Let's take position 574 as an example. We will assume you play
$10 a point and the rake is 5%, with the winner paying 10% (also
paying the 5% for the loser), a very common setting in today's
backgammon online industry. The following calculations are
based on the assumption, that you have at least $80 at the table,
the maximum amount you could win or loose, when you decide to
double.
From the equities shown we see, that we should redouble for
money. Let's quickly verify that and calculate the equities.
Position 574, Category Bear Off
Roll or Double?
Black vs White
Moneygame: Jacoby and Beaver
added at 3/7/2010 9:34 AM, from admin
Pipcount: 7(+1) - 6(-1)
Evaluation Level: 7 ply
Winning Chances:
| Player: | 66.17% | 66.17% | 0.00% | 0.00% |
| Opponent: | 33.83% | 33.83% | 0.00% | 0.00% |
Cubeful Equities:
| No Double: | +0.326 | -0.032 |
| Double / Take: | +0.358 | best |
| Double / Drop: | +1.000 | +0.642 |
Best Cube Action: Double / Take
Cubeless Equities:
| No Double: | +0.323 |
| Double: | +0.647 |
Software: eXtreme Gammon Version: 1.12
From the equities shown we see, that we should redouble for
money. Let's quickly verify that and calculate the equities.
Calculations without rake
Let's assume you play live and there is no rake.
To calculate your equity, you have to look at the next 2 shakes,
36 x 36 = 1296 games. You have 17 direct wins
(66,65,64,63,55,54,53,44,43,33,22), after your 19 misses, white has
23 winners and 13 losers (43,42,41,32,31,21,11)
(Note after the sequence 2-1 followed by a miss from white, you
always redouble and cash the game)
Your equity when you don't double:
|
cube
|
1st roll
|
2nd roll
|
payout
|
$/point
|
total
|
|
2
|
17
|
36
|
100%
|
$10
|
$12.240.00
|
|
2
|
19
|
13
|
100%
|
$10
|
$4.940.00
|
|
2
|
19
|
23
|
-100%
|
$10
|
-$8.740.00
|
|
|
|
|
sum
|
$8.440.00
|
|
|
|
|
equity
|
$6.51
|
Your equity is $6.51, exactly the value, the software displays
(+0.326 x 2 x $10)
Now let's calculate your equity, when you double:
|
cube
|
1st roll
|
2nd roll
|
payout
|
$/point
|
total
|
|
4
|
17
|
36
|
100%
|
$10
|
$24.480.00
|
|
8
|
19
|
13
|
100%
|
$10
|
$19.760.00
|
|
8
|
19
|
23
|
-100%
|
$10
|
-$34.960.00
|
|
|
|
|
sum
|
$9.280.00
|
|
|
|
|
equity
|
$7.16
|
Here your equity is $7.16, exactly the value, the software
displays (+0.358 x 2 x $10)
If you compare these two actions, you see that doubling
wins on average $0.65 (=$7.16-$6.51) more, therefore you should
absolutely double.
Calculations with rake
Now we do the same calculations with the assumption of 5% rake.
Please note that the winner has to pay the rake for both players
(10% total), as the loser pays no rake.
Your equity when you don't double, with rake:
|
cube
|
1st roll
|
2nd roll
|
payout
|
$/point
|
total
|
|
2
|
17
|
36
|
90%
|
$10
|
$11.016.00
|
|
2
|
19
|
13
|
90%
|
$10
|
$4.446.00
|
|
2
|
19
|
23
|
-100%
|
$10
|
-$8.740.00
|
|
|
|
|
sum
|
$6.722.00
|
|
|
|
|
equity
|
$5.19
|
With the rake your equity drops from $6.51 to $5.19.
Now the calculations when you do double, with rake:
|
cube
|
1st roll
|
2nd roll
|
payout
|
$/point
|
total
|
|
4
|
17
|
36
|
90%
|
$10
|
$22.032.00
|
|
8
|
19
|
13
|
90%
|
$10
|
$17.784.00
|
|
8
|
19
|
23
|
-100%
|
$10
|
-$34.960.00
|
|
|
|
|
sum
|
$4.856.00
|
|
|
|
|
equity
|
$3.75
|
As you can see, your rake adjusted equity is only $3.75.
Redoubling this position actually costs you $1.44 on
average, therefore redoubling is a big mistake (eq.:
-0.072).
What is the reason for this?
If you miss, your opponent has a very effective redouble that
you must take. When you get lucky and win these games you pay much
more rake.