The chance thus for his winning is 12/13 or 92.30%. The only way for Bill to lose is if Jack bets $99 on Sprinter B and B wins the race. Chances of B winning the race is 1/13 there fore chance of B losing the race and hence Bill winning is 1-1/13=12/13
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You just beat me to it! :D
Ideally, Bill should just bet equally on whatever Jack is betting on. The problem arises only if Jack's bet is a secret.
very nice @unsungcheese834