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OLM 20140531A The Prime Factors

Posted By: kruidenbuiltje
Date: Sunday, 1 June 2014, at 8:24 p.m.

In Response To: OLM 20140531A The Prime Factors (Bob Koca)

Hi Bob,

you are right with your first remark. I re-analysed it in a different way:

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Can we estimate the number of moves needed (on average) to bear off the checkers after each of the 2 variations?

After 4o 1o we have 31 pips left, 2 pips wastage for the extra checker on the 1-point, that's 33 pips.

And the effective average pips of each move are diminished. Normally it is 294/36= 8,17 pips.

But here with the 6's counting as 5's it is: 280/36 = 7,78 pips.

This is an average of 33/7,78 = 4,24 moves.

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Well how will this look after 5 off. Now we have 4 pips wastage = 35 pips.

The average number of moves is now 35/7,78 = 4,5 moves.

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So the difference between the 2 variations is only 0,26 moves on average.

In a gammon-race for white this counts as 2 pips which will make about 4% gammons.

Compared with the 4% wins, the risk of taking 2 checkers off is clearly too high.

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Just for fun I will calculate also now the 3rd variation which I didn't even see in the first place.

After 5/1 4/3 the pip-count becomes 37 pips.

That is 37/7,78 = 4,76 moves.

So the difference between 5off and 5/1 4/3 is again 4% gammons.

The blotting throws are: {D3,63,53,32} = 7/36 x 11/36 = 77/1296.

The difference in hits = 33/1296 = 2,5%. The difference in wins is lower than 1,25%.

In the normal gammon:win 2:1 ratio the risk would be allowed.

At this match-score the decision will be close.

Since 1off makes us even I tend to go for 5off.

So if we were to consult my new answer would be: 5off.

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You're second remark is also right. But since this "getting hit and thus getting gammoned",

occurs in all 3 variations it is hard to say if it will create a lot of gammon-difference between the variations.

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