Match equity/take-point charts
William R. Tallmadge
I've received a few requests for a match equity table more
comprehensible than the last one I posted.
Here are two such tables. The first (expressed in points-to-go) was
calculated by Kit Woolsey (he's a school of backgammon thought!).
The second table is the minimum winning chance (in %s) to take
an initial double (2 cube). Gammons are NOT taken into account.
It it based on the percentages in table 1.
Table 1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 50 70 75 83 85 90 91 94 95 97 97 98 98 99 99
2 30 50 60 68 75 81 85 88 91 93 94 95 96 97 98
3 25 40 50 59 66 71 76 80 84 87 90 92 94 95 96
4 17 32 41 50 58 64 70 75 79 83 86 88 90 92 93
5 15 25 34 42 50 57 63 68 73 77 81 84 87 89 90
6 10 19 29 36 43 50 56 62 67 72 76 79 82 85 87
7 9 15 24 30 37 44 50 56 61 66 70 74 78 81 84
8 6 12 20 25 32 38 44 50 55 60 65 69 73 77 80
9 5 9 16 21 27 33 39 45 50 55 60 64 68 72 76
10 3 7 13 17 23 28 34 40 45 50 55 60 64 68 71
11 3 6 10 14 19 24 30 35 40 45 50 55 59 63 67
12 2 5 8 12 16 21 26 31 36 40 45 50 54 58 62
13 2 4 6 10 13 18 22 27 32 36 41 46 50 54 58
14 1 3 5 8 11 15 19 23 28 32 37 42 46 50 54
15 1 2 4 7 10 13 16 20 24 29 33 38 42 46 50
Table 2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1
2 30 29 20 20 22 24 21 20 25 22 14 17 20 25
3 25 30 23 26 23 20 22 21 24 23 27 25 29 20
4 17 35 25 26 26 22 25 24 22 27 25 20 22 25
5 27 29 26 25 28 27 26 24 26 24 27 23 27 22
6 25 29 32 24 25 26 24 26 24 26 25 21 23 27
7 29 24 33 23 26 27 25 26 24 25 22 24 27 25
8 23 26 33 22 28 25 25 26 23 24 26 24 25 29
9 25 21 33 24 26 26 26 27 24 25 26 22 24 25
10 19 24 33 21 29 24 27 29 25 25 26 28 24 25
11 25 23 27 24 26 25 29 25 25 25 26 28 24 24
12 20 27 25 27 25 28 26 26 26 21 25 26 22 24
13 29 25 20 31 21 29 24 28 28 22 26 28 24 24
14 17 29 22 27 23 27 25 24 29 24 28 29 25 25
15 20 20 25 33 27 25 21 25 25 29 24 29 25 25
MIKA JOHNSSON
>
> I've received a few requests for a match equity table more
> comprehensible than the last one I posted.
>
> Here are two such tables. The first (expressed in points-to-go) was
> calculated by Kit Woolsey (he's a school of backgammon thought!).
> The second table is the minimum winning chance (in %s) to take
> an initial double (2 cube). Gammons are NOT taken into account.
> It it based on the percentages in table 1.
Thanks a lot of these tables !
I wanted to comment a bit Table2:
One shouldn't trust too much on these figures, look for instance the figures
for 2-away n-away
> 2 30 29 20 20 22 24 21 20 25 22 14 17 20 25
Looks very strange, right ?
look for the sequence starting from 9-away 20 25 22 14 17 20 25
surely there can't be such jumps in taking equity.
This phenomen is understood when one remembers that the figures in Table 1 are
rounded figures. So for instance when counting the 2-away 12-away
one counts loss/(gain+loss) (94-93)/((100-94)+(94-93))=1/7= 14%
but if the real difference between 11-away and 12-away is 1.5%
then we get 1.5/(5.75+1.5) = 21% (I assumed both figures were rounded by 0.25%)
so there is huge difference between 14% and 21%, caused by a small 0.25%
rounding error in Table 1. This phenomen is ofcourse stronger when gain or loss
is very small (the proportion of possible rounding error is bigger)
-Mika
--
MIKA JOHNSSON
> 7In article <CJBy4...@acsu.buffalo.edu>, w...@acsu.buffalo.edu (William R. Tallmadge) writes:
>>
>> I've received a few requests for a match equity table more
>> comprehensible than the last one I posted.
>>
>> Here are two such tables. The first (expressed in points-to-go) was
>> calculated by Kit Woolsey (he's a school of backgammon thought!).
>> The second table is the minimum winning chance (in %s) to take
>> an initial double (2 cube). Gammons are NOT taken into account.
>> It it based on the percentages in table 1.
>
> Thanks a lot of these tables !
>
> I wanted to comment a bit Table2:
>
> One shouldn't trust too much on these figures, look for instance the figures
> for 2-away n-away
>
>> 2 30 29 20 20 22 24 21 20 25 22 14 17 20 25
>
> Looks very strange, right ?
>
> look for the sequence starting from 9-away 20 25 22 14 17 20 25
> surely there can't be such jumps in taking equity.
> This phenomen is understood when one remembers that the figures in Table 1 are
> rounded figures. So for instance when counting the 2-away 12-away
> one counts loss/(gain+loss) (94-93)/((100-94)+(94-93))=1/7= 14%
> but if the real difference between 11-away and 12-away is 1.5%
I meant ofcource 11-away and 10-away
--