Some AvB Events Are AvK Events In Disguise

Many AvB contests (MLB, NBA, and NFL moneyline markets) are exactly what they appear to be - simple win-lose events. But, other AvB contests (soccer win markets) are actually AvK contests in disguise - there are three valid outcomes (win, lose, and draw). This turns a

'single event, single selection' contest into a possible 'single event, multiple selections' one - Kelly's Multiple Personality Disorder.

Treating this soccer match as a single event with three exclusive outcomes leads to an combined investment of 5.93% of bankroll on both the draw and away-win outcomes.

Alternatively, focusing on one or both draw and home-win outcomes as separate selections leads to an investment of 3.75% on the draw outcome and 1.00% on the away-win outcome for a total of 4.75%.

Given your assumed edge relative to the market, this amounts to 'leaving money on the table', in Kelly terms!

All calculations can be replicated using the excellent SBR Calculator.Win percentages are not necessarily realistic for this specific event.

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:

h	p	π	e.v	Σ(π)	a.k	b.k	%
Echo	21.00	7.00%	1.470	0.070	0.048	0.977	2.49%
Charlie	5.50	20.00%	1.100	0.270	0.229	0.947	2.78%
Bravo	3.25	29.00%	0.943	0.560	0.537	0.951	0.00%
Delta	6.00	13.00%	0.780	0.690	0.704	1.047	0.00%
Alpha	2.50	31.00%	0.775	1.000	1.104	0.000	0.00%

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

h	p	π	e.v	Σ(π)	a.k	b.k	%
Echo	21.00	7.00%	1.470	0.070	0.048	0.977	2.56%
Charlie	5.50	20.00%	1.100	0.270	0.229	0.947	3.05%
Bravo	3.35	29.00%	0.972	0.560	0.528	0.932	1.18%
Delta	6.00	13.00%	0.780	0.690	0.695	1.015	0.00%
Alpha	2.50	31.00%	0.775	1.000	1.095	0.000	0.00%

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. In order to calculate the correct stakes, make sure table is sorted by column 'e.v.' in descending order!