quickly calculating odds.

[jmitchell42]

I read this on another site as a way to quicky come up with the percentage that your hand will win. it seems pretty simple and therefore has me pretty sceptical. what does everyone here think?

"After the flop.
To find the odds of catching your card after the flop apply the following formula: (1) Determine the number of outs that you have (2) multiply that number by four (3) take the answer and put it in a percentage. Here's some examples:

Two over cards – 6 outs * 4 = 24%
Flush Draw – 9 outs * 4 = 36%
Straight draw with one over card – 11 outs * 4 = 44%

By using this formula for calculating your odds you will never be more than 3% off on any calculation. When you have 14 or more outs this formula is not as accurate, however, you will be the statistical favorite to win the hand.

After the turn
To find your outs after the turn, follow a similar formula with minor adjustments. (1) After counting the number of outs that you have (2) multiply that number by two (3) add two and (4) take that answer and put it into a percentage.

Straight draw – ( 8 outs * 2 )+ 2 = 18%
Straight flush draw – (15 outs * 2) + 2 = 32%

Calculating your odds by using this formula yields more accurate results, as you will never be off by more than 1% than the real calculation. "

[rufus]

[ QUOTE ]
I read this on another site as a way to quicky come up with the percentage that your hand will win. it seems pretty simple and therefore has me pretty sceptical. what does everyone here think?

[/ QUOTE ]

This approximates the chance to hit, not the chance to win.

Sklansky writes quite well on why calculations like this one don't need to be all that precise to begin with since there are typically some unlikely possibilities that are being discounted. For people who are inclined to do so, calculating the exact probability also isn't really that hard.

Notably, if players raise on the turn regularly (and they should) then it's questionable to calculate the odds for both cards to come.

Regardless, it's very easy to see that for the river, the number of unknown cards is 46, so it's really 2.17.. percent per out, but 2 is certainly a good first order estimate.

For the flop calculation things are a bit more involved, since it makes sense to consider backdoor draws as well, but 4% per out (b/d straights and flushes count as an extra out) is also a good first-order approximation.

[jay_shark]

This is called the 2x and 4 x rule .
That is , when you have 2 cards to come with x outs , then the percentage of time your hand hits is about 4x% . When you have one card to come , then the percentage of time your hand hits is 2x% .

With one card and x outs , the probability is x/47=~x/50=2x/100 . This is how we get 2x % .

With 2 cards to come , the probability is x/47 + x/47 - xc2/47c2 =~ x/47+x/47 =~ x/50+x/50 =~2x/100+2x/100=~4x/100 or 4x % .

Notice that I disregarded the negative term xc2/47c2 since this will be about 0 .

[jmitchell42]

i have never been good at caculating the exact odds in my head slowly or quickly. are there any tips or drills that can be used to gain this skill?

[jay_shark]

If you can multiply by 2 and 4 then thats a start [img]/images/graemlins/smile.gif[/img]

You don't need to know the exact percentage because this is too inefficient .

[peacock]

u see the pros on tv say the percentage when 2 lads go allin and show there cards preflop how do they count that?

[Copernicus]

they use exact probabilities though I believe some shows take into account dead cards and others dont. the rules of 4 and 2 are accurate enough. Youll give away more in your lifetime taking the time to calculate odds and giving away that you have a tough decision than the EV you'll lose from the slight inaccuracies

[orig!naL]

does this calculation still apply when their are more than 2 players seeing the flop?

[rufus]

Yes, this is independent of the number of players seeing the flop. Just remember that this is the chance to hit, and not the chance to win. With more players in the game, you're more likely to be drawing dead, or have bad outs.