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Freezeouts

by Douglas Zare
1 September 2004

Douglas Zare

A freezeout is an unusual form of match play, more common in poker than backgammon. Two players bring money to a table and then play according to table stakes until one player has all of the money on the table. Backgammon freezeouts are often played on TrueMoneyGames, although the rake is significant and players can quit or add money at any time. Freezeouts without table stakes are supported by GammonVentures

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Subject: Re: Freezeouts

From: Chris Yep

Date: 03 Sep 2004 09:28 EST

Do any live tournaments have freezeouts with tablestakes?

The only freezeout that I know about (I mostly am familiar with U.S. tournaments) is the freezeout held at the Michigan Summer Championships for the last (approx.) 7 years. However it doesn't have tablestakes, making it hard to determine a match equity table even for equally skilled players. There is an additional complication (to prevent long matches) in that the centered cube starts on 2 for the 6th-10th games, on 4 for the 11th-15th games, and on 8 beginning with the 16th game. But even without this additional complication it's still not trivial to calculate a match equity table for equally skilled players.

I've attended Michigan 3 times in the last 4 years. I've never played in the freezeout. Mostly this is because I've been too busy in the main event and with other things, but a minor reason for not entering the freezeout is that I wanted to try to calculate a MET before entering the freezeout. (I never had time to seriously attempt this calculation.)

Subject: Re: Freezeouts

From: Chris Yep

Date: 03 Sep 2004 18:13 EST

I believe there is an additional complication with table stakes freezeouts. The variance of a game in a table stakes freezeout match is not constant, but instead is a decreasing function of Min(C1, C2) where C1 = number of chips (or "points") held by Player 1 at the beginning of the current game and C2 = number of chips held by Player 2 at the beginning of the current game.

When Min(C1, C2) is large, the variance of the game is close to the variance of a money game, i.e. about 8-10. (I generally use a variance of about 8-9, but 10 is perfectly reasonable). However when Min(C1, C2) is small, the variance of the game is much smaller. E.g. when Min(C1, C2) = 1, variance = 1.

Overall, this means that when both players have N chips remaining, the average number of games remaining is larger than (N^2)/10.

Subject: Re: Freezeouts

From: zare

Date: 05 Sep 2004 05:03 EST

If the centered cube will escalate later, that gives the stronger player less of an advantage now. The advantage may depend not only on the current centered cube level but also on the number of games or time before the next level.

You are right that the variance depends on the table limit. The dominant effect may be that a lower table limit results in no large cubes, hence lower variance. There is a curious effect in the opposite direction: If the cube will be dead after it is turned, then the early-late ratio tends to be lower than for normal money play. A lower table limit may encourage more double-ins. The other effect is probably larger.

As long as there are no fractional points, each backgammon game corresponds to at least one coin-toss for one point, so the average number of games should be between N^2/10 and N^2. For large N, I think the average number of games ought to be closer to N^2/10.

Douglas Zare

Subject: Re: Freezeouts

From: gammonvillage334455

Date: 08 Sep 2004 06:58 EST

amazing stuff!

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