Poker Odds

[BJsaysso]

In Sklansky's book, "Hold 'em Poker", there is a table of probabilities for making your hand given the number of outs available and the number of unseen cards with two cards to come. How does he get these numbers? For example with 10 outs the proabability of making your hand with 45 unseen cards is 39.9%.

[illunious]

Searching (http://forumserver.twoplustwo.com/dosearch.php?Words=pot+odds&fromsearch=1&Cat=&Foru m=begin&Match=Entire+Phrase&Old=allposts&Limit=100 ) the beginners forum for "pot odds" will return more information than you will ever need.



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For example with 10 outs the proabability of making your hand with 45 unseen cards is 39.9%.

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Unlearn the percentages and probabilities and learn pot odds (http://www.gseis.ucla.edu/courses/ed231c/notes1/prtable.html).

Edit: 45 unseen cards is the river.

[Gramps]

Just calculate the odds that you WON'T make your hand, and from that figure out what the odds are of you making your hand.

36/46 (Turn) * 35/45 (River) = 60.87% of the time you won't make your hand. So 39.13% of the time you will.

[sthief09]

maybe I'm missing something, but aren't there 47 unseen cards on the flop and 46 on the river...

unless the dealer exposed the burn card /images/graemlins/grin.gif

[illunious]

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maybe I'm missing something, but aren't there 47 unseen cards on the flop and 46 on the river...

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47 unseen on the flop, 46 unseen on the turn, 45 unseen on the river.

[jdl22]

There's no card after the river so why would you ever use 45?

There are 46 cards that can come on the river. Before that point you saw your two hole cards, the three flop cards, and the turn so you haven't seen 46.

[sthief09]

ohhh I didn't know we were assuming that the game includes the ocean card /images/graemlins/grin.gif

[Mike Haven]

you know your two cards and the flop so there are 47 unknown cards

you don't turn one of your ten outs 37 out of 47 times = 37/47 = 78.7% of the time

you don't river one of your ten outs 36 out of 46 times of this 78.7% = 36/46 x 37/47 = 61.6% of the time

which means you do turn or river one of your ten outs 100 - 61.6 = 38.4% of the time

from these figures you can easily calculate that:

your odds are 78.7/21.3 = 3.7 to 1 of hitting one of your ten outs on the turn

your odds are 78.2/21.8 = 3.6 to 1 of hitting one of your ten outs on the river

your odds are 61.6/38.4 = 1.6 to 1 of hitting one of your ten outs on either the turn or the river

a very important thing to remember, but one i see overlooked time and time again, is that once you have failed to hit one of the ten outs on the turn the 1.6 to 1 odds become totally irrelevant - only the 3.6 to 1 odds are relevant at that point in the hand

in fact, in real terms, 1.6 to 1 is an academic figure, and important only if you are all in on the flop bet - if you have to put more money in to see the river then you should be thinking that you need 3.7 to 1 to see the turn

[Gramps]

Yeah...I was talking about your chance of hitting your draw by 6th Street... /images/graemlins/grin.gif

Add one to those numerators and denominators (whoa, haven't used those words in a sentence in a long time) - still comes out to 39%

[illunious]

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There's no card after the river so why would you ever use 45?

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I mentioned 45 because it was used in the original post.