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Omaha Equity Question

  
 
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bigspenda73
Old 05-30-2007, 09:56 PM     Post subject: Omaha Equity Question #1 (permalink)  
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 So Im working on the math portion of PLO. Tell me if Im working through
these spots correctly. Sure, I could type this shit into an odds calculator
but I feel I learn more this way.

Hero: :Ad:
Villain:

Board: :Td:

Equity calculation

Hero has 18 outs, 8 diamonds, and 2 6's, 7's, and 3 8's, and J's

First we have to determine villains opportunity to fill up making our draw
null. Villain has 7 outs on the turn or 7/41 for what we'll call 1/6 of a
chance to fill up or 5/6 of a chance to not fill up. After that, on the
river, villain will have 10 outs to fill up, or 10/40 or 3/4 chance to not
fill up.

Therefore, the odds villain does not fill up are (3/4)*(5/6)= 15/24 or 62.5%

With 18 outs twice we have a (23/41)*(23/40) chance of not completing our
draw or about a 68% chance of doing so.

Therefore we complete our hand 68% of the time and dont lose to a boat 62.5%
of the time. This makes us a 42.5% chance to win the pot.

Could someone tell me where I am going wrong. Im getting a much closer race according to our odds calculator and I just read in SSII that you need 17 outs to be flipping with a set. So where am I failing here?
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krimson
Old 05-30-2007, 10:25 PM #2 (permalink)  
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For a start you are incorrectly assuming that villain fills up independently of whether you hit your draw or not. Very few of your outs also improve villain to a boat, so if you do hit your draw then villain effectively has only one card to fill up, not two (you hit your draw 68% of the time, and when you do you lose to a boat roughly 20% of the time).
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bigspenda73
Old 05-30-2007, 10:34 PM #3 (permalink)  
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 Hmmmmmmmmmm, how do you go about throwing that into a calculation?
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gingerwizard
Old 05-30-2007, 10:35 PM #4 (permalink)  
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 Just read that today too. Didnt quite follow his calcs (or that table). I may have a go at this one. Not sure where you are going wrong.

Looking at your numbers you may have a counting twice problem. I.e. things are different if you made your draw on the turn as his river outs are less than you imagined.
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zenbitz
Old 05-30-2007, 10:46 PM #5 (permalink)  
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Another way to do it:
There are 31 cards left. There are 31*30/2 combinations.
465.
Of these combinations, how may result in you winning? (this is how the simulator does it).
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bigspenda73
Old 05-31-2007, 12:15 AM #6 (permalink)  
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Quote:
Originally Posted by gingerwizard
Just read that today too. Didnt quite follow his calcs (or that table). I may have a go at this one. Not sure where you are going wrong.
Yea, I need to review this chart some more.

The section was pretty good in SSII but I really need to find some more information on postflop play in general. Im learning the more and more I play and I've decided to only 2 table 6 max or 3 table FR until I truly learn this game. In the past I've jumped into 4-5-6 tabling without really learning the game and it exponentially damaged my winrate.
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gingerwizard
Old 05-31-2007, 07:53 AM #7 (permalink)  
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 Ok, I have 2 minutes to write this but ill actually follow the calcs through at lunch time if i have time.

You have to separate this problem into all the different events and work out each. Here we have 6 different outcomes (which are partitioning subsets of all possible boards from here):

You improve on the turn and he doesnt improve throughout the hand
he improves on the turn and you are drawing dead
no-one improves on turn, you improve on river, he doesnt
no-one improves on the turn, he improves on the river
you improve on the turn, he improves on the river
no-one improves at all.

You count how many ways each can happen, and this gives you probabilities. I'll do it at lunch
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krimson
Old 05-31-2007, 11:17 AM #8 (permalink)  
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A quicker computation:
1) Count your clean outs (17 in the case), and see what your probability p of hitting the turn is
2) Count his outs to fill up on the river if you hit the turn (9 or 10 depending on whether you have a pair or not, so call it 9.5), and compute the corresponding probability q
3) Then your probability of winning is approximately 2*p*(1-q) - p^2
(roughly 12/25 in this case). Because you have p*(1-q) chance of hitting on the turn without him filling up, and the same to hit on the river. But if you just add those two probabilites you double count the times when you hit both turn and river, which has probability ~ p^2.
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gingerwizard
Old 05-31-2007, 11:55 AM #9 (permalink)  
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 Here we go then.

Case 1, you improve on the turn and he doesnt imporve throughout the hand.

3 6's, 3 7's, 3 8's, 4 J's 5 diamonds = 18 outs so 18 ways to choose turn.
he improves if he pairs the turn card the T, the 2 or gets the case 9. Thats 10 outs. Leaving 30 safe cards.
Probability is 18/41 * 30/40 = 0.329268292.

Case 2, He improves on the turn, you are drawing dead.
He has 7 outs on turn. probability is 7/41 = 0.170731707.

Case 3,
No-one improves on the turn, you improve river he doesnt.
16 blanks can come on the turn. On the river you have 17 clean outs (one of your safe flush cards now pairs the turn).
Probability is 16/41*17/40 = 0.165853658.

Case 4
No-one improves on the turn, he improves on the river
16 turn blanks, 10 river cards help him.
Probability is 16/41*10/40 = 0.097560975

Case 5
You improve on the turn, he improves on the river
18 turn outs, 10 rivers for him
probability is 18/41*10/40 = 0.109756097

Case 6
no-one improves at all
16 blank turns, 3 more blanks pair him and we lost one on the turn so we have 12 river blanks.
probability is 16/41*12/40 = 0.11707317.

Check. Since all events here form a partition their probabilities should sum to 1.
Total Probability = 0.11707317+0.109756097+0.097560975+0.165853658+0.1 70731707+0.329268292
=0.990243899. So either there is a rounding problem or I have missed an unlikely event. Since i can't spot one, and it's not too unreasonable to be 7.5 10000ths out via rounding, im gonna assume it's ok. (Although there is a chance i added an out to someone or wrongly took one away somewhere. I could also have pressed the wrong button on the calculator!)

So since we have partitioned events we can add their probabilities to gove equity for the outcomes.

Probability you win = 0.329268292+0.165853658=0.49512195 which is roughly 50% within my rounding errors.
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bigspenda73
Old 05-31-2007, 02:10 PM #10 (permalink)  
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 Thanks guys, I don't know why I was working each street independently.
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