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Probability to win a unlimited session of 10 games

Posted By: Daniel Murphy
Date: Tuesday, 6 September 2011, at 6:47 p.m.

In Response To: Probability to win a unlimited session of 10 games (eXtreme Gammon)

Thank you, Xavier. The result of your simulation is certainly relevant to Jakob's assertion that we lesser players would have "not more than 3% chances to win" against world class players in an 8 or 10 game money game session. I might add that the probability your simulation found of the 108 ELO underdog coming out ahead in a 10 game money game session is approximately the same as his probability of winning a 13-point match.

Under Jakob's proposed tournament conditions, however, what matters is not whether players have plus scores in any one money game-like match, but how many total points (chips) they have won after all such matches have been completed.

So ... variance is important.

Perhaps we could ask this:

Suppose you are one of 8 players of 32 with a 108 ELO advantage over the field in a modified Swiss tournament. Are you more likely to be among the top 8 chip leaders after 7*10=70 money games, or be among the 8 with the best win/loss records after 7 13-point matches?

Is that relevant? If so perhaps someone could answer that?

My understanding of the key elements of Jakob's proposed tournament structure is this:

(1) Everyone buys chips.

(2) You use these chips in a preliminary competition. This consists of a minimum of 7 rounds of matches where each match is 8 to 10 money games. Each subsequent round pairs players with like results according to how many chips they have won or lost. In the first three matches an undoubled game has a nominal value of 1 chip. In the rest, 2 chips.

There are details about rebuys and initial buy-in size which I ignore here.

(3) At the end of the preliminary rounds, half of the prize money is now divided between all players who still have chips. The 8 players with the most chips go to a double elimination final. The others go to a double elimination consolation. At the end of the competition, the other half of the prize money is now divided between the top 3 players in the final and the top 2 players in the consolation.

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