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Elo calculator relating to holding cube value

Posted By: Michael Sullivan
Date: Saturday, 11 April 2015, at 9:11 p.m.

In Response To: Elo calculator relating to holding cube value (Phil Simborg)

I've read before that 100 elo == .2 ppg at money and that cube ownership is worth about .5 at money, but I've never seen how those numbers were derived. So, since I'm a mathy kind of guy, I made an attempt.

My thought on ppg was just to look at what the average length of a backgammon game is -- how many decisions. I saw posted some old data from a 50,000 game trial with jellyfish(which tells you how old it is). Now I don't trust jellyfish like I do gnu or XG, but it was still a very strong bot, so how far off is it likely to be? Here's my thought: every move in a money game is a cube decision... unless you don't own the cube. So I tried to ballpark what's the frequency of one player owning the cube, and how many decisions that loses. The dataset I saw, had about 40% of games cashed or finishing on a 1 cube. Now, that included a few gammons and backgammons, so this set was obviously played without jacoby. For simplification, I treated those as cashes. Then i figure that in games with a higher cube, it first gets turned at some point through the game, and then after that only one side has cube decisions for the rest of the game, except for when there is a double, which I decided to ignore since I'm interested in a ballpark.

For my first cut I just looked at what happens if the cube gets turned first 50% of the way through he game. The average game has 20.9 moves per side. So this resulted in 38.665 decisions per game per side. Changing to 25% through or 75% through subtracted or added about 2 decisions per side per game.

Then I said that since PR is points per 500 moves, all we need to do is divide by 38.665 +/- 2 to get points per game on average if this sample is representative. That ends up being .232 or pretty close to the .2.

But wait. There's one more key thing. All those error rates are based on EMG, so your error on a 2 cube is not twice as much as on a 1 cube, etc. Which means we have to multiply this rate by the weighted average cube value. Fortunately my dataset included all the games which finished on 2 4 8 16 and 32 cubes by percentage as well. When I did the weighted average, it came out to 1.85.

So this means that the real advantage to the 3 PR better player is probably more like .42 +/- .05 points if this sample is representative.

So the other thing I'm concerned with, is that I may be misinterpreting what XG considers a decision. I've seen some conflicting things in different places. Does it use moves? or moves + non-trivial cube decisions. Does it consider early cubes in non-volatile relative even positions to be "trivial"? If it's dividing purely by "moves", then the standard number I've seen quoted of .2 would be a lot closer. I get .232 in that scenario. I suspect that maybe this is correct, since it's much closer to the standard answer.

Can anyone say with certainty exactly what XG means by a "decision"?'

I'm still thinking about how I would derive the value of owning the cube in a money game.

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