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BGonline.org Forums
SNOWIE ROLLOUTS
Posted By: Matt Ryder In Response To: SNOWIE ROLLOUTS (Ray Kershaw)
Date: Wednesday, 6 January 2010, at 5:26 a.m.
I feel embarrassed by my lack of understanding but would like to ask where I can see a clear explanation of what the equity quoted in a Snowie rollout means.
Don't feel embarrassed: this stuff starts to get pretty hairy. I would recommend the crystal clear explanation concerning equity and rollouts provided in the introduction to Woolsey's Backgammon Encyclopedia.
The Win, Gammon, BG, Opp. Win, Opp. Gammon, Opp. BG figures are always cubeless outcomes, which means that the effect of the cube is ignored.
They may be used to calculate both 'cubeless' and 'cubeful' equities.
'Cubeless' equity is the absolute equity the player on roll has if the cube remains on 1 (but gammons and backgammons count). It assumes the cube is never turned so is estimated based on games reaching a natural bearoff conclusion.
A cubeless equity of .500 equates to a 75% win chance (cube value of 1 * .75) - (cube value of 1 * .25)
By contrast 'cubeful' equity is calculated with an included 'live' cube dynamic. It is derived from the cubeless figures by application of formulae developed by Rick Janowski. This starts to get increasingly complex, especially in match situations where there are varying takepoints AtS and limited opportunities to turn the cube.
Sometimes I can calculate the equity from the 6 probabilities (single, G and BG) but sometimes I cannot, even in a money game.
Push the icon that looks like a "$" to ensure you're viewing cubeless money equities.
I was initially perplexed by one thing:
Woolsey and various others (including the GNU manual) suggest that cubeless equity may be calculated from the 6 probabilities as follows:
(3 x player on roll backgammons) +
(2 x player on roll gammons) +
(1 x player on roll [plain] wins) -
(3 x opponent backgammons) -
(2 x opponent gammons) -
(1 x opponent [plain] wins)
This is true, but it should be clarified that this calculation only works if you separate out the figures you get from the bot first. You must remember that the 'wins' figure from the bot already includes gammons and backgammons (it represents the total chance of winning in any way). So these must be subtracted for the above formula to work.
In practical terms then, using the inclusive numbers outputted by the bot, the following simple formula works to calculate cubeless equity:
(player on roll backgammons - opponent backgammons) +
(player on roll gammons [including BGs] - opponent gammons [including BGs]) +
(player on roll [total] wins - opponent [total] wins)
Good luck!
Matt R.
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