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"Slot Rule" and "Simborg Rule" -- correction

Posted By: Nack Ballard
Date: Wednesday, 20 January 2010, at 9:26 p.m.

In Response To: "Slot Rule" and "Simborg Rule" (Nack Ballard)

I blundered in grabbing the Snowie eval for the player on roll in the opening position. In displaying the equity, Snowie thinks that doublets are allowed! Oops.

My thanks to David Rockwell for sending me a Gnu Supremo 19k rollout of the opening positon with the "rollout as initial position" option selected (i.e., no doublets allowed). This was David's polite way of saying, "Look, you goofed!"

According to that Gnu rollout, the first player's equity is only .0531. (Btw, I did the math on the Snowie eval, factoring out the six doublets, and the adjusted eval closely agrees with the Gnu rollout.)

I apologize to Phil for my claim that the Slot Rule does a better job of equalizing the advantage of going first than the Simborg Rule. In fact, his rule makes it come out close. The Slot Rule transfers the advantage to the second player, as Matt R. suspected.

The corrected recap of the opening roll advantage is

Standard: 1st player +.053
Sim Rule: 1st player +.006
Slot Rule: 2nd player +.038

To put this issue into perspective, I would remind readers that the objectives of the Slot Rule and/or Simborg rule are listed below, and that, as I stated in my original post, my main objective in recommending the Slot Rule is (1), my secondary objective is (2), and, "I don't really care about (3), though I can see how it might be viewed as a benefit."

(1) Make games more exciting/complex through increased chance of recirculation.
(2) Create interesting new decisions on the first two or three rolls of the game.
(3) Decrease the advantage (luck) of getting the opening roll.

As Bob Koca implied (in his inimitable interrogative style), equalizing the first and second player's equity in obtaining the opening roll largely just shifts the kind of luck involved. Further, IMO, there is so much luck in backgammon anyway, that trying to minimize the first player's advantage and/or reduce the volatility of the first player's roll is like trying to plug one's finger into a dam.

In other words, to be clear, my enthusiasm for the Slot Rule has not diminished one iota. I only analyzed and summarized the (in my view) unimportant detail of (3) in response to Matt R's inquiry. Having done so, I naturally felt obligated to correct my earlier misinformation.

Nack

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