[ View Thread ] [ Post Response ] [ Return to Index ] [ Read Prev Msg ] [ Read Next Msg ]

BGonline.org Forums

Show all of your work

Posted By: Daniel Murphy
Date: Monday, 22 August 2011, at 11:36 a.m.

In Response To: Show all of your work (Bob Koca)

Look at each 2 roll sequence and for each look at gain/loss from doubling now.

Ok, but that's 1296 sequences, each looked at for double vs. no double. How would you do this with a minimum of computation and not giving up too much accuracy?

This gets tedious, more so having to write it out, but:

If we know out MET, then we know that when this game ends we will have either 0%, 4%, 33% or 57% match equity. We've also estimated that we win about 25% cubeless.

Our rolls are of 4 kinds:

(a) 2 are gin on the roll

(b) 12 will be gin next roll (D/P with 100% wins) if we get one. We'll get one about 25% of the time (26/36 = 27.7% of the time)

(c) 12 more will be D/P with about 80% wins. Again, that's 80% of the ~3 of the 12 where we actually get a next roll.

(d) Which leaves 10 rolls, the 5 rolls that don't bear off any checkers and the 5 rolls that give D/T (2-1, 3-1 and 1-1).

So that's:

(a) 2 wins double or no double out of 2 rolls

(b) 3 wins double or no double out of 12 rolls

(c) 2.4 wins double or 3 wins double, out of 12 rolls

(d) 1.6 wins (to total 25%) out of 10. Some of these wins are with a redouble next roll, but not many, and some by rolling a doublet next roll after no cube, so I'm going to lump them all together and treat them as if we either double now or never double.

Now let's bring in our match equities from wins and losses:

No double: 9.6 * 33% + 26.4 * 4% = 422.4

Double: 9 * 57 = 513

Conclusion: It's hugely correct to double now. Not doubling gives up over 2% MWC (R-K MET).

That all seems like a lot of work. That's why I didn't originally compare double now to double later. I just assumed that with some 26 market losers, doubling now would be right. But of course that really does depend on how much is at risk or to be gained. Stick wrote: "note how even changing the score to 7 away 13 away instead of 6 away 13 away will have a big effect on whether or not you should cube." At that score Double/win nets 63%, No double/win nets 39% and No double/lose retains 7%. So, with the same guesstimate as I used above, that's

No double: 9.6 * 39% + 26.4 * 7% = 559

Double: 9 * 63 = 567

Which would mean Double now is slightly right. It's actually slightly wrong at 13-away 7-away (with R-K MET) but not by much -- doubling would give up only 0.22% match equity.

Messages In This Thread

 

Post Response
Your Name:
Your E-Mail Address:
Subject:
Message:

If necessary, enter your password below:

Password:
 

 

[ View Thread ] [ Post Response ] [ Return to Index ] [ Read Prev Msg ] [ Read Next Msg ]

BGonline.org Forums is maintained by Stick with WebBBS 5.12.