Flush Odds?

[CCass]

I have read somewhere that the odds of hitting a flush with 4 suited cards after the flop are 1.9 to 1. I can't seem to get the math to work. I get closer to 2.6 to 1. What am I doing wrong? Can someone please walk me thru the calculation?

[BruceZ]

Here is a link which gives 3 different methods.

completing flushes

[CCass]

Bruce:

Thanks for your reply. I was working under method #1, and I did the calculation properly, but I had read somewhere that the odds of making a flush (after a 4 flop) were 1.9 to 1. I was trying to find the math to support this. Obviously, the odds are 2.85 to 1.

[Chris Alger]

For some reason, you're still wrong (Bruce's links were right). I don't know what you mean by a "4-flop," but the odds against completing a 4-flush after the flop, assuming 47 unseen cards, are 1.86-1 against, or about 35% chance. The proof is 1 - (38/47 X 37/46) = .3497. The chance of hitting after the turn blanks is 37/46, making it 5.1-1 against.

[CCass]

Chris,

I was wrong because I couldn't convert 35% to 1.86 to 1. DOH!!!
Time for me to go back to math class.

[Cyrus]

Here's a table that you might find useful, in the context of your question. Check out the line about 9 outs : the probability of completing a 4-fluch flop by the River is 35% which converts to 1.9-1 odds against.

Table of all probabilities for any # of outs in turn & river