Probability question (poker related, but poker knowledge not required)

[Radii]

So most of the simple odds in holdem are second nature to me by now of course, espicially when I'm just looking ahead to the next card, in addition to the common odds for things when there are two cards to come(a draw on the flop, a draw + overcards, blah blah).

But I had a 7 card stud hand I played yesterday and even after the fact I am too dumb to do the simple math here to figure it out(actually, I suck at probability and can't remember how to do this):

The poker setup:

It's 5th street in 7 stud. We started 7 handed, two folded right away(2 up cards), 4 others are in the hand still(12 more up cards, 3 for each), and I am still in the hand(5 known cards). I have 4 diamonds, and of all of the other cards that I have seen, only one is a diamond.

19 known cards, 5 of them diamonds.


So there are 33 unknown unknown cards, 8 of them are diamonds.

With two more cards to come, I just need one diamond to make a flush. What are the odds that I make my flush on either 6th or 7th street? How do you do the math?


Any stud players around? I've been playing it just a bit lately and may continue to off and on, I'm going to pick up 2+2's stud book for sure, any other recommendations? In a low limit stud hand like this, how hard do you push a strong draw like this with this many known cards vs a big field? No one has a pair showing, there are many cards of all the other suits showing so it seems unlikely that anyone else is drawing to a flush. I started with 4 diamonds and pciked up a heart on 5th. Bet/raise or check/call with 4 opponents on 4th? I called a bet. On 5th, it was checked to me(I was next to last to act) and there were just over 4 BB in the pot. My flush would be king high, KQTxx, 4 diamonds, is my hand.

[Maple Leafs]

With two more cards to come, I just need one diamond to make a flush. What are the odds that I make my flush on either 6th or 7th street? How do you do the math?
I believe you'd just divide 8/33 for your odds of hitting on sixth street -- i.e. about 24%.

If that misses, you'll be at 8/32 or exactly 25% on seventh.

To figure out your odds of hitting on either street, you'd multiple the odds of missing, ie. .76 * .75 = 56.8% chance of missing both, or 43.2% chance of hitting.

[GreenMonster]

Have you looked for a stud calc. like they have for holdem yet Radii. My stud skills are poor, and I look would be interest in some info.

[Radii]

To figure out your odds of hitting on either street, you'd multiple the odds of missing, ie. .76 * .75 = 56.8% chance of missing both, or 43.2% chance of hitting.

that's the step I couldn't come up with, 43% sounds about right here. Thanks!

[Radii]

Have you looked for a stud calc. like they have for holdem yet Radii. My stud skills are poor, and I look would be interest in some info.

http://twodimes.net/poker/

It has a stud option too, assuming thats what you're asking about.


I know some very basic tight starting strategy, I have been messing around with some 1/2 and 2/4 stud on the Cryptos and Empire Poker while working on some bonuses, and when I'm paying enough attention to watch all the cards, I feel very good about my decisions most of the time, even without any strong player reads I've felt very very good about my play, and I think I'd like to read a bit more and improve my game.

[Samdari]

If that misses, you'll be at 8/32

If he sees only one more up card, he's already won :).

[Maple Leafs]

If he sees only one more up card, he's already won :).
Isn't there another round of betting? I've never played anything other than hold 'em.

[Radii]

Isn't there another round of betting? I've never played anything other than hold 'em.


The next card is dealt face up to all players still in, so if 4 people remain in then you will see 4 face up cards. However, at the time of calculating your odds to flush by the river, you do not know what those cards may be, so its irrelevant to the calculation.

[Samdari]

The next card is dealt face up to all players still in, so if 4 people remain in then you will see 4 face up cards. However, at the time of calculating your odds to flush by the river, you do not know what those cards may be, so its irrelevant to the calculation.

No, its not irrelevant at all. There is absolutely no way that the probability of getting a flush on the river is 8/32, since in no case will you see only one up card on sixth street. It has to be one of 8/31, 8/30, 8/29, 7/31, 7/30, 7/29 (7 means you saw one diamond) 6/30, 6/29, 5/29.

To properly do the calculation, you would need to multiply each probability above by the probability of getting to that situation (i.e. 8/31*the probability that one player besides you stays and does not get a diamont). But, since you don't accurately know the probability of each player staying when calculating these odds, you need to make some approximation. Using a single probability to estimate is not a bad rough calculation, but I think 8/31 is more appropriate, or better yet, the average of all the above.