Chinese Arithmetic

[DukeOfDeath]

Here's Tatt's Chinese Arithmetic (I'm bored and at work way too late)

First the hand in question:

Everleaf Gaming Game #288525537
***** Hand history for game #288525537 *****
Blinds 75/150 NL Omaha - 2011/07/17 - 17:13:38
Table 1
Seat 2
Total number of players: 9
Seat 1: dtme ( 5860 Chips )
Seat 2: foodz ( 650 Chips )
Seat 3: flipsr ( 1745 Chips )
Seat 5: Ausangel ( 2440 Chips )
Seat 6: DukeOfDeath ( 3340 Chips )
Seat 7: fred913 ( 2260 Chips )
Seat 8: tattmando ( 4255 Chips )
Seat 9: tottey ( 455 Chips )
Seat 10: blondy1010 ( 4495 Chips )
flipsr: posts 75 Chips]
Ausangel: posts 150 Chips]
fred913: nh
** Dealing down cards **
Dealt to DukeOfDeath ]
DukeOfDeath: nh
flipsr: wd
tattmando: g1 B xx
DukeOfDeath 150 Chips]
fred913 150 Chips]
tattmando folds
tottey folds
blondy1010: tys x
blondy1010 folds
tottey: nh
dtme 150 Chips]
foodz folds
blondy1010: ty x
flipsr 75 Chips]
Ausangel checks
** Dealing Flop ** ]
flipsr checks
Ausangel checks
DukeOfDeath checks
fred913 checks
dtme checks
** Dealing Turn ** ]
flipsr checks
Ausangel checks
DukeOfDeath checks
fred913 checks
dtme checks
** Dealing River ** ]
flipsr checks
Ausangel checks
DukeOfDeath checks
fred913 checks
dtme checks
flipsr shows ] two pairs, jacks and nines
Ausangel does not show cards
DukeOfDeath does not show cards
fred913 shows ] two pairs, jacks and tens
dtme does not show cards
fred913 wins 750 chips from main pot with two pairs, jacks and tens ]

And here's the following chat to catch everyone else up to speed:
DukeOfDeath: was wondering the odds someone was holding a bigger pocket pair
DukeOfDeath: I need to sit down and do math on this game lol
tattmando: gl on the chinese arithmatic m8

So in that spot there were really no draws on the board, no one seemed to have a J or set and who's super excited about a pair of 4s or 2s. So when that J came on the turn I almost used up my time bank thinking what are the chances someone had my pair of 8s beat. If it was less than 50% I was obviously betting, not wanting more cards to come. Also it was a semibluff opportunity by representing the Jack. Of course at the time I didn't have time to pull out the abacus, but here goes the after game analysis:

For those that play NLHE, here's something you probably already know: there's about a 1/17 chance to be dealt a pocket pair. Because for any card there are 3 left in the deck to pair it and 51 cards left in the deck after your first card. 51 divided by 3 is 17.

(For those that haven't thought this deeply yet, there's a 0% you can make a pair with one card )

For Omaha, the odds of getting a pair out of 4 cards is tricky. First you have to calculate the odds that someone doesn't have a pair. So 1 * (48/51) * (44/50) * (40/49). Basically for every card added to the first the odds of not pairing are (non pairing cards in deck)/(total cards in deck). Each card takes 3 more away from the total that doesn't pair. All in all 67.6% chance of no pair makes 32.4% that any given opponent has a pair (basically a third of the time).

So of that 32.4%, I'm assuming 1/13 for each pair. So about 2.5% chance someone has any given pair. So in this spot, if I throw out pairs giving sets, there are 5 that can beat me (9s, 10s, Q's, K's, and A's). So about a 12.5% chance a particular player would hold a higher pair. So since I was really only thinking about the two left to act on the turn there was an (87.5%)^2 or 77% chance I was ahead with my pair (barring someone slow playing something set or better or getting lucky on the river). So probably worth a bet had I known and not been short stacked and not been playing with people that like to call a lot or chase. Sure enough Fred did get that 23% chance (and flip did see the river and hit it). Congrats on that Omaha game, all. Still got me thinking about it.

There's my math. It's probably wrong.

[tattmando]

i think i'm gonna have to read that again (maybe 6 or 7 times)

m8 i couldn't even fathom to say right or wrong.......but ya defo put your thinking cap on for that. good thread

[DukeOfDeath]

Originally Posted by tattmando

i think i'm gonna have to read that again (maybe 6 or 7 times)

m8 i couldn't even fathom to say right or wrong.......but ya defo put your thinking cap on for that. good thread

haha. I did it just for you.

