                   |
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| XGID=aDDBB-------------------b-:1:1:1:43:0:0:3:0:10 | |||||
| Blue to play 43 | |||||
| 1. | Rollout1 | 4/1 4/Off | eq: -0,653 | |||
| ||||||
| 2. | Rollout2 | 4/Off 3/Off | eq: -0,664 (-0,010) | |||
| ||||||
| 1 105453 Games rolled with Variance Reduction. Dice Seed: 7198980 Moves and cube decisions: XG Roller++ Search interval: Gigantic 2 105432 Games rolled with Variance Reduction. Dice Seed: 7198980 Moves and cube decisions: XG Roller++ Search interval: Gigantic | ||||||
eXtreme Gammon Version: 2.19.211.pre-release
The position 12 off and one bar. This is a beautiful position to work out and see were the equity in the position lies. I tried to calculate as far as i could go. I think i have better understanding of both the positions. So i calculated the equities of the position manually.
1-ply and 2-ply:
9 /36 = [33-,23-,31-] are fans (EQ? see 3-ply, 4-ply)
3 /36 = [44,55,66] are 99.99% loss EQ = -1 {Evaluation stops}
24/36 = [41+,51+,61+]
have an average of 7,875 pips after, but you have to set it lower because of the fact that you are underdog. So lets take an average of 7 (reason is race volatility). 31-7 = 23 Blue has an EPC of 43 vs White’s 23. So according white is going to have about 10% in the race. EQ = -0,8 {Evaluation stops, no contact}
3-ply and 4-ply:
Those 9/36 that flunked for white can lead up multiple scenario's:
1 /36 [11] :7 checkers off and 3 point board (4 N)|
2 /36 [12] :6 checkers off and 3 point board (5 N)|
5 /36 [22+] :8 checkers off and 2 point board (4 N)|
12/36 [34+,43+,53+,63+]:6 checkers off and 2 point board (5 N)|
16/36 [13+,23+] :5 checkers off and 2 point board (5 N|
Calculating the 4N – [11, 22+] 6/36 4 /36 white fans, blue is gin EQ = +1 {Evaluation stop}
32/36 white enters, he has about 33 pips before the roll and because he has no 11,12,22. I give him an average of 8,5. So average of 26,5 pips left after the roll. In racing equity it would be around 60% for white. So EQ = + 0.6 {Evaluation stop, no contact}
Calculating the 5N with 3 point board – [12] 2/36 9/36 white fans (see 5-ply)
27/36 white enters and on average he is still going to be big favorite. At 2-ply he was given an average of 7 pips due to volatility reasons. I am going to keep this figure to keep it simple. Blue now has an EPC of 36 vs White’s 26. So according white is going to have about 33% in the race. EQ = -0.34 - {Evaluation stops, no contact}
Calculating the 5N with 2 point board – [other] 28/36 4/36 white fans (see 5-ply, 6-ply)
32/36 white enters and on average he is still going to be big favorite. At 2-ply he was given an average of 7 pips due to volatility reasons. Blue now has an EPC of 36 vs White’s 26. So according white is going to have about 33% in the race. EQ = -0.34 - {Evaluation stops, no contact}
5-ply: 5/36 [22+] Is going to leave a shot. But it does make a 3N position with usually 5 checkers left. (see 6-ply)
1/36 [11] The true beauty of rolls, makes a 3N position with no shots given almost gin. Except when the opponent throws a 44,55,66. EQ = +0,9 {Evaluation stops}
30/36 [other] leaves a 4N position and a 2pt board. So calculations where already made at 4N! EQ = +0,6 {Evaluation stops, no contact}
6-ply: White is having a chance at a reshot from the bar. 11/36 hit, this is pretty much out of my possibility to calculate. So I checked XG for it and it said EQ = +0.35. It is also pretty deep in the calculation tree, so it won’t matter much. {Evaluation stops, too difficult}
22/36 [11,13+,33,34+,45+56], miss and lose instantly EQ = +1 {Evaluation stops}
1/36 [44] makes white a little bit underdog, leaving the checker on the 9 point. EQ = +0,3 {Evaluation stops}
2/36 [55+] makes blue an on roll: 3N vs 2N underdog. 25% win chance for blue. EQ = -0,5 {Evaluation stops}
MATH TIME
2-ply: (24/36 * -0.8) + (3/36 * -1) = -0.61667
4-ply: (9/36*6/36*4/36*1) + (9/36*6/36*32/36*0.6) + (9/36*2/36*27/36*-0.34) + (9/36*28/36*32/36*-0.34) = -0.03546
5-ply: (1170/36^3)*1/36*0.9 + (1170/36^3)*30/36*0.6 = +0.013166
6-ply: (1170/36^3)*5/36*11/36*0.35 + (1170/36^3)*22/36*5/36*1 + (1170/36^3)*5/36*1/36*0.3 + (1170/36^3)*2/36*5/36*0.5 = +0.002627
SUM TOTAL = -0,63633
This equity is pretty close to the value XG gives.
After analyzing this position, i think i draw a conclusion. There is still enough racing opportunity for blue. 4/off 3/off, gives 20/36 shots to almost lose the game EQ -0.936 avg. Getting an extra checker off doesn't compensate this fact enough. It seems very desperate to open an extra point and also give 20 shots instead of 0, with only a 2-point board left.
The position with the 14 checkers off the race is too bad to just clear.
Very interesting position, i just hope i understand it a bit better now.. and maybe i still don't :-)! Anyways, thank you for a nice reference position.