The passage I quoted in post #24 is where double counting happens. You count as follow:

1) take a nine
2) take an overcard
3) take any remaining card
4) make every permutation

If correct, the above should generate any permutation only once for every different choice in steps 1)-3). Unfortunately, that's not the case. Think about a Ks9hJc flop. There are two paths in your algorithm leading to it.

Path 1:

1) take the 9h
2) take the Ks
3) take the Jc
4) permute and arrive (among others) to Ks9hJc

Path 2:

1) take the 9h
2) take the Jc
3) take the Ks
4) permute and arrive (among others) to Ks9hJc

See the problem?

If you want to count flops with at least a 9 and at least an overcard, count the following types (O=overcard):

99O
9OO
9OU

Got it. Thanks.

LOL, THANKS. ...LIKE I SAID 24 HR GRIND, IT ENDED KK VS AK.

We should make this thread sticky

The calculation for hitting overcard when we have JJ

A) Deads cards are random

12/50*49/49*48/48 = 0.24 over card * any card * any card
38/50*12/49*48/48 = 0.186122449 no over card * over card * any card
38/50*37/49*12/48 = 0.143469388 no over card * no over card * over card

Total 56.96%

For all pairs…

KK 22.55%
QQ 41.43%
JJ 56.96%
TT 69.47%
99 79.29%
88 86.73%
77 92.14%
66 95.84%
55 98.14%
44 99.39%
33 99.90%

B) at least 1 over and you don’t hit set

12/50*47/49*46/48 = 0.220612245 over card * any card other than J * any card other than J
36/50*12/49*46/48 = 0.168979592 no over card or J * over card * any card other than J
36/50*35/49*12/48 = 0.128571429 no over card or J * no over card or J * over card

Total 51.82%

For all pairs…

KK 21%
QQ 38%
JJ 52%
TT 63%
99 72%
88 78%
77 82%
66 85%
55 87%
44 88%
33 88%

C) Can someone please post the method of calculation for this percentages ?


KK 23.43%
QQ 42.88%
JJ 58.72%
TT 71.32%
99 81.06%
88 88.30%
77 93.41%
66 96.76%
55 98.73%
44 99.68%
33 99.98%

= 1 - 38*37*36/50/49/48


= P(no set)*P(over | no set) = 47*46/50/49 * (1 - 36*35*34/48/47/46)

thanks heehaww!!

can you make the calculation for C also?

KK 23.43%
QQ 42.88%
JJ 58.72%
TT 71.32%
99 81.06%
88 88.30%
77 93.41%
66 96.76%
55 98.73%
44 99.68%
33 99.98%

Sure, but Percentages for what?

hello heehaww

in previous post they wrote that in Mike Petriv's Holdem Odds Book page 99 the percentages are like this...

KK 23.43%
QQ 42.88%
JJ 58.72%
TT 71.32%
99 81.06%
88 88.30%
77 93.41%
66 96.76%
55 98.73%
44 99.68%
33 99.98%

what is the formula of this numbers?

Ok so that's the chance an overcard came given that your set didn't come. Knowing your set didn't come means we can trim 2 cards off the denominator.

KK = 1 - C(44,3)/C(48,3)
QQ = 1 - C(40,3)/C(48,3)
and so on.

In the previous form: 1 - 40*39*38/48/47/46

thanks a lot heehaww!!