Backgammon Cube Handling in Races

Cube Handling in Races

Forum Archive : Cube Handling in Races

Thorp count

From:   Chuck Bower
Address:   bower@bigbang.astro.indiana.edu
Date:   23 January 1997
Subject:   Re: Thorpe count, was Re: Cube action?
Forum:   rec.games.backgammon
Google:   5c6eth$sf2@dismay.ucs.indiana.edu

Robert-Jan Veldhuizen wrote: > I saw the Thorpe count explained here a while ago, but the terms used > in that explanation were so ambiguous that I didn't understand it. > Could someone explain it to me please ? > (snip) > For instance, where does the 74 value come from ? The Thorp Count was popularized in Robertie's "Advanced Backgammon". This method was developed by Edward O. Thorp who is famous for his pioneering work "Beat the Dealer" which explained how to become a favorite at blackjack. Note that the CORRECT spelling is "Thorp" without an "e" at the end (even though Robertie misspelled it in both the 1st and 2nd editions of his classic). The method as described there is for money play only. I have since modified it for match play (and THIS is where the "74 value" comes from): Here is how I perform the Thorp Count (and basically how it is written up in "Advanced Backgammon") 1) Start with the roller's pip count. 2) Add 2 for each checker remaining on the board. 3) Add an additional 1 for each checker on the 1 pt. 4) Subtract 1 for each home board point covered. 5) If the result up to now is 30 or greater, multiply by 1.1. (Call this final result "R" for roller) Repeat steps 1-4 for the NON-roller, BUT NOT STEP 5. (Call this result "N" for NON-roller) Now, subtract R from N ( = T) and compare the result as follows: N - R .ge. -2, roller has an INITIAL double (centered cube); N - R .ge. -1, roller has a REdouble; N - R .le. +2, NON-roller has a take. (here ".ge." means "greater than or equal to", and ".le."--you figure it out!) As far as how to convert this to game winning chances, I noticed the following correlation between the Thorp Count (above) and the percentage cubeless game winning chances required to double/redouble/take as published in the classic (but hard to find) article "Optimal Doubling in BG" by Emmitt B. Keeler and Joel Spencer in OPERATIONS RESEARCH, vol 23 p. 1063(1975). Assuming Roller's pip count is 70, K & S say roller should do the following: Roller's cubeless Cube Thorp game winning chances Action Count 70% Double, Take -2 72% REdouble, Take -1 78% PASS +2 Now if you overlook the "singularity" at 78% (Thorp says "barely a take" and K & S say "barely a pass") you see that there is a linear relation between the cubeless game winning chances and the Thorp Count: W = 74 + 2*T (in percentage). Finally I assumed that you could "extrapolate" the result outside the 70-78% range. A study of bearoffs showed that this "Extened Thorp Method" works rather well (IN GENERAL) for winning chances in the range 55-85%. Happy (Thorp) counting! Chuck bower@bigbang.astro.indiana.edu c_ray on FIBS

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