In Texas Hold’em poker, each player is dealt 2 hole cards from a standard deck t

Question

In Texas Hold’em poker, each player is dealt 2 hole cards from a standard deck that only they can see. There are also 5 community cards on the board that everyone can see. Each player can use any combination of their 2 hole cards and the 5 community cards to form the best possible 5-card hand. Suppose you are playing against one other player and you have the hand K 10 as your hole cards. Assume that you know nothing about the cards your opponent may be holding. The 5 community cards are A, K 7 7 10 1. Count the number of ways that your opponent can have each of the following hands and make a table of your results. Be mindful of double-counting. Any hand that overlaps in multiple categories should only be included in the higher-ranked category. a) 2 pair (of higher ranking than your own) b) 3 of a kind c) a straight d) a flush e) a full house f) 4 of a kind g) straight flush 2. Use the previous results to calculate the probability that you have the better hand.

Explanation / Answer

a. 2 pairs: For a higher 2 pairs, opponent must have an ace and a king

b. For 3 of a kind, opponent can have 2 aces or 2 kings or one 7 and one card other than ace king seven or ten or two tens.

c. For straight, opponent must have a queen and a jack so that straight is ace, king, queen, jack and ten

d. For flush, we see that there are already 3 spade suite cards. Hence 2 more are required. Hence opponent hand must be two spade cards

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