Thursday, March 08, 2018

Kelly And Mutually-Exclusive Outcomes (AvK)

In AvB events, such as baseball, basketball, or football, the general advice to only bet the overlay is technically correct. However, in an AvK event, such as horse-racing, with a number of mutually-exclusive outcomes this advice is not strictly correct. For example, in the following racecard (sorted in decreasing e.v order), even though the handicapper has rated Bravo's win probability (π) at 29%, it is an underlay and not included in the list of bet selections:

hpπe.vΣ(π)a.kb.k%
Echo21.007.00%1.4700.0700.0480.9772.49%
Charlie5.5020.00%1.1000.2700.2290.9472.78%
Bravo3.2529.00%0.9430.5600.5370.9510.00%
Delta6.0013.00%0.7800.6900.7041.0470.00%
Alpha2.5031.00%0.7751.0001.1040.0000.00%

But, if Bravo's price was to drift to 3.35, then this underlay is now added to the list!

hpπe.vΣ(π)a.kb.k%
Echo21.007.00%1.4700.0700.0480.9772.56%
Charlie5.5020.00%1.1000.2700.2290.9473.05%
Bravo3.3529.00%0.9720.5600.5280.9321.18%
Delta6.0013.00%0.7800.6900.6951.0150.00%
Alpha2.5031.00%0.7751.0001.0950.0000.00%

Kelly betting is predicated on maximising the logarithm of the handicapper's bankroll over the long-term. But, in the short-term, that goal is translated into not losing specific events when the price is right! The key role played by overlays in mutually-exclusive events is that there must be at least one such betting option available in any event on which we wish to bet. Beyond that, the specific choices will only be governed by maximising the logarithm of our bankroll!



Note
: Blindly backing high probability combinations such as Alpha, Bravo, and Charlie (total win probability = 80%) will eventually lead to ruin.