# Risk in Horse Betting

A couple of realities make it harder to bet wisely than at first it may seem.

First, consider a big lottery, like Powerball. Let's say that no one has won in a long time, so the jackpot has grown to \$350 million. Suppose that this is a five number lottery (1-40) and that the chance of having a winning ticket in such a game is thus 1 in 40 to the fifth power. That's 1 in 102,400,000. The price of one ticket is \$1. Is it rational to buy a lottery ticket under these circumstances? (This is not the real lottery; do not try this at home.) Yes. Why, because the wagerer has an edge. The "true odds" are 1 in 102 million and the payoff odds are \$350 million to 1. What is the maximum rational bet? Theorists might suggest that it would be all your money. Where else can one bet on odds so favorable? No reasonable person would bet much, if anything at all. Why? Because even though there is a huge edge in the bet, the actual chance of winning is so small as to be negligible in the real world.

This parable explains a difference in approaches to horse race betting. A \$2 bet "to show" on a clear (i.e., deserving) favorite is a low risk bet with a low reward, perhaps the minimum \$2.10 payoff. Yet there was surely an edge in making the bet. On the other end of the scale is a pick six exotic wager, where the payoff odds may be 400 to 1 or more. It is conceivable that a handicapper can calculate that the "real" probability of the six outcomes being linked together and wagered upon is really only 250 to 1, against. So it's a good bet!

Whether a person is comfortable at the one end of this spectrum or the other, or (more likely) somewhere in between, is a matter of personal choice. It deals with the question of risk, which is separate from "edge."

"Risk" does not refer to living dangerously. It refers to two things at once: How big an edge do you need in order to make a bet comfortably? How large a bet can you comfortably make, regardless of the amount of the edge?

The first question deals with the uncertainty of winning and losing. You should know that, over time, you will win more often than you lose if you always make positive-expectation bets. The second question deals with the optimal bet size, and usually relates to the amount of money comfortably available for being put at risk in a gaming situation. Even with a 300% edge in the Powerball example, it would not make sense to spend every dime on it. Even though the bet is a bargain, the chances of winning anything are so low. In horseracing, the "maximum bet" is usually calculated as some fraction of the total bankroll, and the size of the bet in relation to the ceiling may depend in some measure on how remote the chances are of winning anything at all. A good day at the track should involve a few long shot bets, but the more sure and solid payoffs will need to make up a good part of the betting portfolio, just to ensure survival.