Question about pot odds.

[crunny]

Hi,

I'm new to this site and relatively new to poker also.

My question is why do pot odds not take into account the cards that have already been dealt to other players?

[crunny]

You are right we cant tell for sure what cards our opponents have but we can make statistically correct assumptions.

E.g.
10 player SNG
Hole cards: 2,2
Using pot odds:

chances of 2 on flop = 2/50 + 2/49 + 2/48
=12.25% OR approx 1/8

Taking into account dealt cards:
chance of a two being dealt= Approx every 13 cards, therefore 1.5 twos in 20 cards dealt.
We have 2,2 (above average) therefore we can assume that there is two 2's left in deck, therefore
chances of 2 on flop= 2/32 + 2/31 + 2/30
=19.37% OR approx 1/5

Of course in any particular game there is the possibility that someone else holds 2(s). however in the long run 1.5 2's will be dealt, therefore i cannot understand why this is not used as a basis for our calculations.

Perhaps if you provide an example i will understand why dealt cards are not used.

[goofyballer]

Do you have any knowledge which would indicate the is more likely than any other card to come up next? What about the ? Or any card for that matter?

That's why.

You can do it mathematically as well. The way you did it is wrong; you can't possibly say that there's 1.5 twos in the 20 cards dealt when you already have two of them in your hand! You might say that out of the remaining 18 dealt cards, there's a 2/50 chance of any of them being a two, which means that, on average, 0.72 of them will be a two, leaving 1.28 twos in the 32 cards in the non-dealt deck. So the chance of hitting a two = 1 - (30.72/32 * 29.72/31 * 28.72/30) = 11.89%...which is almost exactly the same as 1 - (48/50 * 47/49 * 46/48) = 11.75%. (they're supposed to be the same #, I think I fucked up somewhere, but close enough.) Anyway, it's not a coincidence that those are (almost) exactly the same.

[mervhage]

The bottom line is when calculating odds, you are only allowed to use the information that is known to you.

You cannot assume anything, you must base off of knowns. Any card you have not seen means that that card has an equally likely chance to come. If you have in the hole, that means the two remaining dueces can be anywhere: top, middle, bottom, near the top, closer to the middle, closer to the bottom, etc. You just don't know, hence the percentage likelihood that another duece will show up on the flop calculates in the long run to 12%.