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BGonline.org Forums
OLM 20140602A The Prime Factors -- CONSULTATION
Posted By: Bob Koca In Response To: OLM 20140602A The Prime Factors -- CONSULTATION (Jason Lee)
Date: Tuesday, 3 June 2014, at 6:39 p.m.
A deeper look strengthened my opinion that 5/o is best.
Issue 1: How close is the gammon race?
Their raw count to run off the gammon is 37. From boot camp I think the wastage when running a single checker is 4. With a checker on the 7 and two stragglers it will be a little higher. 1/4th of the time they cannot run the back guys at all and gain only 1 or 2 gammon race pips instead of on average about 5. There may be plays a couple rolls down the line where they waste a little more in order to keep the straggler for one last possible shot. Also they get hit and lose 2 pips in a few variations. Overall wastage is probably a little larger than 6. For an effective gammon count of a little more than 43.
Suppose we bearoff 5/o. Wastage for a flat 12 pip position is 10 and we will be a little worse than that with 6's wasting a pip. Also we will sometimes need to play blotless while he still has a back checker and waste more pips. I will call it wastage of a little more than12. Our effective count is thus a little more than 43.
ii) Issue 2: How much does the greedy play help our gammon race?
The gammon race is very close. It feels strange to agree with Keene over Neil but I think they errored last turn by not running one. In a close race of this length an effective pip is worth about 4%.
Getting an extra checker off gains about half a roll on average. Moving up with the ace does not completely waste it. The gain will be close to 4 pips. If it was just a race about 15% gammons would be swung. After either play we will be hit about 1/5 of the time so of the 80% where it is just a race I estimate about 12% gammons swung by playing 5/off instead of 5/1 4/3.
Issue 3: What is our gammon value?
Winning a single game on 2 cube puts us at 3a 7a for about 76.5% Winning a gammon on 2 cube puts us at 1a 7a for about 91% for a gain of 14.5% Losing a single game on 2 puts us 5a 5a for 50% for a loss of 26.5%. The gammon price is slightly higher than usual 0.5, about .54
Issue 4: So how many additional losses balance the gammon gains?
12% *.54 is about 6.5% additional losses.
Issue 5: How many additional losses are there?
Taper Mike already talked about extra blotting rolls after 5/o. I have a few things to add to that portion of the analysis.
i) Usually they run one checker and this removes 33 as a blotting roll for both plays.
ii) Most of the immediate blotting numbers for both plays thus hit. Most of the misses force him to enter behind us ending forever our shot danger.
iii) The cube will usually be strong if there is a hit in the next sequence. However this is not the case for delayed hits. There will probably be an extra checker off after a delayed hit coming after 5/0 compared to 5/1 4/3.
iv) Points ii and iii show that the increased delayed hit chance is not as important as I think most are thinking.
v) If we ignore any delayed hit danger the swing as Mike wrote is about 1 loss in 36 games which is less than 3%. This is far from the 6.5% needed to make the safe play correct.
When I gave my first answer I just did enough to notice the gammon race is close and that there were three more immediate shots and used a rough recollection from playing bots that it is right to go for it.
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