Counting outs

I continue to be puzzled by this familiar odds formula: 46 X (#of outs) minus 1.
With 5 known cards (my 2 hold cards plus 4 cards on the table) there are 46 cards unknown. Say I need a 3 on the river to complete a gutshot straight. That gives me 4 outs to make the draw.
How can there be 46 remaining cards when I have to consider the cards that have already been dealt to other players and each of the cards the dealer sloughs before the flop, turn and river.
Yes, there are 46 unseen cards, but not 46 playable cards left.

:?: Bill

umm that formula doesnt make sense...

Since you don't know what cards are also out, you can only discount the cards you have seen. The deck is shuffled and dealt randomly so the chances of getting the card you need are assumed to be the same.


If all of your needed 3's were dealt out to other players, there's a zero percent chance to complete your draw of course but that doesnt matter. Over the long run, the chances of hitting your draw stays the same. We can only use what information is available so that is the best way to ensure long run success.


( I hope someone more gifted with words can reword this for me, because I suck at explaining things.)

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Originally Posted by rev81

How can there be 46 remaining cards when I have to consider the cards that have already been dealt to other players and each of the cards the dealer sloughs before the flop, turn and river.
Yes, there are 46 unseen cards, but not 46 playable cards left.

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It's not easy to explain, but that's just the way it is.

Think about it. Let's say you want to know the odds of hitting a 5 on the river to complete your gutshot straight draw.

There are 52 possible cards that can come up MINUS the 6 that you have already seen (2 hole cards + 4 community cards). Those 6 cards cannot come up on the river, so you have 46 possible cards that can come up.

Four of those are fives, so you have a 4/46 chance of hitting that 5 on the river.

Again, it can be a difficult concept to grasp, but that's just how probability works. :?

Since you dont know about the cards that other players have or the dealer burnt they do not affect your statistics.
Lets assume you have 1 out with 9 players
1/46 = 0.0217
If you follow the approach you presented they are 18 cards at the players hands and 3 burnt cards, total of 21, with 25 'live' cards
there is a 21/46 chance that your out card is in the other players hand or burnt and 25/46 chance it is live
your chance of getting the 1 outer
0*(21/46) + (25/46)(1/25) = 0 + 1/46 = 0.0217

You can run this calculation with any number of outs and come to the same conclusion

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Originally Posted by TLR

Since you dont know about the cards that other players have or the dealer burnt they do not affect your statistics.
Lets assume you have 1 out with 9 players
1/46 = 0.0217
If you follow the approach you presented they are 18 cards at the players hands and 3 burnt cards, total of 21, with 25 'live' cards
there is a 21/46 chance that your out card is in the other players hand or burnt and 25/46 chance it is live
your chance of getting the 1 outer
0*(21/46) + (25/46)(1/25) = 0 + 1/46 = 0.0217

You can run this calculation with any number of outs and come to the same conclusion

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Thanks for the explanation...it makes sense. :)

[quote="mgobluefb"]

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Originally Posted by rev81

Again, it can be a difficult concept to grasp, but that's just how probability works. :?

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Honestly, if you are still having problems with this concept, you might want to reconsider poker. This should be elementry :?

That's why we're in the Beginner's Circle... :(

Seriously though, TLR's explanation is very useful.

I've also been trying to understand how the odds work out if you have several outs and only 25 "live" cards remaining vs the fact that 46 of the cards are unknown - succinct and straightforward. Cheers.

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Originally Posted by future_proof

That's why we're in the Beginner's Circle... :(

Seriously though, TLR's explanation is very useful.

I've also been trying to understand how the odds work out if you have several outs and only 25 "live" cards remaining vs the fact that 46 of the cards are unknown - succinct and straightforward. Cheers.

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Don't be afraid to ask any questions here, thats what the forums are for! Almost everybody here is polite and willing to help. I hated counting outs at first as well, but I just memorized the %'s for common situations like straight draws, flush draws, and sets turning into full houses.