basic probability q's

[ryan1986]

Just starting to use my statistics class in poker, wanted to see if im doing it right.

Being dealt a certain pocket pair such as aces, kings, queens etc. is 1/221.

Being dealt any pocket pair is 12*13/2652 or 1/17

Making a flush on the turn OR river if you flopped two and hold two would be 9/47+9/46= .38 so roughly 38% of the time the 5th card of your suit will hit.

The odds for say getting AKs would be roughly 1/332. <-- this seems awfully low but seems to work out since you have 8 combinations to make AKs and 2652 total hands. But this then implies that it is more rare to get AKs than pocket aces(1/221)

Just checking my math trying to understand the wonderful world of probability in cards. More questions to come im sure /images/graemlins/smile.gif thanks to anyone who can help

[MickeyHoldem]

[ QUOTE ]
Making a flush on the turn OR river if you flopped two and hold two would be 9/47+9/46= .38 so roughly 38% of the time the 5th card of your suit will hit.

[/ QUOTE ]

You will hit your flush = 9/47 + (38/47)*(9/46) = 0.349676226

This is the chance you hit on the turn + the odds that you miss the turn and hit the river.

The rest of your calculations look good... It is indeed harder to get dealt ak soooooted rather than AA. There are 4 AKs while there are 6 AAs.... or 8 and 12 respectively if you consider order important.

Get ready to deal with the difference between ordered and unordered hands!!! There are 52*51 = 2652 possible 2 card hands if order matters.... and 52c2 = 1326 hands if order doesn't!

It's important to understand the difference, and not to get them mixed up in the middle of a problem!! /images/graemlins/grin.gif

Welcome!!

[gaming_mouse]

Being dealt a certain pocket pair such as aces, kings, queens etc. is 1/221.
Correct.

Being dealt any pocket pair is 12*13/2652 or 1/17
Correct.

Making a flush on the turn OR river if you flopped two and hold two would be 9/47+9/46= .38 so roughly 38% of the time the 5th card of your suit will hit.

No. P(A or B) = P(A) + P(B) - P(A & B)

Thus it should be:

9/47 + 9/47 - (9/47*8/46) = .35

Note that you are equally likely to hit your card on the turn or river BEFORE you have seen either the turn or river.

You can also do 1 minus the chance that you miss on both streets to get the same answer:

1 - (38/47*37/46)

The odds for say getting AKs would be roughly 1/332. <-- this seems awfully low but seems to work out since you have 8 combinations to make AKs and 2652 total hands. But this then implies that it is more rare to get AKs than pocket aces(1/221)

This is correct.

Also, you might find it easier to work with combinations, rather than perumutations, as you are doing, though both methods give the same answers.

HTH,
gm

[Crooked Paul]

Wow, you asked a lot of questions. Let's see if I can get you some answers.

First off, you figured the flush draw wrong, and here's why. Suppose you have a draw on a heart flush. You hold two hearts, there are two hearts on the board, and 9 hearts left in all the unseen cards. Now, you're correct that the chance to hit a heart on the turn is 9/47. But then you just ADDED the chance to hit a heart on the river without any qualification. This is a mistake because you're counting some outcomes more than once.

Think about this logically for a second. What are the different ways this can play out? You make the flush if:
- You hit a heart on the turn but not on the river
- You hit a heart on the turn and on the river
- You miss on the turn and hit a heart on the river

The important thing to realize here is that these are compound events, so there's got to be some multiplication in your figures or you're missing something. Fortunately, this problem is a little simpler than it looks because if you hit a heart on the turn, it doesn't really matter if you hit a heart on the river also, so the first two cases can be lumped together:
- You hit a heart on the turn
- You miss on the turn and hit a heart on the river

And what are the chances of those? To hit on the turn, you're absolutely right, the chance is 9/47. Now, add to that the chance that you'll miss on the turn and hit on the river, which is:
(38/47 non-heart turn cards)*(9/46 heart river cards)

So:
9/47 + (38/47)*(9/46)
= .19 + .81*.20
= .19 + .16
= .35
= 35%

The thing about being dealt a certain pocket pair (What are my chances of being dealt AA?) is absolutely right, 1/221.

It is more rare to get AKs that pocket aces. Can you see why? Out of 2652 possible permutations (not combinations) of pocket cards, There are only 8 ways to get AKs but 12 ways to get AA.

I find it simpler conceptually to deal with combinations of pocket cards (order doesn't matter) rather than permutations. In that case, there are effectively 1326 possible hands (52*51)/2. If the order they're dealt doesn't matter, there are only 4 combinations that make AKs, or 4/1326 = 1/332. And there are 6 combinations that make AA, so 6/1326 = 1/221. That's pretty clear, right?

Keep at it with the math, man. The better you understand what's actually happening with the cards, the more effective all your actions at the table will be.


Crooked

[ryan1986]

thanks for all the help..working on some harder stuff now...more questions to come probably /images/graemlins/laugh.gif