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Advanced Backgammon #33 ANALYSIS
Posted By: Matt Cohn-Geier In Response To: Advanced Backgammon #33 (Matt Cohn-Geier)
Date: Friday, 19 September 2008, at 5:20 p.m.
7/6 is correct. This one surprised me when I first rolled it out (~ a year ago), I expected hitting to be clear.
Let's look game-by-game a la Robertie:
4/3*:Group 1: 63, hitting and escaping: White is a big favorite, but these aren't necessarily game-winning shots. 33, 43, 46 hit, after which Blue is again a favorite, so Blue can reasonably expect to win some of those games, but he also gets gammoned a fair amount. That means White wins about 1.5-2 games out of these 2.
33, hitting and making the 4 point or 3 point, is a lot better than most of the other threes. Let's say that White's total so far is 2.5/3.
Group 2: All other threes hit but don't escape. White is a slight favorite in those 11 games (well, he is a slight underdog to win, but his gammons outnumber Blue's). Let's say White wins 5.5 of the remaining 11.
Group 3: White enters but doesn't hit (13 rolls): White is around a 10% underdog, plus he loses occasional gammons somewhere. Let's give him 1 out of these 13.
Group 4: White dances (9 rolls): Now White is around a 10% underdog but he loses more than an occasional gammon. Let's say White wins 0/9 here.
All told: White wins 9 games out of 36, including gammons.
7/6:Group 1: White doesn't escape with any non-6 (25 rolls). A few of these are better than others, but breaking them up isn't worth it. Let's say that Blue wins 85% here with about 7% gammons, for about 88.5%. Out of 25, that's 22 wins, so White gets 3 wins here.
Group 2: 66 and 63: White is a big favorite here, but these aren't necessarily game-winning shots. 66 leaves White up by 16 pips in the race with Blue on roll, so effectively up 12 in an ~80 pip race. White has also wasted a bit more than Blue, say 4 pips or so. That means White is close to a redouble after 66 but Blue is also around a take (28%ish). After 63, Blue again has 4 shots from the bar, but can still take as long as he comes in. White may not even have a recube if Blue comes in. Blue wins maybe 30% of these. So we'll give White 2 out of these 3.
Group 3: 61 or 62: The race is even (i.e., Blue is ahead by a bit), and Blue has a direct shot = recube and close take, if the cube were on Blue's side. Let's say White wins 25% for 1 out of 4 games.
Group 4: White escapes with 64 or 65 and is slightly ahead in the race, but Blue is on roll and White is wasting, so Blue is effectively ahead. White owns the cube, so it amounts to about an even tradeoff: let's give White 2 games out of these 4.
All told: 8 games out of 36, including gammons.
Robertie's analysis is considerably accurate here (he gave White 10.5 wins after either play, not including gammons), but it turns out that 7/6 wins slightly more often, so it is best at money and also at DMP. 4/3* does jack up Blue's gammons but it also jacks up White's gammons by about the same amount (White wins a few more gammons than Blue, even).What are the factors that Robertie missed? Mainly White's wastage in the race and White's gammon chances if he hits.
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