For the numbers crunchers

Below is a table that was given to me by a local casino. I think the numbers are off because they differ with the selected odds that Caro provides on PlanetPoker. For instance, he gives a number of 34.97% for making a flush after the flop when you hold a 4 flush (9 outs); the number given here is 36.36%.

What I ultimately want to do is build a table that expresses probabilities as a ratio in relation to number of outs on both the turn and the river. Are these numbers correct, and if not, how do I figure the values for the second and fourth columns? Thanks for your help in advance!


Hold Em Probabilities


Outs %Flop Outs %Turn

1 4.44 1 2.27

2 8.79 2 4.55

3 13.03 3 6.82

4 17.17 4 9.09

5 21.21 5 11.36

6 25.15 6 13.64

7 28.99 7 15.91

8 32.73 8 18.18

9 36.36 9 20.45

10 39.90 10 22.73

11 43.33 11 25.00

12 46.67 12 27.27

13 49.90 13 29.55

14 53.03 14 31.82

15 56.06 15 34.09

16 58.99 16 36.36

17 61.82 17 38.64

18 64.55 18 40.91

19 67.17 19 43.18

20 69.70 20 45.45

21 72.12 21 47.73

22 74.44 22 50.00

oh jeez, what a disaster.... if you can read it, terrific. if not, i can forward the table to you in a seperate email. my email address is:


captmarlow@yahoo.com


thanks.

-Marlow

I only checked the exemple you gave (4 outs) where Caro is right: 34.97%


Here is how you calculate these numbers:

If you have n outs and there are N cards left in the deck, you will hit one of them by the next card with probability n/N

N is 52-2-3=47 on the flop, 46 on the turn.


If you want the probability to make your hand with 2 cards to come, it is:

1-n*(n-1) / (N*(N-1))=1-n*(n-1)/2162

That is, 1 minus the probability of not making your hand.


It should be trivial to make a spreadsheet to get all these numbers.

These numbers are only correct when you're heads-up against a single opponent and somehow know that all your outs are still in the deck.


cu


Ignatius

NM