Drawing to 732xx

From LowballWiki

David Sklansky works through the "drawing to a 7" case for 237KA in the March 2007 Two Plus Two Internet Magazine [1] and gives the same number, 26.2%. He also says:

Again in real life you are more than a 3-to-1 shot because this calculation assumes you will always discard any eight or nine you catch. It also assumes that you will not give up after catching four bad cards. Thus the real life answer is more like 5-to-1.

[edit] Drawing to a 7

Resulting Hand	Probability	Cumulative Probability
7 5 4 3 2	0.087374	0.087374
7 6 4 3 2	0.087374	0.174748
7 6 5 3 2	0.087374	0.262122
8 7 4 3 2	0.0206947	0.282817
8 7 5 3 2	0.0206947	0.303511
8 7 6 3 2	0.0206947	0.324206
9 7 4 3 2	0.0206947	0.344901
9 7 5 3 2	0.0206947	0.365596
976xx	0.0206947	0.38629
98xxx	0.00406498	0.390355
T-high	0.0702141	0.460569
J-high	0.0742791	0.534848
Q-high	0.058758	0.593606
K-high	0.0610446	0.654651
A-high	0.0844415	0.739092
pair of deuces	0.0663799	0.805472
pair of threes	0.0663799	0.871852
pair of fours	0.0144918	0.886344
pair of fives	0.0144918	0.900836
pair of sixes	0.0144918	0.915328
pair of sevens	0.0663799	0.981708
pair of eights	0.00152437	0.983232
big pair	0.00762183	0.990854
trips	0.0091462	1

[edit] Drawing to an 8

Resulting Hand	Probability	Cumulative Probability
7 5 4 3 2	0.072155	0.072155
7 6 4 3 2	0.072155	0.14431
7 6 5 3 2	0.072155	0.216465
8 7 4 3 2	0.072155	0.28862
8 7 5 3 2	0.072155	0.360775
8 7 6 3 2	0.072155	0.43293
9 7 4 3 2	0.0147192	0.447649
9 7 5 3 2	0.0147192	0.462368
976xx	0.0147192	0.477088
98xxx	0.0147192	0.491807
T-high	0.0612363	0.553043
J-high	0.0635957	0.616639
Q-high	0.0494664	0.666105
K-high	0.0507935	0.716899
A-high	0.0694943	0.786393
pair of deuces	0.0538903	0.840283
pair of threes	0.0538903	0.894174
pair of fours	0.0105509	0.904725
pair of fives	0.0105509	0.915275
pair of sixes	0.0105509	0.925826
pair of sevens	0.0538903	0.979717
pair of eights	0.0105509	0.990267
big pair	0.0044239	0.994691
trips	0.00530869	1

[edit] Drawing to a 9

Resulting Hand	Probability	Cumulative Probability
7 5 4 3 2	0.059365	0.059365
7 6 4 3 2	0.059365	0.11873
7 6 5 3 2	0.059365	0.178095
8 7 4 3 2	0.059365	0.23746
8 7 5 3 2	0.059365	0.296825
8 7 6 3 2	0.059365	0.35619
9 7 4 3 2	0.059365	0.415555
9 7 5 3 2	0.059365	0.47492
976xx	0.059365	0.534285
98xxx	0.059365	0.59365
T-high	0.0506129	0.644263
J-high	0.0518696	0.696132
Q-high	0.0398447	0.735977
K-high	0.0405515	0.776529
A-high	0.0550112	0.83154
pair of deuces	0.0422009	0.873741
pair of threes	0.0422009	0.915942
pair of fours	0.00742902	0.923371
pair of fives	0.00742902	0.9308
pair of sixes	0.00742902	0.938229
pair of sevens	0.0422009	0.98043
pair of eights	0.00742902	0.987859
big pair	0.00931399	0.997173
trips	0.00282745	1