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Why not double here?

Author Topic: Why not double here?  (Read 6794 times)

Offline zbilbo

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Why not double here?
« on: August 29, 2013, 10:21:06 PM »
Analyzing some stuff and at this position:

 GNU Backgammon  Position ID: aAEAQAYAAAAAAA
                 Match ID   : UwmgAxAAkAAE
 +13-14-15-16-17-18------19-20-21-22-23-24-+     O: expertBotII
 |                  |   | O  O  O          | OOO 1 point
 |                  |   |    O             | OO 
 |                  |   |                  | OO 
 |                  |   |                  | OO 
 |                  |   |                  | OO
v|                  |BAR|                  |     29 point match
 |                  |   |                  | XX
 |                  |   |                  | XX 
 |                  |   |                  | XX 
 |                  |   |       X          | XXX On roll
 |                  |   |       X     X    | XXX 18 points
 +12-11-10--9--8--7-------6--5--4--3--2--1-+     X: You (Cube: 8 )



I very much would like to double. So much in fact Im pretty sure opponent would reject.

Gnubg disagree very much, but I do double. Opponent takes... And I get a 54. The cause is lost and the opponent doubles still...

The question still remaining is: Why was it bad to double at that point?


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Why not double here?
« on: August 29, 2013, 10:21:06 PM »

Offline NIHILIST

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Re: Why not double here?
« Reply #1 on: August 30, 2013, 05:46:42 AM »
The score. You lead 18 - 1 to 29 and hold an 8 cube. By redoubling to 16 you create a situation called OVERAGE which basically means you can't use the full value of the cube, 16 points, cuz if you win on your roll you'd have 34 points, 5 more than you need to win.

Your opponent rewhips to 32 because he wins the match by rolling 6-6.

In situations where your redouble creates overage it's generally better to just roll.

Bob
Robert J Ebbeler

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Re: Why not double here?
« Reply #1 on: August 30, 2013, 05:46:42 AM »

Offline Julia_H

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Re: Why not double here?
« Reply #2 on: August 30, 2013, 09:10:02 AM »
Even without overage, with this sort of huge lead you want to keep the cube under as much control as possible. The bot's chances of grinding its way back into the match in 1's and 2's, even against a relatively weak player, is significantly less than its chances of rolling a joker with the cube turned up high. (Conversely, the further behind you are, particularly to a more skilful player, the more willing you should be to turn it into a crapshoot)

Offline dorbel

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Re: Why not double here?
« Reply #3 on: August 30, 2013, 10:51:00 AM »
Good cube action increases your equity. Bad cube action decreases it.

For X, no double/win means he leads 3-away, 28-away, for a Match Equity of 99% (actually 99.74%!).
Double/win means that he wins the match and goes to 100%, a gain of 1%.
No double/lose means that he leads 11-away, 20-away, for an ME of 82%.
Double/lose means that he loses the match (because 0 will redouble) for an ME of 0%.

We can see that doubling for X risks 82% to gain 1%. How big a favourite must X be in this game to make the bet cost effective? We do a risk/gain analysis. The formula is Risk/Risk+Gain or here 82/82+1 = 82/83 = 99%. X needs to win this game 99% of the time for a double to be correct. Can he do that? Pretty clearly not. If X rolls less than 4-4 (33/36) and 0 rolls 6-6 (1/36) that equates to 33/1296 losses which is 2.5% straight away and of course 0 has other winning sequences.

We can ignore future cube action if X doesn't double, because in fact he will never have a correct redouble. Cubeless, he wins this game 96% of the time.
If he doesn't double then his equity will be 96% x 99% and 4% x 82%, = ME 98%
If he does double, then his equity will 96% x 100% and 4% x 0 = ME 96%.

Good cube action increases equity, bad cube action decreases it. A redouble to 16 reduces X's equity from 98% to 96%. No double is correct.
The instinct to avoid massive overage provides the right answer. This is just the theory behind the instinct.

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Re: Why not double here?
« Reply #3 on: August 30, 2013, 10:51:00 AM »

Offline zbilbo

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Re: Why not double here?
« Reply #4 on: August 30, 2013, 11:10:19 AM »
The score. You lead 18 - 1 to 29 and hold an 8 cube. By redoubling to 16 you create a situation called OVERAGE which basically means you can't use the full value of the cube, 16 points, cuz if you win on your roll you'd have 34 points, 5 more than you need to win.

Your opponent rewhips to 32 because he wins the match by rolling 6-6.

In situations where your redouble creates overage it's generally better to just roll.

Bob

This "easy" explanation was exactly what I did not see. Your other mathematical explanation, I need somewhat more time to contemplate over ;-)

Thx!

Offline FancyPrince

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Re: Why not double here?
« Reply #5 on: February 06, 2014, 09:43:44 PM »
hello everybody. this is my first post here.. ;)i think it depends on your opponent's skill ! you have played some games and reached to 18...umm..so you know your opponent's playing power..if he is very strong player then you should double  :thumbsup2: else simply dont double and let match contiunes..

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