Quick math checkup: Ranges

[WSOP2007]

Hi, I’m trying to master the math behind calculating hand ranges. To practice, I came up with this one. Is it any good?

What is the probability of a player having made a straight on a QcJdTh flop given that his preflop range is 22+,ATs+,KQs,QJs,JTs,T9s,98s,87s,76s,65s,54s,ATo+, KQo,QJo,JTo?

AK(s) and 98s make a straight, a total of 12+4+4=20 combinations.

The preflop range has 13x6(pocketpairs)+6x12(off-suit hands)+12x4(suited hands)=198 combinations.

To get the denominator we have to subtract the hands cancelled out by the flop. These are:
1 pair hands: AxTh,AxJd,AxQc,KxQc,T9h9 ,which make (4x7+1)=29 combinations.
2 pair hands:QxJc,Qd,JxTh,JdTx, which make(2x12)=24 combinations.
Sets: QxQc,JxJd,TxTh, which make (3x3)=9 combinations.

So the denominator is 198-29-24-9=136.
Divide de straight possibilities by the denominator: 20/136=0.147 or 14.7%

Another question I have is if perhaps anyone knows of a program better then pokerstove so it allows you to make calculations like this one? Thanks!

[jay_shark]

Denominator :
1) pocket pairs :10*6 + 3*3
2) a10s+ : 3+3+3+4
3) kqs : 3
4) qjs : 2
5) j10s : 2
6)109s : 3
7) 98 s :4
8) 87s :4
9) 76s:4
10) 65s:4
11) 54s:4
12) a10o+: (12-3) + 9+9 +12
13) kqo : 9
14) qjo : 9-2
15) j10o : 9-2

Add everything up and you get your denominator which is 174 .

The answer is 20/174 = 11.49%