July 27th, 2001, 11:38 am
Just like in pricing derivatives it's not the actual probabilities that matter when the odds are set. Depending on how the betting goes, the odds will be set so that the House/Bookie cannot lose. For example, in a soccer match between England and Germany the Germans are more likely to win, but the patriotic English will bet more heavily on England (presumably). The odds given by the bookies will reflect this betting and make it look like England is more likely to win. Of course, in Germany the situation is reversed. The best bet would be on Germany, but placed in England, and one on England placed in Germany! In practice bookies in one country would lay off their bets on bookies in other countries so all bookies have roughly the same odds. Otherwise there would be straightforward arbitrage opportunities.In practice it's unlikely for there to be a sure-fire bet (unless the bookie has made a mistake, the race is fixed, or you can find two or more bookies that aren't directly or indirectly laying off their bets on each other). But you can win, on average. By exploiting the difference between the real probability of a horse winning and the odds you can get. (There are differences between real odds and what you get paid in all casino games, but it's only in Blackjack that this can be exploited.) Give me a few minutes to write a simple Excel spreadsheet to illustrate this, and we'll upload it.P