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This problem arises in two different situations. The first is where, as in draw Poker, you get multiple cards at one time and need to call only one round of bets to get them. The second situation is where, as in seven-card stud, you have successive betting rounds for each additional card.

The probability calculations are the same in the two cases, but their relevance is not. Suppose you hold a pair of jacks either in draw Poker or after the fourth card in seven card stud and you’re looking for a third jack. In each case you have three cards to come to improve your hand.

In draw, where the additional cards are received simultaneously, you do not care whether the desired card is received as the first, second or third card. In stud it is critical; if you have a pair in four cards at seven card stud and you do not get a third one on the fifth card, you’ll have to reconsider whether you want to pay the price required to get a sixth card. And if you don’t get any improvement on the sixth card, you are even more unlikely try for a seventh card hit.