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

BGonline.org Forums

LV Finals Play #1 ROLLOUT

Posted By: Sam Pottle
Date: Thursday, 4 December 2008, at 8:21 a.m.

In Response To: LV Finals Play #1 ROLLOUT (Matt Cohn-Geier)

White should run after either play if he rolls a 6. There are 5 numbers after either play where he should stick around: after 2/1*, it's 33, 23, and 42; after 3/2, it's 11, 31, and 41. If White sticks around, I have 5 numbers to win a BG after 3/2 vs. only 4 to win a BG after 2/1*.

There are lots more BG's than that. This first exchange accounts for 25/1296 backgammons after 3/2, and 20/1296 backgammons after 2/1*, or 1.9% and 1.5% respectively. Compare this to the rollout results of 4.1% and 3.2%.

I analyzed the positions with Blue on roll, after White has already failed to escape. From here, Blue's 5 BG numbers (after 3/2) account for 180 games out of 1296. I got a total of over 297 backgammons from this position. Most of the extras come from two variations: Blue rolls 1x (3/2/off), White fails to escape, Blue bears off (about 72 games); and Blue blots, White rolls 32 (40 games).

Similarly, if Blue plays 2/1* and White enters and stays on the deuce point, Blue gets a bunch of extra BG wins on his many nonblotting numbers, when White has 5 rolls of fewer than five pips.

Blue wins lots more backgammons when White dances with 33; this raises the average result after 2/1* to around 278 backgammons. So the difference between the two plays is about half that suggested above (20 backgammons in 1296 games vs. 1 in 36 games).

However, I have 20 numbers that leave a shot after 3/2, vs. only 10 after 2/1*.

Only if White entered. If he danced, Blue leaves a shot on 23 shakes. This is the case only 1/5 of the time that White keeps contact, so the difference in shots left is still almost 8 (instead of 10).

So, none of these nits affect Matt's conclusions: 3/2 wins a few more backgammons, but gets hit significantly more often. The numbers work out to all of 0.2% and 0.9%, respectively, which is why they're dominated by White's greater winning chances after a hit (after 2/1*).

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.