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Daily Quiz 2/16

Posted By: kruidenbuiltje
Date: Thursday, 16 February 2012, at 2:08 p.m.

In Response To: Daily Quiz 2/16 (Daily Quiz)

Daily Quiz 16 february 2012

Number 1:

Purely based on his position (even without the threat), blue already has a double, but the race and the 4-point board give white a take.

After hitting and white entering without a hit, white’s race-advantage is too low and he will have to pass.

Answer: DT

Number 2:

The extra contact after playing 18/15 should create extra hits (and wins) for blue to compensate for the extra lost gammons after being hit.

The white hits: (15,D1,31,21,35,D3,32) have on average 4/36 returns: 12/36 * 4/36 = 48/1296

But the moves D3 and 31, would be more problematic for white when black would have played 3/1 2/1, then black would have a 18/36 hit: 3/36 * 18/36 = 54/1296.

So it seems that the extra contact here creates less wins and more lost gammons. The main reason for this is that the most awkward moves after the contactplay (D6 and 63) are equally awkward after the non-contact-play.

Answer: 3/1 2/1

Number 3:

The chance of blue turning this into a win by staying another move is very low, but on the other hand the chance of white gammoning blue in either variation (staying or running) is very low as well.

Lets make an estimation of both chances:

After running (21/15) white can gammon by throwing 2 doubles in 3 moves (chance about 3%) and blue has to throw 2 low moves in a row (on average less than 5 pips) (chance about 15%): Gammonchance 0,45%.

After staying white still has to throw 2 doubles to get a gammon, but now blue has to throw 2 medium moves (on average), chance about 50%: Gammonchance 1,50%.

Now the other half of the equation, the chance of blue to win: 1. White throws (61,51,41) = 6/36. 2. Blue hits 11/36. Total chance 1. and 2. = about 5%.

To compensate for the extra gammons (1,05%), blue needs to win 0,525% (at equal score), so blue needs to win in 10,5% of the case after he has hit. Because 10,5% * 5% = 0,525%.

One of ways Blue can win is when white stays out for a while. The chance of staying out trice is 16/36 ^ 3 = 8,8%. By then blue is a clear favourite to win, on top of that blue has the chance of containing white in the outfield, let’s add because of that a third to this number: that brings us to about 12%.

Answer: 6/1 5/4

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