Tuesday, April 13, 2010

How does a horseplayer determine the odds?

Ask most horseplayers about odds and wagering startegy, and they will respond "I don't play chalk," or "I like the number 8 today in race 5 because he's 10/1 on the morning line (or ML, for short)."

While it's true that MOST favorites are overbet (their offered odds are lower than their true odds) and SOME longshots are underbet (their offered odds are higher than their true odds), many players do not know how to quantify their advantage. This blog post will hopefully explain how to quantify a player's advantage when betting to win.

Suppose a player thinks a horse is fair odds at 4/1. That implies that he or she believes this horse will win the race 1 out of every 5 times, or a win probability of 0.20 (1/5 = 0.20).

In general, the win probability for a horse at THEIR TRUE ODDS, not the ML, is:
1/(true odds + 1).

Example: A player thinks a horse's true odds to win a race is 9/1. This implies the probability to win a race is 1/(9 + 1) = 1/10 = 0.10.

Why is this important? Because the player can now quantify his or her edge (if one exists) if the crowd offers HIGHER odds on their preferred horse.

Example: Say that a horse at Saratoga is 9/1 on the player's personal odds line but is 13/1 on the board with 3 minutes to post (not really that rare of a scenario). We saw above that the 9/1 horse has a probability of winning of 0.10. That means the horse has a probability of losing of 0.90 (either the horse wins or loses, right? All the total probabilities, win and lose, in a race for each individual horse have to add to 1.0). So what would be the player's edge in this case?

If the player bets $1 to win, the "expected win return" is ($1)*(13)*(0.10) = $1.30
If the player bets $1 to win, the "expected loss return" is (-$1)*(0.90) = -$0.90
If we add the win to the loss, then we have a POSITIVE EXPECTATION of $0.40.

In other words, IF the player is a good handicapper, and only bets when the odds on the board are HIGHER than the true odds, the player has the ability to grind out a profit. If the player bets on UNDERLAYS (short priced favorites that don't have advantages in speed and/or pace figures, for example), they can't "handicap their way to profits."

The bet size is CRITICAL. If the player bets too much of their bankroll on any one race, short-term financial ruin (or worse) can be the result.

A mathematician named Kelly came up with the KELLY CRITERION, which is a guide to determining how much to bet on a single wager. It works best with win betting but can be adjusted to suit any parimutuel situation IF the risk is known.

The Kelly Criterion is an estimate of how much of a fraction of bankroll to wager on any one race. Of course, the player should NEVER wager on any event that has a negative expectation (i.e. underlays).

The formula for the Kelly Criterion is as follows:

Fraction of bankroll wagered = (Positive expectation)/(True odds of horse)

Going back to our Saratoga horse, the positive expectation was $0.40 and the true odds were 9/1. So the Kelly Criterion would be 0.40/9 = 0.0444

What does this number tell us? If the player is an EFFECTIVE AND CONSISTENT handicapper, over the long-term he or she can bet roughly 4% of betting capital on the Saratoga horse with little fear of "tapping out" because of over-betting their advantage.

Suppose the player had $120 in his wallet for wagering and that represents his total bankroll. Then the ideal bet size on the Saratoga horse would be ($120)*(0.0444) = $5.328. Rounding down to the nearest dollar, the player should wager $5 on the Saratoga horse to win.

Now let's suppose the player won the race at 13/1. The player would get back $70, but $5 was wagered originally, so the "profit" on the bet was $65. This means the player now has a bankroll of $185 ($120 + $65 in profit). In the next good betting race this $185 is the new bankroll total which sets the wagering amount. Also, the next betting race will probably have a different Kelly Criterion (it varies every race, depending on the positive expectation of the next horse and the horse's true odds).

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