[john_dope]

Hi I have been reading Ganchrow's posts regarding Kelly betting and came to this example regarding mutually exclusive outcomes.

The results seem to imply betting a percentage of your bankroll on an negative EV bet (Bet C) is optimal. Am I missing something here? How can it be right to bet at 1.99 odds an event which occurs 50% of the time?

Thanks



Consider the following bets on 4 mutually exclusive outcomes:

• actual prob=50%, odds=1.99
• actual prob=25%, odds=4
• actual prob=15%, odds=6.5
• actual prob=10%, odds=10.5

Sorting by edge yields:

1. p=10%, odds=10.5, edge=5%, implied prob=9.5238%
2. p=25%, odds=4, edge=0%, implied prob=25.0000%
3. p=50%, odds=1.99, edge=-0.5%, implied prob=50.2513%
4. p=15%, odds=6.5, edge=-2.5%, implied prob=15.3846%

The running implied probabilities totals are:

1. 9.5238%
2. 34.5238%
3. 84.7751%
4. 100.1597%

Because the sum of implied probabilities is 100.1597% > 100%, no true arb exists and we proceed.

The running actual probabilities totals are:

1. 10%
2. 35%
3. 85%
4. 100%

The quotients are then:

1. 0.994736842
2. 0.992727273
3. 0.985225933
4. 0

The minimum quotient greater than 0 is 0.985225933.

Hence the stakes for each bet are:

1. stake=max(10% - 0.985225933 * 9.5238%,0) ≈ 0.6169%
2. stake=max(25% - 0.985225933 * 25.000%,0) ≈ 0.3694%
3. stake=max(50% - 0.985225933 * 50.2513%,0) ≈ 0.4912%
4. stake=max(15% - 0.985225933 * 15.3846%,0) = 0%

[Data]

Hi I have been reading Ganchrow's posts regarding Kelly betting and came to this example regarding mutually exclusive outcomes.

The results seem to imply betting a percentage of your bankroll on an negative EV bet (Bet C) is optimal. Am I missing something here?

Keep reading, you will learn that making -EV bets is not uncommon while trying to maximize EG. This applies to offsetting +EV bets on mutually exclusive outcomes which includes such methods as arbitrage and "buying back".

[u21c3f6]

Keep reading, you will learn that making -EV bets is not uncommon while trying to maximize EG. This applies to offsetting +EV bets on mutually exclusive outcomes which includes such methods as arbitrage and "buying back".

+1

Joe.