1 Problem:
I think you are giving equal weighting to each suit, despite the fact that if you hold 2 cards of 1 suit the chance of cards of that suit coming out are slightly lower.

My calculation on flopping a made flush:

You hold 2 suited cards leaving 11 of that suit out of 50 total cards remanaing. Assuming you hit this then becomes 10 out of 49 and 9 out of 48.

Giving odds of:

11/50 x 10/49 x 9/49 = 0.008418 or about 1 in 118.

You have to include the multiple possibilities for the way each suit can fall. So the number all types of flops is much higher

For example:

Rainbow flops: 123 can actually be expressed as 132, 213, 231, 312, and 321. Likewise, 112 can be expressed as 121 and 211.

I also don't think you can express 111 to have the same odds as 123.

This is an interesting attempt to figure this out, but I'm afraid it's somewhat flawed. What we have here is an event that is actually the combination of multiple probabilities.

So we can't just add up all the different combinations of what a flop would look like then divide the number of times that flop occurs by the total number of flop configurations, because those combinations do not occur with the same probability. The reason: For each consecutive card dealt, there are fewer cards of that suit in the deck and fewer cards in the deck.

So we have to look at what the chances are that the board will come as a flush by figuring out what the probabilities that each card will come as a specific suit, and multiply them together (to see how often these events occur together), which is:

(probability that card 1 is a particular suit) * (p of card 2 of that suit) * (p3 suited)

So If I have 2 spades, what is the probability I'll flop a flush:

(10/50) * (9/49) * (8/47) = 0.066% of the time (though I've seen it published as 0.084%).

Not sure where the error comes in, but the actual differential is small, so I'm not going to worry about it.

Originally Posted by Av8tor009

use a post to attack someone again and you will be banned...

are you a phantom mod?

Oh, I see my error now, I'm not playing with a full deck!!!!! LOL!!

Should be 11, 10, and 9 instead of 10, 9, 8 in my calcs.

And is it just me, or did we all post a reply to this at the same time?

I need a stats guru to correct me here, I'm def doing something wrong. The odds of hitting a flush draw would be 11/50 * 10/49 * 39/48 * 9 possible ways for it to come down (say your suit is 1, so the possiblities are 112, 121, 211, 113, 131, 311, 114, 141, 411) but that's giving me like 30% and I'm almost positive odds to hitting a flush draw are closer to 4:1. Where's my error?