Calculating Odds on Improving your Hand

[JTrue]

I was just wondering what the odds are for normal draws on the turn compared to the river. ie four flush or runner runner flush, gut shot and open ended straight draw, getting a boat with a set or two pair. Please show in x-1 form as it will be easier for me to look at both pot odds and improving odds in order to see if a bet warrants a call. TIA for your replies.

[jdl22]

Here is a link with the odds situations for the turn+river as well as the river: outs and odds (http://www.pokersavvy.com/article/holdemodds.html)

For the runner runner flush you have to consider that there are 5 cards in the deck you have seen and 47 you haven't. With the 47 unseen cards there are 47 C 2 (47 choose 2) = 47!/(2!(47-2)!) = 47*46/2 = 47*23 = 1081 possible two card combinations. Of those you need both flush cards to make a flush. There are 10 flush cards that will do so and thus you have 10 C 2 (ten choose two) = 10!/(2!(10-8)!) = 10*9/2 = 45 possible two card flush giving combinations.

Hence the probability of hitting runner runner is 45/1081 ~ 0.042.

To calculate the odds against :1 you divide the probability of missing by the probability of hitting. Since the probability of missing is 1 - probability of hitting we have .958. This gives you about 23:1.

Runner runner straight is a bit more complicated but can be done similarly.

Hope this helps.