I spent several hours today working on the math to answer this question: when open-raising an sc like 98s, what type of flops occur with what frequencies? You often hear that someone is opening a certain combo because "it flops good." How good? Here's what I found.
Hero is UTG and open-raises 98s. Of the 19,600 possible flops, there are:
2 Quads
18 Full Houses
165 Flushes
216 Straights
36 Straight + FD's
264 Trips
396 Two-pair
276 Pair + FD
270 Pair + OESD
18 Pair + OESD + FD
540 Pair + GSSD
36 Pair + GSSD + FD
4536 Pairs
1368 OESD's
225 OESD + FD
2304 GSSD
378 GSSD + FD
1356 FD's
7196 "air"
A quick explanation: in the chart above, "pair" means naked pair with no FD or SD (but this includes "two pair" hands when the board pairs). There are 1368 OESD's, but these do NOT include the 225 OESD+FD flops. And so on.
So we can summarize the flops as follows:
2247 Pair + draw or better (11.4% of flops)
225 15-out draws (1.1%)
378 12-out draws (1.9%)
1356 9-out draws (6.9%)
1368 8-out draws (7.0%)
2304 4-out draws (11.8%)
4536 pairs which I think of as 5-out draws (23.1%)
7196 "air" flops (36.7%)
We can compare this a hand like AQ (see Daven's interesting Playing AQ UTG thread). AQ flops TP or better (trips, 2 pair, full house, quads) 6356 times, or 32.4% of the time. We can also expect 2112 GSSD's, or 10.8% of the time. There are some combo hands I've not run the numbers on. But the idea should be clear: we're cbetting TP or a decent draw about 45% of the time.
If we're willing to open-raise 98s and cbet pretty much all of our 5-out draws or better, we'll be continuing confidently ~52% of the time. So the comparison with AQ shows we can cbet confidently just as often, possibly more often, even when we're oop.
Another difference with sc's is the number of times we have draws to HUGE hands, which isn't normally the case with TPTK hands, and is almost impossible to have happen with pp's.
Now, as a caution, I'm not suggesting you start opening EVERY sc from every position. But this is the mathematics of why folks say hands like 98s "flop good." Also, while most of my numbers checked out using several different calculation styles to verify them, I appear to have over-counted 180 FD's (~1.1%). But I can't find the mistake.
Still, it is helpful to know that if we add sc's into our open-raising range from a particular position, we'll have lots of solid draws we can cbet or 2-barrel on. The same thing is true for flat calling with sc's in LP in games where 3betting isn't rampant. We have lots of ways we can continue.
I'll add more of the mathematics later in the thread. Covering every bit of the mathematics would a book. My spreadsheet has hundreds of calculations on 11 worksheet pages, so you'll just have to trust me.
Final two notes:
1. Hands like 97s flop significantly worse (I haven't run all the numbers, and don't plan on it in the next few weeks).
2. These flop numbers aren't accurate for hands like AKs since not all the straight draws are available (98 can be part of Q-high, J-high, T-high and 9-high straights, but AK can only make a Broadway straight). Of course, hands like AK have other outs we like, so it's not that big a deal. Just don't go opening 32s and pretend I didn't warn you it sucks so hard it leaves bruises.
