Conundrum: Poker Game 2
Our four old poker friends have migrated from five-card stud to no-limit Texas hold ‘em, which they always play with a single deck of cards.
During one hand, the flop was an Eight, Ten, and King – all clubs. Ron went all-in, and the other three players called with money remaining.
The turn card was the Nine of Hearts. Nick went all-in, and the other two called with money remaining.
The river card was the Ten of Hearts. Frank went all-in, and Lennie called with money remaining.
As it turned out, nobody went broke on this hand.
What is the best possible hand that Lennie could have had?
January 6th, 2009 at 8:46 pm
Interesting… in solving this I assumed that the players didn’t necessarily go all-in at the point that their cards ‘finished’ their hands. Also, I first tried to come up with the best hand possible for Ron, and ended up with the following arrangement:
Ron is holding 10 of diamonds and 10 of spades for a 4 of a kind
Nick is holding a pair of kings for a full house kings over 10s
Frank is holding a pair of 9s for a full house 9s over 10s
Lennie is holding a pair of 8s for a full house 8s over 10s
However, thinking about it again, I realized that if Ron’s winning hand isn’t so strong, then Lennie could be holding a better hand:
Ron is holding a pair of kings for a full house kings over 10s
Nick is holding the remaining king and one 10 for a full house 10s over kings
Frank is holding the remaining 10 and a 9 for a full house 10s over 9s
Lennie is holding the remaining two 9s for a full house 9s over 10s.
Did I get it?
January 6th, 2009 at 9:06 pm
You did! Pocket nines, completing a full house, is the best hand Lennie could have. Way to go, Kimi!
Note that we don’t know for sure what Nick and Frank have, except that they both have tens full, and Nick’s hand can’t beat Frank’s. The configuration you have works, or Nick could have T8 and Frank could have TK, T9, or even T8 as well.