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Historic BG Quiz problem 1

Posted By: Chuck Bower
Date: Saturday, 30 August 2008, at 11:11 p.m.

In Response To: Historic BG Quiz problem 1 (Chuck Bower)

First instinct was 13/10. But then I noticed how much trouble White could have safetying that back checker. Staying on the 13-point is 15 shots (most -- 13/10 is 11 -- least).

Staying on the 13-point results in direct shots for Blue 15/36 times: {6-6, 6-5, 6-3, 6-1, 5-1, 5-2, 2-1, 3-2}. Moving to the 10-point leaves three directs {6-5, 6-6} and quite a few indirects {2-3, 2-4, 2-5, 3-4, 3-6, 4-5} = 12/36 which is crudely equivalent to about 5/36 directs, so call it 8/36 directs. Tweener plays leave in between number of shots.

Does Blue need the 5-point? Most of the time. Can Blue make it without the immediate slot? Yes. Often enough? Not sure. It seems like slotting the five might not take full advantage of Blue's cube ownership. (I say "seems like...".)

Estimating Blue's wins by both paths: let's say 15% without an immediate (Blue) hit and 50% with an immediate hit. Similarly, I estimate 20% increase in gammons if White hits. So, 35% wins gain (going from -2 to +2 -- swing of 4) vs. 20% gammon losses (going from -2 to -4 -- swing of 2) means gain 1.4 while risking 0.4 trading shot for shot. That's a 3.5::1 trade (White's shots for Blue's shots). Looks like a no-brainer to leave the extra shots; in fact the max shots (by staying on the 13-point).

So now it comes down to whether or not to slot. Slotting play is 8/5. Non-slotting plays are 6/3 (no homeside shots; 2 builders for the 5-point) and 8/7, 6/4 (6 homeside shots and 3 builders for the 5-point). That's a difference of six immediate shots for an extra three immediate building chances. Doesn't seem worth it.

So, 8/5 or 6/3. Tough choice. Because of the cube location I think 6/3 is going to be good enough to win by hitting.

Finally, what about the tweener plays, leaving fewer immediate shots than staying put on the 13-point but not the minimum number of immediate shots (by moving to the 10-point). Based on the tradeoff numbers I calculated, they don't appear to be worth it.

Conclusion: 6/3.

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