Wednesday, May 02, 2007

LHE ramblings

The trend of NLHE killing off LHE games has been well reported and is, in general, very widespread. However, in large part due to municipal laws, live LHE games in my area are still very much alive and well.

Local municipal laws disallow any single bet to exceed $200. The motivation for the law is to help protect people (who, of course, are incapable of protecting themselves) by limiting players' overall rate of losses. States like Florida and Colorado have similar statewide laws, although much more extreme. Florida has a $2 max bet (although rumors are that legislators are considering a modest increase), and Colorado has a $5 max bet. A lot of points could be made on this whole subject matter, but I digress.

At any rate, in regards to how this local law affects the types of games that get spread locally, the effect is this: All high stakes hold'em games are of the limit variety. The relative stakes of a $100/$200 LHE game positively dwarf any type of NLHE game (or actually spread limit HE as it is called) that is restricted by a $200 max bet.

The end result is that there is a very healthy size player pool for midstakes games in the $20/$40, $40/$80 and $100/$200 range. (The area I live in is very affluent)

I'm fine with this as I do enjoy LHE more than NLHE, in spite of the substantially higher number of bad beats taken.

an LHE hand

I joined a local $40/$80 LHE game for the first time in an extremely long time. After having played in the $40 game at Commerce a few times this year (which is an absolutely great game), I told myself to restrict any $40 play to the times I can make it to Commerce. There is a frequent tendency in card rooms that the toughest games in a card room tend to be at the 2nd highest stakes. In the case of the largest local card room, the $40/$80 game is the 2nd highest stakes, and I do believe that the above trend applies to this case.

However, one local club that previously had $20/$40 LHE as the highest stakes game in the room recently added a $40/$80 table.

Here is a hand from that session that I found interesting. In this hand, it made a substantial difference to me that it was a live (vs. online) hand.

hand #1
9 handed $40/$80 LHE
Villain #1 in the SB is an observant thinking player who I believe has a fairly good understanding of people's hand ranges. He has been losing, but I do not believe he is even remotely on tilt.
Villain #2 on the button is a talkative, observant, thinking and moderately aggressive player who has not gotten involved in a single hand with me thus far in the session. He is having a good session.
I've been playing a solid, unimaginative style for ~1 hour that I have been at this table. However both players have a moderate amount of previous table time with me, so they would understand my late position open stealing range is fairly wide. Both I and SB understand that button's pf 3 betting range is also somewhat large.
preflop: mucked to Hero in CO, Hero raises with AhKc, button 3 bets, SB cold calls, BB mucks, Hero calls. (3 players, pot size 10 small bets)
flop: Kd9s9c, SB checks, Hero checks, button bets, SB just calls, Hero check raises, button pauses for less than 1/4 second and calls, SB calls (3 players, pot size 16 small bets)
turn: Kd9s9c3h, SB and Hero both check call (3 players, pot size 11 big bets)
river: Kd9s9c3h5c, SB checks, Hero checks, button bets, SB mucks, Hero calls.

On the flop when facing the button's bet and SB's call, I make Villain #1's range to be QJs, JTs, T9s, J9s, 98s, etc. I don't put him on any K as he didn't CR, and no big PP as he didn't 4 bet pf. Button's range at this point is very wide as, naturally, he will cbet the flop 100% of the time: 33+, ATo+, KTo+.
I CR this somewhat dry board to define my hand (I assume I am representing any Kxo or better) and observe both opponents' reactions.

My line of decisions beyond this point was substantially influenced by the fact that the button did not react in any upset manner when CR'd on the flop. I was quite surpised that he had no visible reaction as he is a talker, and this to me represented strength (AA, AK, KK).
Thus my read is the scenario is a way ahead, way behind situation vs. the button and SB, although I put them on very different hands.

On the turn, I felt a check was prudent for the above reason. My check was with the intention of folding to a SB CR. Button's turn bet and mannerism re-enforces my earlier read. However, as I mentioned earlier, he is an aggressive player and a very small % of the time he will have a worse decent made hand , and if so I would expect him to fire both the turn and the river given the way the hand has been played since he will always bet when the pot is big and he is sure he can't win in a showdown. (This playing line is essentially described in Stoxtrader's new book "Winning in Tough Hold'em Games" in the section on postflop play - "Check-Raise/Check-Call line when playing out of position")
SB's turn call actually made me revise his range to JTs, QJs, and include some very passively played medium K's like K7 and K8. I have definitely ruled out trip 9's by this point, and I think he will also not slow play a full house at this point. I do not want to see any broadway card other than K on the river.

The river card changes absolutely nothing. Button bets and SB mucks giving me 12:1, but really 5.5:1 to chop vs his legitimate hand range and 12:1 for his bluffs.

This is a straight bayesian analysis. The only unknown is how small a % of the time button has a bluffing hand. Let's assume 5%.
AA - 3 possibilities
KK - 1
AK - 6
The EV of calling is +3.3BB; an easy call.

Assume for a moment that SB calls the river, and that 90% of the time it is with a worse K, and 10% of the time it is a worse non-K hand. (A King in SB's hand SUBSTANTIALLY reduces the % of button's legitimate hands that I can chop with...)
The EV drops to +1.85BB; also an easy call.

Assume for a moment that SB calls the river with the above guidelines, and that button is NEVER bluffing.
The EV drops to +0.75BB. (I was actually surprised this number was so high until I did the calcuation)

Doing a similar analysis on the turn is substantially more complicated due to the necessity to factor in scenarios like SB drawing to the best hand, Hero improving on the river to beat a legitimate button hand, Hero improving to a still 2nd best hand, etc..

Anyway, on to the results.
End Result: Button's AA is good.

Regarding the live vs. online thing with respect to this hand: online I would definitely played the hand much more aggressively and lost 2-3BB more. Playing live provides more information, and is also more entertaining.... :)

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