quick odds calculation question

[Goodnews]

If i had two overcards and a flush draw on the flop, how would i go about calculating my odds of hitting one of my outs by the river?

is it 15/47 + 15/46 = 65% ? Or am I calculating these odds incorrectly?

My friend argue that the real percentage is around 50% (through some method through permutations), and I'm not sure how they got this number, as you can probably see, an 15% difference is something to be concerned about.

He mentioned something about HPFAP, but i was quite drunk when we were discussing this.

[TStoneMBD]

if you need to do on the fly calculations, the 4/2 rule is your best bet.

for instance, if you have 8 outs, the odds of connecting in the next 2 cards is about 8x4=32%. if you have 8 outs on the turn, your odds of connecting on the river is about 8x2=16%.

once you get up to around 14 outs though the system doesnt work.

[Balla2hot4u]

i want to fully understand why these out percentages are what they are.. thanks
-Adam

[TStoneMBD]

quite honestly, i have no clue, but they work out pretty well.

[Balla2hot4u]

[ QUOTE ]
if you need to do on the fly calculations, the 4/2 rule is your best bet.

for instance, if you have 8 outs, the odds of connecting in the next 2 cards is about 8x4=32%. if you have 8 outs on the turn, your odds of connecting on the river is about 8x2=16%.

once you get up to around 14 outs though the system doesnt work.

[/ QUOTE ]

ok so why is it 8 X 4 on the turn and 8 X 2 on the river? is it because your outs are automatically multiplied times 2 ( because the math of the amount of outs u have divided by the cards remaining almost always multiplies it by 2?) then times the amount of cards remaining to come.. so u have 8 outs on the flop to hit a straight right.. 8X2(x2 again for the amount of cards still to come) = 34% then now on the river u have 8 outs still but only one card to come so its just 8X2= 16%? im just a little confused and would to clarify to myself thanks

[TStoneMBD]

it should be pretty selfexplanitory why its Xx4 and Xx2 since youre getting half the cards you divide by 2. again, i dont know why this system works, all i know is that it works.

[ianlippert]

[ QUOTE ]
it should be pretty selfexplanitory why its Xx4 and Xx2 since youre getting half the cards you divide by 2. again, i dont know why this system works, all i know is that it works.

[/ QUOTE ]

It because you are changing your outs into a percentage. The reson the 2x works is because there are almost 50 cards in the deck. If you wanted to change 8/50 into a percentage you multiply top and bottom by 2 to get 16/100 or 16%. The 4x is because you are getting a second card your percentage is doubled. Once again, this system gives you an estimate and gets very sketchy around 15. I remember one play I had 18 outs and calculated it as 72%, when really it was more like 66%. Still good enough to call the guy all in though.

[buriedbeds]

This is from the Full Tilt Poker newsletter a while back (yes, I'm enough of a poker nerd to keep them for future reference... [img]/images/graemlins/smile.gif[/img] ), discussing the same basic concept:

"It is very difficult to calculate the exact odds of hitting a drawing hand when you're sitting at the poker table. Unless you're a genius with a gift for mathematics like Chris Ferguson, you will not be able to do it. That leaves two options for the rest of us: The first option is to sit at home with a calculator, figure out the odds for every possible combination of draws, and then memorize them. That way, no matter what situation comes up, you always know the odds. But for those of us without a perfect memory, there's an easier way. Here is a simple trick for estimating those odds.

The first thing you need to do is to figure out how many "outs" you have. An "out" is any card that gives you a made hand. To do this, simply count the number of cards available that give the hand you are drawing to. For example: suppose you hold Ac 8c and the flop comes Qh 9c 4c. You have a flush draw. There are thirteen clubs in the deck and you are looking at four of them -- the two in your hand, and the two on the board. That leaves nine clubs left in the deck, and two chances to hit one.

The trick to figuring out the approximate percentage chance of hitting the flush is to multiply your outs times the number of chances to hit it. In this case that would be nine outs multiplied by two chances, or eighteen. Then take that number, multiply times two, and add a percentage sign. The approximate percentage of the time you will make the flush is 36%. (The exact percentage is 34.97%.) Now let's say that on that same flop you hold the Jd Th. In this case you would have an open ended straight draw with eight outs to hit the straight (four kings and four eights). Eight outs with two cards to come gives you sixteen outs. Multiply times two and you will hit the straight approximately 32% (31.46% exactly) of the time.

One important thing to keep in mind is that the percentage stated is merely the percentage of the time that you will hit the hand you are drawing to, NOT the percentage of time that you will win the pot. You may hit your hand and still lose. In the first example, the Qc will pair the board and may give somebody a full house. In the second example both the Kc and the 8c will put a possible flush on the board, giving you the straight, but not necessarily the winning hand. Still, knowing the approximate likelihood of making your hand is a good beginning step on the road to better poker."

Hope that's helpful...

-jake.

[jimmyd2]

Clonie Gowen wrote a poker tip on computing % on Fulltiltpoker.com. She used the 4X2.
# of outs X number of cards remaining X 2. It is not exact but can help you while in play. The exact site is:
http://www.fulltiltpoker.com/proless...olessons1.html

[Cobra]

The easiest way to figure the probability of getting an out on the turn or the river is 1 - the probability of not getting it on the turn and river. This gives you the probability of one or more of your outs hitting.

In this 15 out example:

= 1 - (32/47*31/46) = 54.11%

Cobra