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Looking at the second chart below, note how place payoffs for your horse can change depending on which horse it places with.


Note: The order of the place horses has no bearing on the payoffs. If #1 and #2 finish first and second, the order does not effect the place price.
Note, the lowest paying combinations are the #3 and #4 (highlighted in red), and the highest paying combinations are highlighted in green.
Show payoffs are calculated in the same way as place payoffs, except there is one more horse. Show payoffs pay less due to three main reasons:
The presence of overwhelming favorites (usually even money or less: odds of 1-1, 4-5, 3-5, 1-2, 2-5 or 1-5) can often drastically drive down the price of the other horses that place or show. The reason is simple.
Let's say a horse is 2-5 and 75% of the place money is bet on this overwhelming favorite, but you are considering a place or show bet on a 30-1 longshot. The problem is that if the favorite places or shows, only 25% of the dollars are bet on other horses. So by the time the entire pool is taxed and the winners of both horses are returned their $2 bet, and then the remainder is split, there is very little left to go around. In these cases, a 30-1 longshot that would pay $62.00 to win, might pay only $4.00 to place and $2.40 to show.
The end result is that place and show bets against overwhelming favorites is a bad idea IF you think the favorite is likely to place or show.