Double open ended straight draw odds in Omaha

[frankthebunny]

Anyone know the odds of completing a straight by river from double open ended on flop?

 

[FailX21]

You have 4 cards in your hand, there is 3 cards on the board, this leaves 45 cards in the deck. You have 8 cards that completes your straight, so you have 8/45 chances to get it, which is 17.7% to get on the turn. If you don't, there is 44 cards in the deck and now you have 18.2% chances to get it on the river.


You can estimate the probability to get it after the river by adding those two. So this leaves you with 8/44 + 8/45, which is approximately the double of the initial chance, so around 36%.


The exact probability would be 8/44 + 8/45 - ( 8/44 * 8/45),
or if you put it in percentage : 0.177 + 0.182 - (0.177*0.182), which is around 33% chance of getting it.


Hopes this is clear

 

[Maurits92]

You have 4 cars in your hand, there is 4 cards on the board, this leaves 44 cards in the deck. You have 8 cards that completes your straight, so you have 8/44 chances to get it, which is 18%.

I like your reasoning, but there's other players and dead cards involved making this a more complicated matter

 

[elizeuof]

I do not know if I understood correctly, but because of the possibilities of possible hands in omaha, I think the villain may end up getting a bigger straight, a flush or a fullhouse, so beware of chasing yours outs.

 

[Maurits92]

Paired board on Omaha when chasing a flush or straight is always trouble..

 

[8bod8]

The reasoning of failx21 give you a starting chance of success.
I usually:
- reduce the chance of success because of the 32 cards held by other players (if 9 seated), but this might be wrong mathematically, although opponents may have a similar draw when it applies and leads to:
- keep an eye on bids by opponents, guessing what they might have (they may have the cards you want, or a bigger straight/flush or worse)

 

[FailX21]

I like your reasoning, but there's other players and dead cards involved making this a more complicated matter

I don't take into account the dead cards and the other players cards cause they are dealt randomly. So, after the flop, you see your 4 cards (2 if you play HE) and the 3 cards on the table, so that leaves 45 cards that you don't see. I didn't really now how to explain it in a good way, so I googled it for you :

That 47 magic number is the key, in a 6-max table the actual number of cards left in the deck is 37, as ten other cards have been dealt to the other players but to calculate the odds you're including that as if those cards were still in the deck and the effect is exactly the same. You could calculate it as:

• The odds of taking two random cards over a 47 deck with 9 remaining hearts and one being a heart or
• The odds of taking two random cards over a 37 deck with x remaining hearts and one being a heart minus the odds of dealing x hearts when picking 10 random cards when taking x cards from a deck of 47.

The second formula is equivalent to the first (produces the same results) but it's harder to calculate so we use the first.

From this website :
https://poker.stackexchange.com/questions/1129/outs-counting-correction

There is nothing different in Omaha than in HE in this, excepts the number of cards in each hands.

 

[Maurits92]

I don't take into account the dead cards and the other players cards cause they are dealt randomly. So, after the flop, you see your 4 cards (2 if you play HE) and the 3 cards on the table, so that leaves 45 cards that you don't see. I didn't really now how to explain it in a good way, so I googled it for you :



From this website :
https://poker.stackexchange.com/questions/1129/outs-counting-correction

There is nothing different in Omaha than in HE in this, excepts the number of cards in each hands.

Thanks for clarifying! That explains a lot

 

[braveslice]

The exact probability would be 8/44 + 8/45 - ( 8/44 * 8/45),
or if you put it in percentage : 0.177 + 0.182 - (0.177*0.182), which is around 33% chance of getting it.


Hopes this is clear

Do you think we can use rule 2 and 4?
Here we would get 8*4 = 32%

 

[FailX21]

Do you think we can use rule 2 and 4?
Here we would get 8*4 = 32%

That rule is made to have a quick approximation of the probability, so it's never exactly the same, but it's quite accurate.

For the x2 : You have 8/44 chance of hitting, which is 18.1% while the rule gives 16%, so it's pretty close.
Fort he x4 : The exact probability is around 33% and you get 32% with the rule, so it's again quite accurate.
And it's pretty much the same for every number of odds possible. I tried with a few different values and found that it always gives a bit smaller pourcentage, so it's a good thing cause it means you're a bit more cautious if you play around equity and EV.

I don't think the rule is based on math, instead it's probably based on an observation that it always gives a quite accurate results. So yeah, that rule works for Omaha too.

 

[FailX21]

Edit :
I tried to do some math, and found that the x2 and x4 rule is based on the estimation that there is 50 cards left in the deck. In reality, there is less than that, 47 (45 in Omaha) on the turn and 46 (44 in Omaha) on the river. So it's a bit less accurate in Omaha than in HE, but it's still quite close.
You can calculate the error (to add to the result of the x2/x4 rule) with the following formula :
On the river (x2 rule) :
Error = x(50-a) / (50*a)
On the turn (x4 rule ) :
x(50a+25-25x-a²-a) / 25(a²+a)

Where x is the number of outs you have and a=44 in Omaha and 46 in HE. You can see that if you have more outs, the error will be bigger and if there is more cards on the deck (that's what "a" represent), the error will be smaller.

Was a bit lazy to write the details, but if you want them I'll make an effort

PS : For some reason I couldn't edit my original post, so I just made another, sorry for the double post.

 

[braveslice]

You can calculate the error (to add to the result of the x2/x4 rule) with the following formula :

Sweet, I know from who I’m asking math question from now on =D
The calculated error is quite small though, almost too small…

http://i63.tinypic.com/2wqsr41.png

 

[FailX21]

Sweet, I know from who I’m asking math question from now on =D
The calculated error is quite small though, almost too small…

http://i63.tinypic.com/2wqsr41.png

Ahah, don't hesitate to ask me, I would love to try to help you out !

Don't forget this is a percentage, so 0.03 is 3%. But yeah, there is something weird in that, I probably have done a mistake somewhere. I'll do the math again this evening or tomorrow and come back with the details this time !