By Request, an Intro to Poker Math

[Sushiglutton]

Oooooh, sorry [img]/images/graemlins/blush.gif[/img] [img]/images/graemlins/blush.gif[/img] [img]/images/graemlins/blush.gif[/img] [img]/images/graemlins/blush.gif[/img] [img]/images/graemlins/blush.gif[/img] [img]/images/graemlins/blush.gif[/img]

[bozlax]

Edited because Sushi beat me to it.

And, Str8, if you're going to do something you should do it right, dontcha think? 38% vs. 35% can be the difference between this being a value bet/raise on the flop and not, dontcha think?

[Befolder]

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Now, if we flop a FD, the probability of making it by the river (ie hitting a flush card on the turn OR the river) is:

probability turn is a flush card + probability river is a flush card

= 9/47 + 9/46 ~ 0.3871 = 38.71%



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This is not exactly correct. If we have a flushdraw on the flop the chance to make a flush (one or both turn and river are flushcards (fc)) is:

(9/47)(38/46) + (38/47)(9/46) + (9/47)(8/46) = 1-(38/47)(37/46) = 35.0%

'The chance that the turn is a fc while the river is not' + 'The chance that the river is a fc while the turn is not' + 'The chance that both the turn and the river are fc' = 1 -'The chance that neither turn nor river are fc'


The chance that turn or(strict or) river are fc:
(9/47)(38/46) + (38/47)(9/46) = 31.6%


The reason ur calculation is incorrect is that the two events:
A = 'The turn is a flushdraw'
and
B = 'the river is a flushdraw'

are not disjunkt (in swedish [img]/images/graemlins/wink.gif[/img] ) (meaning: A AND B != 0 ('!='-not equal to) that is: it's possible that BOTH A and B are true) and thus: P(A U B) != P(A) + P(B)

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I think doing all that extra math is -EV, and worth whatever time it took times your win rate in trade. Somebody would have to do the math to figure out how -EV doing that extra math is, but again that would also be -EV.
[img]/images/graemlins/cool.gif[/img]

[milesdyson]

<font color="red">* * * NIT ALERT * * *</font>

[Befolder]

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<font color="red">* * * NIT ALERT * * *</font>

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Tough to be a nit when I don't even follow half of the complicated math stuff, so me seriously making a complaint about it or opposing it would be fruitless.

I was just making a joke.
[img]/images/graemlins/smile.gif[/img]

[jaxUp]

sushi, right on with your correction. I double-counted the situations where a flush card hits on the turn and river.

I made a note of it, but for some reason did not think it would make much of a difference in the calculations. I was certainly wrong in this regard. 3% is nothing to scoff at, and I stand humbly corrected.

(oh, and disjunkt is mutually exclusive, or distinct in english)

[jaxUp]

befolder, as you can see, the EV calculations can get a little complicated and you really can't figure them out at the table a lot of the time. However, when you review your hands you can do them then, and when the same situation arises next time you will already know how to maximize your EV.

[Str8Fish]

Guess nobody else is doing the hand example at the end, so give me 30 minutes and I'll have it pumped out for you all.

[Manhammer]

SWEEEEET!!
Thanks a lot, jax. I'm sure this will be very helpful. Unfortunatly, I have to leave for work [img]/images/graemlins/frown.gif[/img], so I'll have to wait until tonight to really get into it. Thanks again.

[jaxUp]

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Guess nobody else is doing the hand example at the end, so give me 30 minutes and I'll have it pumped out for you all.

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str8fish, please make it explicit so it's easy for others who aren't as experienced to understand.