I've been reading books on O8, but there aren't really any statistical tables like Hold'em. I'd think the math is even more important the more complex the game is, and I am surprised there isn't much math that's published. What do I need to know math-wise that I don't know with Hold'em? For example odds of a runner-runner low coming. Odds of A2 hands, Odds of A3 hands, etc. It'll make pre-flop decisions easier. Odds of three broadways. I can do all these calculations of course. I am wondering if there's a resource.

http://www.propokertools.com/simulations

For more advanced stuff you'll need to use PQL though, which is on the same site. Read the guides there and if you have any further questions about it just post them here.

Simple and important math. I should say approximations since Buzz isn't here to correct me with exact numbers. If two low on the flop 25% no low possible by river. If one low on the flop 25% low possible by the river.

And the chance of being dealt A2 (or any specific combination of two different cards) is 6.4%

This might help OP: http://www.o8poker.com/Strategy/keypercent.php

Thank you for that link—very helpful. I've always wondered about a few of those, like the chance that someone else has A2 when I do (~36%).

But what if I have AA2x or A22x—what's the chance that someone else has A2 then?

If I have A3, the chance that someone else has A2 is ~52%. But what if I have AA3x, or even AAA3—what are the chances that someone else has A2 then?

Once I raised pre with AAA3 and sure enough someone beat me for the low with A2. And I recall a handful of times when I've raised pre with hands like AA34ds, AA35ss, or AA3Jds only to find myself up against an A2 for the low. Now I wonder if I'm overvaluing these AA3x hands preflop.

to be clear, the ~36% chance is at least 1 of the other 9 players that were dealt cards was dealt A2**. ~3.5% of the time its 2 players that are also dealt A2**, and ofc, when fewer players are dealt cards the probability decreases, ie. when 9 handed rather than 10 handed its ~32.4%.

when hero holds AA2 or A22 it's ~25.6% at least 1 of the other 9 players that were dealt cards was dealt A2**. ~1.25% of the time its 2 players that are also dealt A2**. decreases to ~23% when 9 handed.


simulation gives me the result ~44.6% and not ~52% as the probability that at least 1 player was dealt A2 when hero's holding A3 and 9 other players were dealt cards.

when hero holds AA3 the probability decreases to ~32.6%.
i don't think its possible to overvalue AA3*. you can play it poorly postflop.

Nevermind. I miscounted (to four).

Thank you for running those simulations and giving such a detailed response!

Good point. AA3* with a suited Ace has a rank of 1.04, but that doesn't mean it's a ticket to showdown. I still have to play poker, as Buzz liked to say.

these are good to know, but what you're really interested in is the conditional probability - the probability that another player holds A2 GIVEN that they VPIP preflop.

if you raise AAA3 and everyone folds, it's pretty safe to say nobody else had A2. if you raise AAA3 and there's a call and a reraise, it's much more likely A2 is out there somewhere.

you need to look at the range of hands your opponents will play and THEN apply the card removal to see what % of the time they have A2.

Could you show how you calculate this?
Cheers

If you hold AAA3, the odds of one your opponents holding holding A2 is 17.4%, assuming a 9 handed game.

The other 8 players hold 32 cards in their hand out of the 48 remaining so the odds of one them being dealt the ace is 2/3. In the event that one of them gets the ace, they get three cracks at one of the deuces. This is 4/47 + 4/46 + 4/45 or 26.1%.

26.1% * 2/3 = 17.4%.

The odds of them catching Ax2x would be about 4.3%.

Thanks for the link

Those are great resources.

How often are my winning percentages accurate knowing all of these dead cards?

If I have As2sJh3h with board 4h5cTdQs
I am ~1/6 to scoop with the K or 2, if you're sure nobody is drawing with 36.
I am ~2/5 to get half or hopefully not a quarter.

What is a fair way to estimate my outs that are unfortunately dead because they were dealt to someone else. Should I take 2/3 of my percentages?

On the flip side!!!, What swing in the percentages could I expect if I optimistically think nobody was dealt my outs? The inverse 3/2!?!

That depends on what player(and howmany are in the hand) you are playing.And how the action went.
But don't worry, this is a snap get it in spot vs 85% of the players.

Vs a huge nit i you can already take the A & 2 low cards (maybe just one)
You can pot it here hoping he folds his low draw, but most players dont tend to fold if they have a low draw (or any kind of low).

Vs a random/fishy player i count there are some high outs gone. But there is more fold equity vs this player then there will be vs the 'nit'.

In total there are 16 different players.

Sorry. Couldn't help myself.
But now that I got that gag out of the way, the actual, simplified calculation for what you're trying to compute is to take the complement of the probability that each player does NOT find a deuce in their three other cards, much as you do when computing the likelihood of a 3rd flush card hitting the board, post flop. Doing additive probability of a compound event overcounts the instances where multiple deuces find their way into the hand.
Try 1 - (43/47 * 42/46 * 41/45) = 23.9%

The rest is fine.
23.9% * 2/3 = 15.9%

That site's terrible. You should ignore it.

http://www.o8poker.com/Strategy/keypercent.php

Just wondering...are those numbers on the page accurate?

+1. There's a learning curve to PQL, but this is the most reliable and efficient way, given we're fallible at math, and it can be time consuming to do by hand.

You don't have to factor in someone being dealt your outs. The probability remains the same because your outs and non-outs are distributed between players hands and the deck with the same frequency.

Gergery, seriously, do people not realize that o8poker is your site?

Anyway, I got a chuckle out of your comment. Thank you.

Calculator is great, because it takes into account the fact that most omaha 8 hands have 2 good cards and 2 fairly random cards. Say flop is K75. In a normal PLO8/NLO8 setting involving preflop hand selection there will be 2 or 3 players seeing flop. Most A2 hands will see the flop and A2 is nut low draw, weak A2 hands have good semibluffing hand and strong A2 hands make most of value range. Many KKxx hands are also playable but given board, about 7% preflop hands have A2 while 1,4% have KK; also of that 1,4% of KK hands 1% or less is playable thus for every KK set there will be 7 A2xx combinations in good hands. My point is that A2 hands rarely have good outs against top pair in high game while KKxx hands are usually losing low even against weak low draws: many hands that have only few nut outs are ahead of random A2 hands and some others are ahead of random KKs. Calculator gets you out of thought pattern "what cards I need to get nuts for one side or the other to surely win X% of the pot". Building extremely nutted hands to win one pot out of 20 is only relevant in extremely loose fixed limit games.

Bill Boston has a book with starting hand stats in it.