Did I win this bet?

[BruceZ]

[ QUOTE ]
Did the two errors cancel out just in this case, or will they always cancel out.

[/ QUOTE ]

They will always cancel out, if by "always" you mean for any number of outs when computing the probability of completing a hand by the river.

[ QUOTE ]
As far as how I derived it, I am proud to say that I came up with that sloppy formula on my own. I can't really say why I thought it would work.

[/ QUOTE ]

In other words, you could not prove it would work.

[jayboo]

i use a little bit simpler method to calculate odds on the flop when in a hand. It works for different types of draws not readily memorized. You have AK with flop 10j3 which leaves u 2 overs and a gutshot. 6 outs on overs and 4 on the queen which equals 10 out multiply (out x cards to come X 2) 10 outs = roughly 40% chance of hitting. with 1 card to come its roughly 20% to hit. this is what i use on the fly when in hands and i find it is very fast and easy to use.
good luck [img]/images/graemlins/wink.gif[/img]

[Stork]

So Billy, if your thinking had been "I have 9 outs, times 2 more cards, times the 2 cards I hold in my hand= about 35, so I hae a 35% chance to hit the flush, or 1.9-1 odds to hit my flush."
Would you win the bet?

[TomBrooks]

[ QUOTE ]
An acquaintance bet me that I don't know how to calculate how flop outs correspond to odds.

[/ QUOTE ]
Billy,

While your technique might not have been perfect, it provides an accurate solution every time.

Therefore:

A) If your bet was that you knew how to calculate, every time, the correct drawing odds with two cards to come given x number of outs, you win.

B) If your bet was that you could provide a mathematical proof of your method that would survive the technical scrutiny of mathematicians, you appear, based on the opinions of the two obviously mathematically knowledgable persons above, to have lost.

-TomBk

And I hope no one considers this either silly or assinine.

[eurythmech]

OK, I don't know if there's need to post more...
But I read a few posts and people didn´t look like they knew what the hell they were talking about =)

Your original post almost got it right, but for some reason you rounded off the percentage to exactly 35%.

You do it like this

1 - (38/47)(37/46)

Which means you take 1 (which is all possibilities, or 100% of the outcomes) and reduce all cases where you miss your flush out on both the turn and the river (ie, don´t make the flush at all). Since it is necessary for you to miss on the turn AND the river we need to multiply those probabilities.

38/37 means 38 of the 47 possible cards for the turn are no good, and 37/46 is self explainatory.

You then get roughly 34.97% or in your strange American way of writing things roughly 1,8598:1

So the general formula for figuring out the probability for any number of outs to hit on either the turn or the river is

1 - ((47-x)/47)((46-x)/46) where x is the number of outs you have.

For instance, if you were to have 61 outs (like, if you include an Uno deck) you would have about 90.2% and also our formula inevtiably leads us to the following conclusion

((47-x)/47)((46-x)/46) = 1

(1-x/47)(1-x/46) = 1

1 -x/47 -x/46 + x²/2162 = 1

1 - 93x/2162 + x²/2162 = 1

x²/2162 - 93x/2162 = 0

x² - 93x = 0

x² = 93x

x = 93

x = 47 + 46

If we have 93 outs we will make it 100% of the time!!!!!!!!