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..