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.