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OK, I haven't sorted out how to partition out straights/flushes from paired/trips hands, yet, but here's the first batch of probabilities for the best 5-card poker hand.
- 1 pair (includes some straights/flushes) = 63258624 /133784560 ~ 47.28%
- 2 pair (includes some straights/flushes) = 29652480 /133784560 ~ 22.16%
- 3 pair (no full houses) = 2471040 / 133784560 ~ 1.85%
- Trips (includes some straights/flushes) = 6589440 / 133784560 ~ 4.93%
- Flushes (+ 6-card + 7-card flushes) = ( 3814668 + 267696 + 6864 ) / 133784560 ~ 3.06%
- Full Houses (+ double-trips) = ( 3294720 + 109824 ) / 133784560 ~ 2.54%
- Quads (+ Quad/pair + Quad trips) = ( 183040 + 41184 + 624 ) / 133784560 ~ .17%
As you can see, the big hands are much more likely, while naked 1 pair hands should occur with about the same frequency, after the straights/flushes are subtracted out. Everything else is much more likely.
The hand raking is still the same, though flushes and full houses are nearly identical in frequency. That seems strange, but I'll double-check the maths and think about it some more.
I have some ideas on how to count flushes + pairs/trips, but straights are going to be a pain in my backside. The calculations for straights are unique, quite different from the standard combinatorics we use for pairs, trips, flushes, etc. I'll keep thinking about it.
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