Beginner's Question Re: Outs

[Civiliste]

X-posted: Probability

Okay, I have a reallllly n00b question about calculating percent chance to catch:

#1.) One of my outs on the Turn (calculation at the Flop)
#2.) One of my outs on the River (calculation at the Turn)
#3.) One of my outs on either the Turn or the River (calculation at the Flop)

What are the correct formulae for these calculations?

Am I correct that:

Given:
X = number of (clean) outs
Y = probability (%) of hitting an out

Is the formula for:
#1: Y = (X/47)*100
#2: Y = (X/46)*100
#3: Y = ((X/47) + ((47-X)/47)*(X/46))*100

Given the preceding equations, I arrive at the conclusion that:

Given 11 outs at the Flop:

Is it correct that:
Percent Chance to catch on the Turn: 23.4%
Percent Chance to catch on the Turn or River: 41.72%
Probability to catch on the Turn: 1147-11) = 1:3.27
Probability to catch on the Turn or River: (Need a formula for this)

Secondly, how do you discount possibly tainted outs? If I have a read on opponent, or a suspicion that an out is tainted that equates to a 40% confidence, should I:

#1. Discount the tainted outs by .4
#2. Not discount the tainted outs at all
#3. Discount the tainted outs to 0
#4. Discount the tainted outs to 0 if confidence > 50%, do not discount the tainted outs at all if confidence < 50%

It seems that #1 would be the mathematically correct approach, but that #2 would result in a looser approach, #3 might result in playing too tight, and #4 would be baloney [sic], but would impart to my game at least a minimal measure of the appearance of randomizing play styles. What approach is recommended?

Am I calculating correctly? I really want to get the formulae down cold before I proceed with my game. I have a degree in Economics, but it's been 3 years since Econometrics, and 7 years since STAT 214, so I can't remember formulae to save my life!

Thanks for any help,
-Zak

[snowlarbear]

numbers look correct, didn't do the exact calculations though. might want to try probability forum, they love numbers.

[Msogard]

I don't know if you're really trying to crunch the numbers or not, but there is an easier way. Multiply your outs by 2 after the flop to get the (%) chance of hitting on the turn. Multiply by 4 to find the chance of hitting one of your outs by the river. This is pretty accurate.

Read SSHE for discounting outs.

[Civiliste]

[ QUOTE ]
Read SSHE for discounting outs.

[/ QUOTE ]

Still waiting on it. I inherited ToP and HPFAP from a friend. I don't really want to delve into them, though, until I have a stronger grasp of the basics behind the math these advanced texts set forth.

I'm waiting on SSHE and WLLHE to arrive in the mail. And I'll probably even order Harrington if I get around to it.

And, yeah, I am more interested in the formulae than the results. I can do the math in my head, but it doesn't help if I don't understand the formulae. I think an understanding of the formulae will be better for me than just learning tables and shortcuts.

Thanks for your help,
-Zak

[Big Country]

What msograd was getting at was the easy way to calculate chance of hitting your outs.

Each card has approximately a 2% chance of hitting the board. (1/50 = 2%, close enough for live play)

After the flop, you have two chances of hitting your outs, the turn and the river.

If you are looking to hit just on the turn, multiply your outs by 2 to get the percent chance they will hit. This works, because as stated above, each card is about 2% to hit. SO if you have an ace as an overcard and think it will be good if it hits, you have a 6% chance of hitting it on the turn (3 aces * 2% chance = 6%), so the pot would need to be laying you about 15 to 1 to give the correct odds to call if you are looking at just the turn. If you had AK and figure either would be good, then you have 6 outs, or a 12% chance to hit on just the turn, and would only need about 8 to 1 odds to call (really alittle less, using whole number for simplicity)

To figure the odds of hitting an out by the river, multiply your outs by 4, as each card has a 2% chance of hitting twice (one chance on the turn, one chance on the river).