Calculating Outs % in Hold'em

[thadrl]

I have been calculating the Chance of hitting your outs for the river and turn. But my numbers are coming slighlty different than the only published table I can find. The error in my % for the turn is progressivly getting larger per the number of outs. ie 1 out, im getting 4.25% whereas the table states 4.3%. For 10 outs, I'm getting 42.5%, and the table shows 38.4%. This table is the only one I can find, and it's in Poker Nation by Andy Bellin. Am i even using th right formula? My numbers for the river are dead on with his, but for the turn I'm using: 2(Outs)/47
what is the correct formula? or is the book wrong?

[Homer]

For 10 outs, I'm getting 42.5%, and the table shows 38.4%.

The book appears to be correct.

P(hitting 10 outer) = 1 - P(not hitting 10 outer) = 1 - [(37/47)*(36/46)] = 38.39%

Am i even using th right formula? My numbers for the river are dead on with his, but for the turn I'm using: 2(Outs)/47

Your formula isn't correct. You should use the equation I used above...

P(x) = 1 - [((47-x)/47)*((46-x)/46)]

-- Homer

[kingstalker]

Wish I knew math like you Homer!

[BruceZ]

My numbers for the river are dead on with his, but for the turn I'm using: <font color="red">2(Outs)/47</font>

This is a standard mistake which gets made about once a month on this forum. You cannot simply double the number of outs to compute the odds of making your hand with 2 cards to come. This effectively double counts the times you catch an out on both the turn and the river. You want to only count outs on the river when you miss on the turn. Here are 3 correct formulas which all give exactly the same result:

method 1:
outs/47 + (1-outs/47)*outs/46

for 10 outs: 10/47 + 37/47 * 10/46 = 38.4%.

method 2:
2*outs/47 - (outs/47)*(outs-1)/46

for 10 outs: 2*10/47 - 10/47 * 9/46 = 38.4%

method 3:
1 - (1-outs/47)*(1-outs/46)

for 10 outs: 1 - 37/47 * 36/46 = 38.4%

See also this post which uses these same 3 methods (numbered differently) for a flush draw (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&amp;Number=326125&amp;page=&amp;view=&amp;sb =5&amp;o=&amp;vc=1).

[surfdoc]

Or, when in doubt....cheat just like high school all over again.. and see page 309 in HEFAP.

[N4CER1]

Hi Unless you just want to learn the math..??..do it the easy fast way even right in the game your in...

A little trick:

If your going to take only off the turn card multiple you outs by 2 and if you are going to take the turn and river multiple your outs by 4.....Its that easy!

Example: you have an open end straight draw (8) outs...Multiple 8x4= 32 % you have aprox: 32 % chance of making your hand. (9) outs Flush draw...9x4= 36 % chance you will hit it.....

Try this and you will see how simple it really is......