.
Hence, the multi-matcher allows you to select your risk tolerance, which limits the odds of the maximal selection. The good news is that, most of the time, we can get decent expected value even for multi odds within the 2.0 to 5.0 range.
Multi efficiency
There is also one other factor that’s important for selecting positions for a multi, and that’s efficiency. Efficiency is how close the bookmaker’s back odds are to betfair’s lay odds for that event, calculated by the percentage (back odds/lay odds) x 100. The higher the efficiency, the less value we are losing to the bookie through their overround and/or mispricing.
Because efficiency is so important, the multi-matcher will only consider odds that are above an efficiency threshold. It also displays the efficiency % of each leg so you can explore how different selections affect the EV calculation for your multi.
Lay at the start staking
When taking advantage of a multi promo, there are two main approaches: ‘no lay’, or ‘lay at the start’.
We recently improved our multi-matcher’s ‘lay at the start’ staking strategy by optimising lay staking. The new approach involves using the mean back odds across the multis to calculate lay stakes, instead of the individual back odds. This gives the adjusted lay stake formula:
lay_stake = (mean_back_odds x back_stake) / (lay_odds - commission)
For a three leg multi, this adjustment effectively balances the outcomes for each scenario: all bets win (WWW), 1 bet loses (WWL, WLW, LWW), 2 bets lose (WLL), (LWL), (LLW)…
When we tested the adjustment, we found it had a (small) positive effect on EV in 99.9% of simulated cases. More importantly, the adjusted formula also reduces variance and the maximum possible loss in 100% of cases.
The graph above shows how the new and old staking strategies are highly correlated in EV. And the graphs below show how the new EV strategy reduces the variance and mean of the maximum possible loss.
Long story short, the ‘lay at the start’ multi-matcher is now even better at reducing your risk and variance for multis promos!
To learn how to use the multi-matcher, see this thread.