| |
BGonline.org Forums
I see what you did, here.
Posted By: fomalhaut In Response To: How to calculate equity from probabilities (leobueno)
Date: Monday, 21 February 2011, at 7:59 p.m.
I think I've deduced the problem, here.
http://www.bgonline.org/forums/webbbs_config.pl?noframes;read=89753
I believe you copied the position in the above thread into GnuBG assuming that it was a double at money. (This is evinced by how you cited the cubeful equity amounts in net points, and not MWC.) However it is actually a redouble during a match at a specific score; these are very different things.
During money play, your 'market window', or the range of winning chances within which it is acceptable for both you and your opponent to take an offered double or redouble, is always the same: a static 25% to 75%. (Duly tweaked by gammons, of course.) This is because there is no set goal to reach: your only objective is to pile on as many points as possible. In match play, however, there is no added reward to winning the match by any more than the minimum required amount of points. This consideration is constantly affecting the cube and the chequer decisions of both players, with the leader leaning toward more conservative play and the trailer toward more aggressive; it slides up and down before each game according to the various scores reached in the match, as well as when the cube is notched during a commenced game.
So, as Bob Koca wrote earlier, your original numbers don't add up, because they do not pertain to the assumed scenario. This is neither a double nor a redouble at money—although it failed to augment communications that GnuBG did not readily provide you (and, consequently, us) with a value for the staggering volatility of the position.
If you want to evaluate this scenario as it occurred in the match, then copy the following line of text to your clipboard, open a fresh GnuBG window, and press Ctrl + V.
Position ID: 2W4DABa4rQ0CGA Match ID: UQkgATAACAAA
The board configuration from the diagram should appear. (If it makes things any easier, press the 'Direction' button should you not already be reviewing positions in clockwise play.) Now press 'Hint'. A window will open showing GNU's default analysis of the pending cube action. When you're done reviewing that, press 'Temp. Map'. The six-by-six grids shown represent the 36 possible rolls, and the colors of the squares represent what the resulting equity from the position will be if the player on shake makes the best possible play with any of those given rolls—the whiter the square, the lower the equity; the redder the square, the higher. The values within this range are defined at the bottom of the window. In this particular situation, that range is from 30.68% to 60.50%: a staggering disparity. This is because the position is highly volatile: something very good for Blue could happen on this next roll, or something not so good could happen. In particular, you'll notice a dark streak running from the bottom left corner of the right-hand diagram to the upper-right corner: that represents the scenario where White takes Blue's recube, and then Blue rolls a 7 to complete the prime. Blue then having the far superior timing, White's position would surely crumble first, and Blue would likely be able to coast to a four point win. When a position is this volatile, it is often correct to offer what might normally seem a thin or incorrect double for the risk of "losing one's market"—or improving so much on the next roll that your opponent would no longer be able to take a recube.
I hope this is helpful (and not patronizing). Please feel free to fire away if you would like clarifications.
fomalhaut
| |
BGonline.org Forums is maintained by Stick with WebBBS 5.12.