In a way, the question in the OP is not really a relevant question to play of the game or betting of hands. However, you can readily understand that there will be different odds simply by doing some relatively simple probability calculations. The real key difference between the games is that, in 7-card stud, the betting is based on the percentage chance that your hand (which you know in full) beats the other hands (which you see all but two initially, then all but three after the last card is dealt), whereas in Hold-'em, you are simply betting on the chance that your two hole cards are making a better combination than the hole cards everyone else has. This is a significant dynamic difference for betting purposes.
Personally, I find myself much more active in Hold-'em.
These odds are based on 5 cards, not 7, and are thus not accurate for either hold em or 7 card stud.
If you don’t count betting patterns that cause players to fold, the odds for holdem and stud are the same. Betting changes things though. You’d have to analyze the specific players to see how, which is no longer a mathematical question.
hand````````````````number```Probability
straight flush:41,584``.00031 4-of-a-kind:````````224,848``.0017 full house:```````3,473,184``.026 flush:````````````4,047,644``.030 straight:`````````6,180,020``.046 3-of-a-kind:6,461,620.048 two pairs:```````31,433,400.235
pair:````````````58,627,800.438 high card:```````23,294,460.174
This applies to both Stud and Hold’Em; the difference is the community cards in Hold’Em means when ‘fancy’ hands come, they often come for multiple players.
If I may, several people here are talking about “probability” without defining exactly what parameters they are using.
If you want the probability that any given 7-card hand out of all possible 7-card hands, using a 52-card deck, will be each of the various types of identified hands, then those odds are exactly the same for any 7-card game.
If you want the probability that any given type of hand will appear in a given 7-card game, those odds will be different for 7-card Stud from Hold-'em, because of the number of cards dealt out of the 52-card total deck. Indeed, those numbers change as the number of contestants in any given game changes.
Calculating the probabilities in Hold-'em would be interesting, because of the community cards. You’d have to look at all possible combinations of the 5 community cards, and combine that with the possible combinations of hole cards.
And the statistics posted by According to Pliny were not, I don’t think, an attempt to do anything except demonstrate the type of probabilities he was searching for. Which at least resulted in some references to hard data.
