Aces in PLO
note: cross posted from Andrew's blog at http://www.thinkingpoker.net/Blog/
Two kind of interesting spots from a recent PLO session. They don't have much in common other than the fact that both involve AAxx hands.
Full Tilt Poker
Pot Limit Omaha Ring game
Blinds: $2/$4
6 players
Stack sizes:
UTG: $616.70
UTG+1: $236
CO: $345
Button: $806.40
Hero: $1024.30
BB: $929.40
Pre-flop: (6 players) Hero is SB with 
UTG calls, UTG+1 calls, 2 folds, Hero calls, BB checks.
Flop: 
($16, 4 players)
Hero checks, BB checks, UTG checks, UTG+1 checks.
Turn: 
($16, 4 players)
Hero checks, BB bets $18, UTG folds, UTG+1 raises to $72, Hero raises to $252, BB folds, UTG+1 calls all-in $160.
Uncalled bets: $20 returned to Hero.
River: 
($498, 1 player + 1 all-in - Main pot: $498)
Results:
Final pot: $498
Hero showed
UTG+1 showed 
I just complete because I'm in the worst position and I have dry Aces, which is to say no suited cards or connectivity or anything to go along with them. These limpers are never folding, and I can pretty much only win the pot by flopping a set, so I might as well keep it small.
So when I do flop the set, I'm looking to check-raise the flop. If I led out for pot, I'd be showing a fair bit of strength and not really setting myself up to win a big pot. Probably either everyone would fold or someone would call with a draw and then either draw out on the turn or fold to a pot bet on the turn (or maybe pick up enough equity on the turn that calling pot wouldn't be a big mistake). The only hand I can really make some money from is a worse set, and I expected those to bet the flop if I checked anyway.
Then the turn brought a ton of draws, though I still had the nuts. This time I was pretty sure it wouldn't check around again, and if it did, no big deal, because the pot is so small. If I led out here, most draws were just going to call which means I wouldn't be able to get all that much money in. And since I wouldn't know which draw my opponent was on, pretty much a bazillion river cards would be bad for my hand. So I checked again, this time looking to check-raise and get a bunch of money in while I was still ahead. Plus no one would ever put me on top set. And bada bing, bada boom, it worked.
Next hand:
Full Tilt Poker
Pot Limit Omaha Ring game
Blinds: $2/$4
5 players
Converter
Stack sizes:
UTG: $450.50
Hero: $843.80
Button: $594
SB: $420
BB: $351.80
Pre-flop: (5 players) Hero is CO with : 
UTG folds, Hero raises to $14, Button folds, SB calls, BB folds.
Flop: 
($32, 2 players)
SB checks, Hero bets $24, SB raises to $72, Hero calls.
Turn: 
($176, 2 players)
SB bets $100, Hero raises to $476, SB calls all-in $234.
Uncalled bets: $142 returned to Hero.
River: 
($844, 1 player + 1 all-in - Main pot: $844)
Results:
Final pot: $844
Hero showed
SB showed 
This is a pretty classic PLO bluff where, knowing that my opponent can't have the nuts, I represent it. The controversial part is the flop. Folding to the check-raise may be the correct play. The fact that I have the Ac actually makes it more likely that my opponent has AA beat than that he has a draw. But I was thinking I could take it away if a club turned even if my hand wasn't good. Oh well.
FTOPS Event 4 / Rebuy Tournament Theory
note: cross posted from Andrew's blog at http://www.thinkingpoker.net/Blog/
Event 4 was a $300 NLHE tournament that allowed one $300 rebuy and one $3000 add-on. The initial $300 bought 2000 chips, the rebuy bought 2000 chips anytime during the first hour that you had 2000 chips or fewer, and the add-on bought $2500 chips at the end of first hour.
There are two seminal books that address the value of tournament chips: David Sklansky's Tournament Poker for Advanced Players and Mason Malmuth's Gambling Theory and Other Topics. I haven't read Malmuth's book, but my understanding is that both make a similar argument that this value is non-linear. Another words, your last chip is worth more than your second to last chip is worth more than your third to last chip etc. Each chip you add to your stack increases the value of your stack, but by less than the preceeding chip did. So if you have on chip worth x, and you double up, your stack is worth marginally less than 2x. And if you double again, your stack will not be worth 4x. This is because survival has value in a tournament where all of the prize pool is not paid to the winner.
The countervailing principle is that chips are worth more in the hands of a skilled player than an unskilled player. This is because better players will have the opportunity to use those chips to win more chips. They contain within them the player's expected value for the tournament. In FTOPS Event 4, the first 2000 chips, which cost $300, were probably worth $750 or so to the best player in the field. Conversely, they were probably worth about $50 to the worst player.
You can see that at this rate, it is clearly correct for the best players to rebuy immediately in a tournament that allows unlimited rebuys. Even though his second $300 buys him less than his first expenditure, it still buys him more than $300 worth of value. Conversely, it is incorrect for the worst players to rebuy. In fact, it is incorrect for them to play at all.
When only a single rebuy is permitted, this could at least theoretically change. If a skilled player uses his rebuy immediately to double his starting stack, he risks losing all 4000 of his chips at once. Although his rebuy was a good investment, he missed out on the opportunity to make an even better investment in a second tournament life. Remember, going from 0 to 2000 is worth more than going from 2000 to 4000. By opting for the latter, the player cost himself the chance to do the former a second time.
However, this must be balanced against the risk of immediately getting over 2000 chips, remaining there for the entire rebuy period, and thus losing the opportunity, to invest that second $300 at all.
The one other thing I haven't mentioned yet is that it matters how many chips the other players at your table have and how good they are. A player cannot realize the extra value that his skill imparts to his 4000 chip stack if no one else at the table has more than 2000. If several bad players to his right all rebought immediately, then the good player should do so as well, so that he will have the opportunity to invest his additional 2000 chips well against those weak players. If several very good players to his immediate left rebought to 4000, the same player might be better off saving his rebuy as an insurance policy against elimination. Otherwise, he risks playing larger pots out of position against very good players- a scenario where those additional chips would not be invested well. If the first hour is drawing to a close and his stack is below 2000, he can always take his second rebuy then.
Unlike an unlimited rebuy tournament, where it generally makes sense to push any edge during the rebuy period since survival is never at risk, this structure makes survival during the first hour particularly important. This is because the player will have the opportunity at the end of the first hour to buy chips at a discount. $300 will buy him, not 2000 chips, as with the rebuys, but 2500 chips for an add-on. It is pretty much always profitable for a good player to add-on, and if he is eliminated in the first hour, he won't have a chance to take this good investment.
I include this exegesis on rebuy tournament theory because I have nothing interesting to say about the tournament itself. No one at my table rebought immediately, so I didn't either. I lost my first 2000 chips with two pair in a limped pot at the 10/20 level. My opponent seemed like a fish, so I thought he would call me down with worse, but he ended up having a better two pair. Then I rebought, added on, lasted for about an hour more despite missing tons of flops, shoved over a very weak limper with K7s, and got called by one of the blinds who had AK.
I'm not all that good at PLO, but I do want to learn, and I'm sure it will be a weak field, so I'll probably play today's 2:00 $500 PLO 6-Max. I'll be playing the Stars $300 anyway. Then at 4:30 there's a $100 rebuy FTOPS that I'll play if I'm not sick of poker by then.
Thanks Everyone!
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Time to record another video! Best of luck at the tables,
Andrew "Foucault" Brokos