BGonline.org Forums

Rolls vs. Pips algorithm

Posted By: rambiz
Date: Monday, 25 April 2011, at 8:55 a.m.

In Response To: Rolls vs. Pips algorithm (rambiz)

Thanks to Bob Koca's proof reading, the average EPC gained by the no-miss side turns out to be exactly the same number as it is for the pipish side, namely 49/6~8.167.

(5/6)*7+(1/6)*2*7=49/6

So there is no intrinsic advantage for the no-miss side regarding the mean. Sigh of Relief!

Now the examples again with the modified code. Hopefully, it works now also for the cases, when the no-miss side is behind in the race:

Example 1:

White	48
Blue on roll	12
Position ID: dHcAAPh/AAAAAA Match ID: cAkAAAAAAAAA

Cube decision
4-ply cubeless equity		+0.858
	0.929 0.000 0.000 - 0.071 0.000 0.000
Cubeful equities:
1.	Double, pass	+1.000
2.	Double, take	+1.677	+0.677
3.	No double	+0.972	-0.028
Proper cube action:		Double, pass

The algorithm works: RollsVsPips(6,55)=0.915

Example 2: (The Trice Prop)

White	50
Blue on roll	30
Position ID: uHcAAPi+DwAAAA Match ID: cAkAAAAAAAAA

Cube decision
4-ply cubeless equity		+0.261
	0.631 0.000 0.000 - 0.369 0.000 0.000
Cubeful equities:
1.	No double	+0.415
2.	Double, pass	+1.000	+0.585
3.	Double, take	+0.311	-0.104
Proper cube action:		No double, take (15.1%)

The algorithm works: RollsVsPips(8,57)=0.623

Example 3:(Blue is behind in the race)

White	15
Blue on roll	8
Position ID: qAAA8A8AAAAAAA Match ID: cAkAAAAAAAAA

Cube decision
4-ply cubeless equity		-0.508
	0.246 0.000 0.000 - 0.754 0.000 0.000
Cubeful equities:
1.	No double	-0.783
2.	Double, pass	+1.000	+1.783
3.	Double, take	-1.635	-0.852
Proper cube action:		No double, beaver (32.3%)

The algorith works better now: RollsVsPips(4,20)=0.286

In comparison, the old value with the flawed mean value for the no-miss side was: 0.325 . Maybe the inaccuracy left is due to the relative short length of the race, so that the normal approximation doesn't apply well. Let's try a longer race:

Example 4: (the no-miss side is behind in a middle long race)

White	30
Blue on roll	12
Position ID: 2AYAgP8HAAAAAA Match ID: cAkAAAAAAAAA

Cube decision
4-ply cubeless equity		-0.235
	0.383 0.000 0.000 - 0.617 0.000 0.000
Cubeful equities:
1.	No double	-0.310
2.	Double, pass	+1.000	+1.310
3.	Double, take	-0.825	-0.515
Proper cube action:		No double, beaver (28.2%)

The gap between the true winning chance and the one reported by the algorithm closes: RollsVsPips(6,36)=0.395

Messages In This Thread

• Rolls vs. Pips algorithm
  rambiz -- Sunday, 24 April 2011, at 11:52 p.m.
  • Rolls vs. Pips algorithm
    Bob Koca -- Monday, 25 April 2011, at 12:50 a.m.
    • Rolls vs. Pips algorithm
      rambiz -- Monday, 25 April 2011, at 7:56 a.m.
      • Rolls vs. Pips algorithm
        rambiz -- Monday, 25 April 2011, at 8:55 a.m.