Betfair Pari-Mutuel Equivalence

For those handicappers fortunate enough to have access to both Betfair and Pari-Mutuel markets for the same events and who wish to arbitrage their positions for a "no loss" outcome, they should add the following formulae to their toolset:

• o = 1 - (d * 1/(x - 1)) and
• d = -((o - 1) * (x - 1))

where o = betfair decimal odds, d = pari-mutuel dollar payoff, and x = betfair tax (combination of commission and discount). These prices are equivalent in terms of expectation and volatility..

Betfair InPlay Hedge Stake

Trading an event in-play on Betfair is not for the feint of heart as, ultimately, no position is safe until it is successfully hedged. Psychologically, however, if you have carried out a fundamental analysis of the event then you want to be paid a premium for that analysis should your selection prove to be successful. On the other hand, Cumulative Prospect Theory confirms that we hate losing (loss aversion >= 2.25) more than we enjoy winning. In order to balance those conflicting forces, you could calculate a hedge stake to green-up your position, as follows:

  z = (s*(o+m-1))/(h+m-1)
  where  z = hedge stake
        s = original stake
        o = original price (back)
        m = win multiple (ratio of win payout to loss payout, if greened up)
        h = hedge price (lay)

For example, if I back a selection for $100 @ 6.00 and wish to green-up at 2.00 then the default option is to lay $300 @ 2.00 for a guaranteed $190 whatever the result of the event. By contrast, the above calculation (e.g., m = 2.25), gives a stake of $223.08 with a win payout of $264.74 and a loss payout of $117.66 giving you a win premium!