[tattmando]

lol thx pretty cool stuff for sure

[stevo_58]

Originally Posted by DukeOfDeath

(For those that haven't thought this deeply yet, there's a 0% you can make a pair with one card )

LOL....................................I enjoy your posts mate, even if they do do my head in!

[DukeOfDeath]

Originally Posted by stevo_58

LOL....................................I enjoy your posts mate, even if they do do my head in!

haha. Thanks! I added that line in specifically for you just kidding

[CherryPie]

Interrresting...i like it.. yup looks like your maths adds up to me.

The gr8 thing about Omaha is it's never that simple!!

I dont think i would be confident in ruling out someone having a J or the ppl acting before me having an overpair becos they checked - i can see where ur coming from, - ud certainly have expected them to bet, but id still see a real chance of those options there, ...
then considering there are str8 & fl draws & overcards to u that could still hit a pr, i wouldnt be looking at my odds as anywhere nr 77%.. i think in that scenario in a tourny i would just accept that im in a 1v4 situation & check it, if u bet & look weak, even without a hand someone else could bluff it out on the river.. and wouldnt be confident enough to push with that. maybe i am being a bit of a chicken.

in a 1on1 or 1on2 situation then i would probably show some cajones.

[DukeOfDeath]

Originally Posted by CherryPie

Interrresting...i like it.. yup looks like your maths adds up to me.

The gr8 thing about Omaha is it's never that simple!!

I dont think i would be confident in ruling out someone having a J or the ppl acting before me having an overpair becos they checked - i can see where ur coming from, - ud certainly have expected them to bet, but id still see a real chance of those options there, ...
then considering there are str8 & fl draws & overcards to u that could still hit a pr, i wouldnt be looking at my odds as anywhere nr 77%.. i think in that scenario in a tourny i would just accept that im in a 1v4 situation & check it, if u bet & look weak, even without a hand someone else could bluff it out on the river.. and wouldnt be confident enough to push with that. maybe i am being a bit of a chicken.

in a 1on1 or 1on2 situation then i would probably show some cajones.

I agree and that's exactly what was going through my head at the time and what I ended up doing. However I think whether you check down or bluff (or semi bluff in this occasion) has a lot to do with opponents, situation in the tournament, and prior action. And I'm really new to Omaha, but from what I can tell it relies A LOT on reads. Trips, straights, and flushes win a lot. But you can never go all the way with them because with a board pair there's always a chance someone has a boat or quads. However you can't always assume you're up against whatever's the nuts or redraw to the nuts on the board. You just have to know how often your opponent will bet call or reraise with how good of hands to judge where you're at. Now against 4 totally random hands there's no way my hand is even better than 50%, but I have a little more information. I feel like based on how things were going that someone with a J or pocket 2s or 4s would bet the turn and someone with A3 wouldn't call a bet to hope a 5 would come on the river and just lose to a boat or higher straight anyway. And I have the A of spades for anyone else to have nut flush (and you never should chase any flush but A high in Omaha). So yes I don't KNOW but my READ (and it ended up being right) was that no one had better than 2 pair. I just wanted to know the odds that someone (or at least the two to act) was holding a pocket pair higher than 8s. I mean take a deck of cards. Take out the 4 cards I was holding and the 4 cards on the board by the turn. Then just start dealing in fours until you have a hand with a higher pocket pair. Do it more than once to even it out, but I've done it several times, and over half the times I've made it through the entire deck without a higher pair. Very rarely have I dealt one in the 1st 2.

All in all you're correct. Omaha is NOT simple, and you can't rule anything out until the cards are flipped, but you also have to make some reads. Only 1 hand was ahead of me when I had that choice and even those 10s are looking for a 2 outer to beat the many hands I can have. A bet would very likely have won me the pot. And even if the "bluff" hadn't worked, my hand is decent in that spot a lot of the time if the reads I had held up. I guess the thing is there are rare times when no one seems to want a pot and even if it's 5 way, a middle position bet can take it down. And if someone IS slow playing, you can always just give up the attempt.

Really good feedback. Thanks, cherry pie!

[CherryPie]

Originally Posted by DukeOfDeath

.. but you also have to make some reads. Only 1 hand was ahead of me when I had that choice and even those 10s are looking for a 2 outer to beat the many hands I can have. A bet would very likely have won me the pot. And even if the "bluff" hadn't worked, my hand is decent in that spot a lot of the time if the reads I had held up. I guess the thing is there are rare times when no one seems to want a pot and even if it's 5 way, a middle position bet can take it down. And if someone IS slow playing, you can always just give up the attempt.

yup agreed gh to analyse, & i enjoyed ur post.. definitely one of ur better threads