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Elo calculator relating to holding cube value

Posted By: Timothy Chow
Date: Saturday, 11 April 2015, at 4:46 p.m.

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

Well, the conventional argument goes something like this: PR is supposed to measure how much equity you're blundering away per move. A 10 PR player blunders away 10 "units" of equity per move on average, and similarly for a 7 PR or 5 PR or 2 PR player. If I blunder away 10 units per move but you blunder back 7 units per move, I should bleed away 3 units per move on average. Similarly for the 5 PR and 2 PR players.

Where might there be loopholes in this argument? The formula for PR is complicated and doesn't measure equity directly. The above argument makes more logical sense for Snowie ER in place of PR. However, people seem to believe that Snowie ER and PR are more-or-less linearly related. If that is true then the argument should still work regardless of whether PR or ER is used.

What I think might be a more serious issue is that ER/PR is normalized so that D/P is 1.000. In real life with real money, you lose twice as much money on a 2-cube as on a 1-cube. For the argument to work, we should really be counting true equity lost per move, and in particular we should be taking into account how often the cube is on 2, 4, 8, etc. If we did this, perhaps the ER/PR difference would change.

What about your argument that there are more blunders per game at the 7 PR/10 PR level than at the 2 PR/5 PR level? I agree that this is true but the point is that the blunders are occurring on both sides, so they have a tendency to cancel each other out.

As for whether the 10 PR/7 PR "knowledge gap" is the same size as the 5 PR/2 PR "knowledge gap," I think this is hard to quantify because it's hard to quantify knowledge. In any case what ultimately matters is not the size of the knowledge gap but how much equity you actually blunder away per game, and it would seem that PR, or at least ER (adjusted for cube value as I suggested) should be more or less the right tool for that.

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