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© Copyright 2000, Jim Loy
In international 3-cushion billiards two formats are most common, a game to 50 points and best three out of five sets to 15. In preliminary rounds, they may have two out of three sets to 15. In general, the longer a game, the more it favors the stronger player. After all, even a novice might win a game to 5 against a top player, but he/she would probably never win a game to 50. Three out of five sets to 15 may seem to give the underdog a better chance than a game to 50. But I contend that it favors the stonger player slightly more than does a game to 50. The lower averaged player has a good chance to win one or two sets. But the higher averaged player should win three sets more often than he/she will win a game to 50.
I did what is called a Monte Carlo simulation on my computer. I played 1000 games or matches with each format. It turns out that 1000 games or matches may not be enough, as the results are somewhat inaccurate. Here is a table. On the left side are listed the various formats. At the top we see the average of the better player. The average of the weaker player was 1.0. The results should be similar for lower averaged players (.500 and .600 should be similar to 1.0 and 1.2). The numbers in the body of the table are the percentage of wins for the stronger player:
| format \ average | 1.1 | 1.2 | 1.3 | 1.4 | 1.5 |
| game to 45 | 59.6 | 71.2 | 88.9 | ||
| game to 50 | 62.3 | 73.4 | 83.2 | 85.6 | 90.4 |
| game to 60 | 63.9 | 73.1 | 83.9 | 87.0 | 92.3 |
| 3 of 5 sets to 15 | 62.7 | 74.8 | 82.8 | 85.5 | 91.7 |
| 2 of 3 sets to 15 | 62.4 | 63.3 | 77.5 | 79.3 | 85.3 |
The results of my test are a little inconclusive, because 3 of 5 sets to 15 scores very close to a game to 50. It would seem that I need several thousand games and matches. I will try it with 10,000 matches and games, later.