It’s important to understand the fundamental difference between starting with a smaller pair in hold ’em and starting with a smaller pair in seven-card stud. In stud, you can improve by making a bigger two-pair than your opponent or by simply catching another pair when your opponent doesn’t.
In hold ’em, you cannot win these ways. In order to draw out in hold ’em when you’re holding the smaller pair, you must catch a third card of your pair’s rank, make a straight or flush using one card, or play the board to tie (which, by the way, can happen when two pair and a kicker hit the board — all ranking higher than either your or your opponent’s original pair).
So, as an example of the difference in difficulty of overcoming a bigger pair in hold ’em, let’s use a pair of sevens vs.. a pair of sixes as an example. The assumption is that the first two cards in hold ’em are your private two cards, of course, and the remaining five cards are the communal board. The assumption in seven-card stud is that the pairs are the first two cards in the hole, with five cards to come (including the not-yet-dealt random door card [first face-up card] for each player). We will make these two individual pairs consist of four different suits.
Based on computer simulations involving 4,000,000 individual hands dealt, here’s the difference:
In hold ’em, the pair of sevens wins 81 percent of the time, leaving you with only a 19 percent chance of winning with your pair of sixes.
In seven-card stud, the pair of sevens wins 58 percent of the time, leaving you with a much-more-significant 42 percent chance of winning with your pair of sixes.