View Full Version : Calculating drawing odds on the flop

Eric P
11-01-2002, 03:28 AM
Can someone tell me the formula to doing odds combining the turn in the river. I know most the important ones but i'm not 100% how to do the calculations

For example. what are the odds to improve if you flop trips (banning straights and flushes)
I see it as:
you've seen 5 cards so 47 left in the deck, 7 ways to improve (board pairs or you quad) so 7/45 or 15%, then on the turn you have 10 outs so 10/45 or 22%. Do i simply add these percentages? If some one could explain this to me i would apprciate it. I had just been adding them but i want to make sure i'm right.

11-01-2002, 11:42 AM
When calculating probabilities on the flop, particularly "what's my probability of improving at all," it's often easier to calculate the probability of the opposite, then taking 1 minus the result.
You have 99. Flop is 49A. At this point, let's take A9 and AA out of the equation, and assume that any A, 9, or 4 will be a good thing. Since there are 7 such cards (3 A's, 3 4's, and one 9), the probability of success (call it 'p') is 7/47 (.149). Equally important, the probability of failure is 1-p, or .851.
Now, let's say the turn doesn't help you, and the board now reads 49A[X], [X] being any non-A, 9, or 4. Now your probability of success on the river (call it 'q') is 10/46 (can you see where the 10 and 46 come from?), or .217. This time, the probability of failure, 1-q, is .783.

Now, if you're on the flop, and you want to calculate the probability of improving at all, you could calculate:
The probability of improving on the turn and not the river, the probability of improving on the river and not the turn, and the probability of improving on both (adjusting the numbers for the different-looking river scenario).
Sum them all up, and you have tediously gotten your answer.

Simpler, though, you can calculate the probability of improving on NEITHER:
(1-p)*(1-q)=.851*.783=.666. Subract this number from 1, and you find that, as of the flop, you have a 33.3% chance of improvement.

Clear as mud?

Jim Brier
11-01-2002, 02:44 PM

11-03-2002, 02:50 AM
So, if I flop 4 to a flush, the way I would calculate my percentage of making it by the river would be:

1-9/47= .8085 * 1- 9/46= .8043 = 65% of not making it by the river, or ~ 1 in 3 times I should make my flush by the river.

Let me know if I am calculating this properly.


Eric P
11-04-2002, 12:13 AM
Ok that's what i thought. Thanks.