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Average number of rolls to come in from the bar against a four-point board

Posted By: rambiz
Date: Friday, 8 March 2024, at 5:20 p.m.

In Response To: Position of the Day 02-28-24 - All options cube (Bob Koca)

Please proof read the calculations below at your leisure.

Let E1=Avergage Number of rolls to come in against a four-point board with one man on the roof
E1=20/36+16/36*(1+E1) ---> E1=36/20=1.8 rolls

Let E2=Avergage Number of rolls to come in against a four-point board with two men on the roof
E2=4/36+16/36*(1+E1)+16/36*(1+E2) ---> E2=(36/20)^2=3.24 rolls

Let E3=Avergage Number of rolls to come in against a four-point board with three men on the roof
E3=2/36+2/36*(1+E1)+16/36*(1+E2)+16/36*(1+E3) --->E3=4.572 rolls

Let E4=Avergage Number of rolls to come in against a four-point board with four men on the roof
E4=2/36+2/36*(1+E2)+16/36*(1+E3)+16/36*(1+E4) --->E4=5.7816 rolls

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