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# Computing Competing Probabilities

### Solutions

1. The team with initial possession has over a 60% chance of winning.
2. For an 11-point game, under a "winner-takes-out" rule, the probability that the team with initial possession wins is 61.5%.
3. "Loser-takes-out" reduces the first player's advantage to 58.6%.
4. Adding in a four point shot makes the odds for the first player to win an 11-point game to 57.7% in the "loser-takes-out" scenario.
5. Having an inside shot be worth 1 and an outside shot point worth 2 makes the 11 point game longer so the initial team has only a 56% chance of winning.

An Analysis of Alpha-Beta Priming [PDF] by Donald E. Knuth and Ronald W. Moore presents a classic approach on increasing the efficiency yet further.

— Dennis Shasha can be contacted at [email protected].

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