FIBS Board backgammon forum

Pay now or Pay Later? 

15/6 is the "pay now" option.  We start to clear our back point by moving one checker te safety.  We leave 2 blots, but we duplicate 2s, reducing the number of shots to 16.  (did I get it right this time?)  rkb has a four point board with a blot, which will soon become a 5 point board - if we're going to be hit, now is better than a move or two from now.

There are two "pay later" options: 7/3, 6-1 and 7/2, 6/2.  I don't see much difference between the two, so I'll consider them together as the "safe play".  The safe play puts off leaving a shot for another move.  Unfortunately, there are few rolls that force rkb to leave a shot.  It looks pretty likely that safe play will just cause us to leave a shot (or 2!)  next roll.

Still, two blots are harder to clean up than one, and two checkers on the bar is very gammonish.  That steers me to the safe play, even though we'll probably be paying soon against a 5 pt board.

So, which safe play?  Spares on the 3 and 1 look slightly better than two spares on the 2, so 7/4 6/1

er, that option isn't there, but I think I get the gist  :blink:
agree about pay now or later though - and I am going for later too  ;), albeit a different way!

Quote from: diane on August 24, 2009, 10:35:58 PM
er, that option isn't there, but I think I get the gist  :blink:
agree about pay now or later though - and I am going for later too  ;), albeit a different way!

Yeah, I meant 7/3, 6-1. Sloppy typing.

Anybody care to offer an opinion on why 7/2, 6-2 is better?  I doubt there's much difference, but I'm curious what would point most votes in that direction.

Working as I do with every move, when there is something I dont like, I eliminate the worst cases until we have a least unpleasant option.  The 6-1 is the one I dont like, because putting checkers on the ace point, particularly when it is stacking and not making a point, whilst we still have men out there to bring home, feels like a bad idea.  I did angst over this one for ages and then go with my gut feel - it would be nice to see if there is an answer to whether there is any real advantage to 2 on the 2 point over 1 on the ace and 1 on the 3?
It is one of the things I considered when I was making up the poll, it would be nice to see this discussed and reasoned out.

Quote from: diane on August 25, 2009, 01:33:11 PM
The 6-1 is the one I dont like, because putting checkers on the ace point, particularly when it is stacking and not making a point, whilst we still have men out there to bring home, feels like a bad idea. ... it would be nice to see if there is an answer to whether there is any real advantage to 2 on the 2 point over 1 on the ace and 1 on the 3?

Agree that burying a checker by placing a spare on the 1 point is not very useful in a contact position.  But spares on the 2pt are just as "burried" when the one point is already made - there's nowhere for them to go other than  off or the one point.  My take is that a spare on the 3 allows us to "waste" a 2 roll at some point which might be useful if we get an awkward roll. Stacking the 2pt only allows us to waste a 1 roll.  The slightly more flexible position steered me towards the spares-on-3-and-1 play.

As I said, I doubt there's much difference between the plays, but seeing how lopsided the vote is I feel I must be missing something...

Ah_clem - I think you're right. Leaving the spares on the 3 point allows us to play either four '1s' or two '2s'. In contrast, the alternative move allows  four '1s' but only one '2'. 

As someone who played 6/2, my reasoning at the time was: we want flexibility --> spares generally equal flexibility --> a checker on the ace by definition is not a spare --> pile them on the 2 point.

I suspect this train of thought was fairly common...

Paying now has something going for it with the duplication of twos and a tough position to bring home if we don't pay. Still, I don't like the two blots it leaves. We can survive getting hit ( as already happened before), but if both checkers get sent back we're in serious trouble.

rkb has to move too, and his next move might detoriate his position, making a future hit less damaging.

From the safe moves, it looks like a wash between 7/2 6/2 and 7/3 6/1. The latter gives us an extra two to play, but do we need more than one? Stacking two on the twopoint is likely a bit better in a race; checkers on the acepoint are the worst for that, and generally stacking on even points is more efficient for the bear off than stacking on odd points. If we get hit again and escape at some point, the race might become close and then it could matter. But that's quite a parlay and the difference will be very small anyhow.

So I think it's a cointoss; mine landed on 7/2 6/2.

Zorba is correct that paying now has merits.  It's gnubg's choice on both analysis and rollout. The safe plays are pretty close with the forum's choice ( stacking on the 2)  a close third.  Not a blunder though.

Why pay now? rkb has very few rolls that make him leave a shot, so we're probably going to be faced with clearing our trailing point next move.  Now we face a four point board with a blot and next move it'll probably be a 5 point board.  So now is our best chance to clear since it'll be worse later. The duplication of 2's is icing on the cake.




Analysis:

    1. Cubeful 2-ply    15/6                         Eq.:  +0.279
       0.642 0.079 0.001 - 0.358 0.050 0.001
       
    2. Cubeful 2-ply    7/3 6/1                      Eq.:  +0.257 ( -0.022)
       0.645 0.053 0.000 - 0.355 0.047 0.001
       
    3. Cubeful 2-ply    7/2 6/2                      Eq.:  +0.256 ( -0.023)
       0.643 0.055 0.000 - 0.357 0.051 0.001
        2-ply cubeful prune [world class]

Rollout

    1. Rollout          15/6                         Eq.:  +0.250
       0.630 0.078 0.001 - 0.370 0.065 0.001 CL  +0.341 CF  +0.250
      [0.001 0.002 0.000 - 0.001 0.003 0.000 CL   0.004 CF   0.005]
       
    2. Rollout          7/3 6/1                      Eq.:  +0.230 ( -0.020)
       0.629 0.055 0.001 - 0.371 0.062 0.003 CL  +0.293 CF  +0.230
      [0.001 0.001 0.000 - 0.001 0.002 0.001 CL   0.004 CF   0.005]
       
    3. Rollout          7/2 6/2                      Eq.:  +0.222 ( -0.028)
       0.626 0.055 0.001 - 0.374 0.065 0.003 CL  +0.282 CF  +0.222
      [0.002 0.001 0.000 - 0.002 0.002 0.001 CL   0.004 CF   0.005]
        Full cubeful rollout with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 867797248 and quasi-random dice
        Play: 0-ply cubeful prune [expert]
        Cube: 0-ply cubeful prune [expert]

Paying later looks like an error. Paying now wins a few more games, but most of all it wins 2.5% extra gammons, probably because of the possible exchange of hits.

    1. Rollout          15/6                         Eq.:  +0,2272
        61,78   8,19   0,16 -  38,22   6,60   0,33 CL  +0,3172 CF  +0,2272
      [  0,08   0,09   0,02 -   0,08   0,23   0,08 CL   0,0020 CF   0,0025]
    2. Rollout          7/3 6/1                      Eq.:  +0,1949 ( -0,0323)
        61,54   5,57   0,09 -  38,46   6,24   0,36 CL  +0,2643 CF  +0,1949
      [  0,08   0,11   0,01 -   0,08   0,16   0,08 CL   0,0020 CF   0,0024]
    3. Rollout          7/2 6/2                      Eq.:  +0,1946 ( -0,0327)
        61,48   5,66   0,10 -  38,52   6,13   0,42 CL  +0,2629 CF  +0,1946
      [  0,08   0,12   0,01 -   0,08   0,14   0,09 CL   0,0020 CF   0,0023]
        Full cubeful rollout with var.redn.
        2592 games, Mersenne Twister dice gen. with seed 866958214 and quasi-random dice
        Play:  2-ply cubeful prune [world class]
        keep the first 0 0-ply moves and up to 12 more moves within equity 0,16
        Skip pruning for 1-ply moves.
        Cube: 2-ply cubeful prune [world class]