On Saturday, February 26, 2022 at 11:35:33 AM UTC,
peps...@gmail.com wrote:
On Saturday, February 26, 2022 at 7:05:37 AM UTC, Stick Rice wrote:
On Friday, February 25, 2022 at 5:52:34 PM UTC-5, peps...@gmail.com wrote:
I Ohaganized this based on the juicy hits, but I was completely unsurprised by XG's hold verdict. I'm a favourite to hit so
I have tons of market losers but I think my problem is that
my misses are worse than I thought they were. Maybe missing
is about as good for XG as hitting is for me. So being a mild
favourite to hit is no reason to annoy the neighbours by
cranking up Irene Cara's hit song "Flashdance ... What a Feeling" at full volume.
Paul
XGID=---BBBBa----cE---ace---bB-:0:0:1:00:0:0:3:0:10
X:Daniel O:eXtremeGammon
Score is X:0 O:0. Unlimited Game, Jacoby Beaver +13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O | | O O X |
| X O | | O O X |
| X O | | O |
| X | | O |
| X | | O |
| |BAR| |
| | | |
| | | |
| O | | |
| O | | X X X X |
| O O | | X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 149 O: 120 X-O: 0-0
Cube: 1
X on roll, cube action
Analyzed in XG Roller+
Player Winning Chances: 56.66% (G:20.69% B:0.64%)
Opponent Winning Chances: 43.34% (G:10.34% B:0.47%)
Cubeless Equities: No Double=+0.238, Double=+0.497
Cubeful Equities:
No double: +0.296
Double/Take: +0.172 (-0.124)
Double/Pass: +1.000 (+0.704)
Best Cube action: No double / Take
Percentage of wrong pass needed to make the double decision right: 13.0%
eXtreme Gammon Version: 2.10
The opponent being a favorite to enter immediately when hit and you having little ammo to continue the attack are large factors. I think you may be overestimating the amount of market losing sequences you have. You have to hit and the opponent has to
fan.
I did actually realise that hit-fan doesn't lose the market, but I accept that my post might have hyperbolically
overstated this factor. All the 6s work which is 17 numbers. We add 52 and 34 to get 21 numbers. The dancing
probability is 4/9. This gives a market-losing probability of 26% (I did this accurately without a calculator in just
a second or two -- I'm ultra-good in mental arithmetic but weaker than Tim in backgammon.)
So we cross the O'Hagan threshold by a very small margin.
Clearly we have to adjust for the fact that our misses are bad rather than neutral, but I didn't do this.
So I think that, with more patience and more time, I could have OHaganized correctly. I'll do better next time.
Paul
Corrections:
As usual, my above post needs correcting.
One of the corrections is obvious.
However, the other correction is so egregious and shocking that it might be advisable
for people only to continue reading this post if they are seated and haven't eaten recently.
The obvious error is that I meant that "only hit-fan loses the market".
The shocking and unforgivable error is that, if we assume the above as a simplifying hypothesis,
I actually failed in the easy task of identifying the probability of a market-losing (hit-fan) sequence!!
How could I fail in such an elementary task??
I missed the fact that after 66, the opponent's entering probability is only 11/36, and not 5/9.
So we need to add 1/36 * (1-11/36 - 4/9) = 1/144. The correct market losing probability (with the simplifying assumption)
is therefore 7/27 + 1/144 = 1035/3888 which is just over 26.6%.
Paul
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