Game 6, move 21 : roadkillbooks 2-2 *plus end of the game *

[diane]

I will let rkb decide what he wants to do with this one  

rkb, white, to move 2-2

u90GACB2AAAAAA:sAGpACAAIAAA

[roadkillbooks]

Ok here if i bear two off forum has seven rolls that miss and don't get out of my inner board 24,41,51, 11.. I can then win backgammon with 22 or better. so thats 35 backgammons in 1296 games..slightly more becasuse after 11 ther is the chance that forum wont save on the second roll as well.  It also leave me 2 extra hit numbers..any 3 plus 2-1.  If I am hit i have an extra piece of the board.

with 3/1 hit with 3 and 2 off.  I pull one piece off and I will win BG with a 11,31,41,51.. seven numbers followed by a 22 or better... so there Im the same.  I am only hit with 11 numbers.  Either way there is no practical way for forum to pick up a second blot..although it would be esier leaving only 2 on the one but that possiblilty is close to nil...

so even though Im not pulling off an extra piece Im gonna go for..

I can see myself making a chart of chances of victory with a hit straggler and pieces on the ace point after this.  Since I can type I suppose Im allowed to use a pen and paper..but maybe not..Im not sure so I wont now.

But in a less than perfect bear in.. if I had 5 pieces off and closed out Id be 25%.

with 8 pieces off im about even...

with 14 pieces im like 94%... a double is between  10 pieces off is a money double so say 75%

so 4 left on one point 75%
    1 left on one point 94% a difference of 19% so each piece in between is worth about 6.5%

so if im hit ill lose 12.5% of the times if I leave 2 on my 1 point
ill lose 19% of the time if I leave 3 one my one point.

So a crossover of 1296 games would be 11/36 times 19% versus 13/36 times 12.5%
12.5% is 4.5 games..19% is more than 6.5 less than 7 (sorry about this incoherent rant I promise to do a good table with pen, paper, and non wild ass guesses)

13/36 x 4.5/36 versus   11/36 x 7/36  or 58.5 versus 77 even if I do 6 its 58.5 versus 66 so the 13 shots is better.
Now Im confused but I got to go and the answer is actually not the one I was going to do but those are approx the number of games out of 1296 that forum will win in the situation. It is clearly better to bear the extra piece of.  I obviously need to speed those calucuations up in the future and its too bad I cant use my computer at the table...
3/1*(2), 2/off (2)

[diane]

I will reply here, so we can start the next game in a new thread.

The next few rolls played out as nexts...and the Forum saved the gammon - see the plays below.