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BGonline.org Forums
XG and Luck ~ VR and the pitfall of equity based luck.
Posted By: eXtreme Gammon In Response To: XG and Luck (DJansen)
Date: Friday, 17 August 2012, at 3:35 a.m.
Error and Luck data are derived form 2 different measurement so luck+Skill=result is not a correct assumption.
Very early version (far before release) of XG was calculating luck using "best known value of the position before roll"-"Best known value of the position after roll".
I reverted, before release, to the usual system: Luck="N-ply value before roll"-"(N-1)-ply value after roll".
UBK will tell you this system as the great interest of not depending on what the computer suggests to play. I agree, this is the best way to measure luck: in the grand scheme of thing Luck measurement (in MWC) is 0 biased, like VR in RO. How good the evaluation is, determines how accurate Luck calculation is reliable, but in all case it is not biased.
About Equity based luck: just imagine the following 25 point match played by 2 players who do not make mistake :
- player 1 win 16 games in a row with cube at one (always getting the joker that make the game switch from not good enough to double/drop): luck equity gained is +1.000 for each of the 16 games. Total luck for Player 1=+16.000
- game 17 start: player 1 get enough luck to reach his equity to +1.000, doubles, opponent takes the optional drop. Total luck for Player 1=+17.000
- Still game 17, cube 2: player 2 gets lucky and reach a position where is equity is +1.000. doubles/take Total luck for Player 1=+15.000
- Still game 17, cube 4: player 1 gets lucky and reach a position where is equity is +1.000. doubles/take Total luck for Player 1=+17.000
- Still game 17, cube 8: player 2 get lucky and reach a position where is equity is +1.000. doubles/take Total luck for Player 1=+15.000
- Still game 17, cube 16: Cube is dead.. player 2 is still lucky and win a gammon and the match: Total luck for Player 1=+13.000 (gammon price @-9/-25 is 1.000)
So overall Player 1 had a largely positive luck per move (+13/moves), but in term of MWC he lost -50%/move and was unlucky (which is what matter on that single match)
This is, obviously, an extreme example of the difference between equity and MWC. but you can have the same thing happening on a 3-pointer.
On the long run (hundreds if not thousands of games) both will converge to the same value. using Equity has, however, and big interest: it allows to merge luck for money game and matches.
PS: It's late and hope i did not make any calculation mistakes
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