Optimal Betting

[rdiam]

There have been a lot of opinions on betting expressed on this board recently regarding "how to bet". Instead of opinions, let's deal with facts, since optimal betting can be precisely defined by math and statistics.

Briefly, optimal betting is defined as "you bet when you have an edge, you pass when you don't have an edge". Now "edge" is sometimes hard to precisely define and may be subjective, but is roughly approximated by the formula "is the horse paying more based on its implied odds than I estimate the horse to win?" So if you think a horse can win more than 50% of the time, it is a bet at 1-1 or better. Similarly, if you think a horse can win 25% of the time, you should bet at anything better than 3-1. Otherwise, you pass.

The best way to calculate how much to bet is to determine your percentage "edge", divide it by the odds, to show the maximum percentage of your bankroll to bet. You bet more on low odds horses, and less on high odds horses. In words, this is Kelly betting, and is very aggressive. Most will cut this bet size in half or even by 1/4, with some even cutting it by 1/10. This will maximize the growth of your bankroll and minimize your chance to bust out.

Now, here is where it gets a little tricky. Humans tend to be risk averse, feeling more pain when losing $100 than the pleasure received from winning $100. So when you bet while only considering your edge, you may be subject to large runs of losing bets before your edge kicks in. Even when betting even money shots, you will lose 3 in a row 12.5% of the time. How many of you can push the money in and make that fourth bet after such a mild losing streak?

Enter Dr. Sartin, who recognized that the psychological aspect of betting also needs to be considered, and came up with a bankroll smoothing technique of 2 horse betting. More precisely, as long as your 2-horse bet has an "edge" to overcome the losing bet, you will increase your win probability over a 1 horse bet, be able to bet a larger percentage of your bank, have fewer and shorter losing streaks, and watch your bankroll grow faster.

In fact, there is nothing magical about 2-horse bets: if you can find an edge with 3 horses (including your "losing" bets), then bet 3 horses. If you only find an edge with 1 horse, then bet 1 horse.

Finally, it is often advantageous to include a low odds horse in your group bet that, on its own, may not show an "edge", but when combined with another horse creates a group of bets that not only show an edge but create a higher win probability from the group enabling you to bet a larger percentage of your bankroll and grow it more smoothly and faster. For example, some will bet an 1-1 favorite to "breakeven" if it wins to cover the group bet, and let the longer odds horses provide the profit when they win.

Bottom line, look for your edge, check to see if by including a low odds horse will maintain your edge, and bet as many horses in your group that will keep your edge: in any given race, it might be none, one, two, and maybe even three. Be flexible and not dogmatic.

Richard