What's the odds on NLHE runner straights and flushes?

Question

What's the odds on NLHE runner straights and flushes?

Answer 1

Let's say you have three cards to a flush after the flop.  If your opponent doesn't have a card of that suit (which we'll assume) then there are ten cards left, one of which must hit on the turn.  Then there are 9 cards left, one of which must hit on the river.  We'll assume you both are still unaware of each other's cards.

Turn:  10/47 = 0.213

River: 9/46 = 0.196

Together = 0.196*.213 = 0.042 = 4.2%

So hitting a runner runner flush is about 25 to 1 if all the cards of that suit are still in the deck.

Straights are a little more difficult to figure, as there are more combinations.  Does the turn give you an open ended draw or a gutshot?  Let's say, for simplicity, that you need one of three different values on the turn, and then one of two values on the river.

Turn: 12/47 = 0.255

River: 8/46 = .0174

Together:  0.255*0.174 = 4.4%

As you can see, you have about a 4% chance of hitting runner runner cards to make a straight or flush.  The straight odds will vary depending on what you catch, but for general purposes you can figure you're about a 25 to 1 underdog if you need to catch runner runner.

Answer 2

http://en.wikipedia.org/wiki/Poker_proba...

Answer 3

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