There are several card combinations that allow you to have a full house. One is to have a pair of pocket cards that match one card on the board and an unrelated pair also appears.
A full house also occurs with two unmatched pocket cards when one matches a pair on the board and the other matches one of the other board cards.
You have two 5s as pocket cards and the board has 8, 8, 5, K, 10 (you have 5s full with 8s).
Notice that in this case, you could 10se to someone holding 8, A. They would have 10s full with Aces. That person could 10se to someone with a pair of Jacks who would have Jacks full with 8s.
When multiple players have full houses, the person with the highest three of a kind wins.
The pair only comes into play when players have the same three of a kind. Given this board, a person holding A, 10 beats a player hold 10, J. Each player has 10s full, so the pairs play and the Aces beat the Jacks.
A less common way to have a full house is when three of kind appears on the board and you hold a pair in the pocket. Again, if two or more people hold a pair in the pocket, the highest pair wins.
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Five cards of the same suit.
In Hold'em, at least three suited cards must appear on the board for someone to have a flush.
Note that since only five cards appear on the board, it is not possible for two players in the same hand to have flushes in different suits. All flushes will be of the same suit and the highest card wins.
If three Hearts appear on the board, a person holding A, 2 of Hearts beats someone holding K, Q of Hearts. If four Hearts appear on the board, a person holding an A of Hearts, and a 2 of a different suit beats someone holding any other pair of Hearts, because only one card is needed to complete the flush.
Having an Ace-high flush is referred to as having the nut-flush. Of course, if the board showed 3, 4, 5, 6 of Hearts, someone holding a 2 of Hearts beats someone holding an Ace since the 2 completes a straight flush.
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