Quiz: Best hand is losing

ScottyZ · January 2004

Holdem. [Assume all hole cards are exposed for the purpose of computing outs, and that favorite means a strictly greater than 50% chance of winning the hand.]

Can you think of an example of a hand between two players (say A &

such that:

Player A has a better poker hand on the flop, and Player B is the favorite to win the hand

and

Player A has a better poker hand on the turn, and Player B is the favorite to win the hand.

ScottyZ

Jack King · January 2004

"Player A has a better poker hand on the flop, and Player B is the favorite to win the hand "

How about player A has Kh Kd, player B has 9s 10s

flop is 8h 7s 5s

"A" has a better hand, but I would think B is the favourite in this case.

"Player A has a better poker hand on the turn, and Player B is the favorite to win the hand"

A: has Ac kc

B: has 8d 9d

board is 7d Ad 10c Kh

not sure if these are right or not, but in this case, player B has any diamond (except the king) any 6 or any jack for the str8.

am i right?

ScottyZ · January 2004

For this question, I had in mind using the *same* hole cards (and flop) for both the flop and the turn.

For your flop example, yes, this 15 out draw (straight and flush draw) is a favorite over the Kings with 2 cards to come.

For your example on the turn, Player B has only 14 outs (straight and flush draw minus Kd as you noticed) from 44 unseen cards, and therefore is not the favorite.

You need a hand on the turn which is behind with 23 or more outs.

[Hint: yes, that's possible]

ScottyZ

Jack King · January 2004

hrrmmm...okay, I'm gonna think about this one..

vinsanity · January 2004

I'm sure there are a lot of possible answers. Here's one.

Low Pair against 2 higher suited connectors, for example

A: 2d 2h
B: 9s 10s

Flop: 7s 7d 8s

So B has 9 spades, 3 sixes, 3 jacks, 3 10's, 3 9's, and more so at least 21 outs.

Turn: anything except for the above or 2's, 7's, and 8's can fall on the turn. Let's say: 7s 7d 8s 3d

So, add 2 3's and 2 8's for a total of 25 outs.

ScottyZ · January 2004

That's right! The key idea on the turn is that you have the best possible draw (straight flush draw and drawing to two good overcards) *and* your opponent's hand can be counterfeited without directly hitting your hand.

This hand has 25 outs on the turn. Is that the most outs you can have on the turn while losing?

I don't know the answer to that, but I have a strong feeling that the answer is yes. Now, *proving* that is another story.

Is there a prof specializing in enumeration in the house?

ScottyZ