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A Newbie's Neil's Numbers alternative

Posted By: Kevin Whyte
Date: Saturday, 27 August 2011, at 5:32 a.m.

One of the first things I ran into when starting to look at backgammon seriously was a match equity table for matches up to 11 points. I spent awhile trying to find a pattern and came up with a formula that I thought was pretty close. After wasting as much time as I did finding it, it is pretty much etched into my brain so I still use it even though it isn't so great, On the off chance someone else might care, I'll share it (but you should just learn NNN).

Anyway, I was so new to the game when I came up with this that instead of using language like 2-away 3-away I just converted everything to the corresponding 11 point score ( so that would be 9 to 8). In what follows I'll call those "scores". With that said, my formula:

equity = (score diff)/(10 - (product of "scores")/14)

So 2-away 3-away is an equity of 1/(10-72/14) = 7/34 = .20588... (I think most ME tables have this around .2, so not bad).

If one player is 11-away their "score" is 0, so the formula just say .1 in equity (or 5% winning chances) per point the leader is ahead. If Neil's number at 11 is 5 then they agree here.

One more example that's easy to compute: at 4-away, 9-away (so "scores" of 7 to 2) it gives an equity of 5/9, or a winning chance of 7/9=77.777% and I think the right answer here is more like 79%.

It definitely doesn't work very well at 1-away, but otherwise does a decent job, I think. I haven't checked it against any more modern MET, and never looked at how it works for matches beyond 11.

Messages In This Thread

• A Newbie's Neil's Numbers alternative
  Kevin Whyte -- Saturday, 27 August 2011, at 5:32 a.m.
  • A Newbie's Neil's Numbers alternative
    Gregg Cattanach -- Wednesday, 31 August 2011, at 12:30 p.m.