General strategy in short-handed vs. loose opps?

What is generally the best way to play in a short-handed or heads-up game against very loose opponents? I'd appreciate answers for either low-limit (3/6) or for PL/NL (i.e. near end of tourny).


I usually don't try any true bluffs in limit games with 5 or more (semi-bluffs excluded). Against 1 or 2 loose players, should I take more chances? It sounds dumb but blinds dig into my bankroll quickly so I'm wondering if I should be playing overcards (with nothing else) on the flop aggressively, etc.


I haven't found any sites with detailed short-handed strategy, could someone help me out?

Hello,Kevin,

Chris posted these hands for short-handed play:

Button: 44,A4o,A2s,K9o,K6s,Q9o,Q8s,J9o,J7s,T9o,89s

************************************************** **************************************************

Cutoff:

66,A7o,A3s,KTo,K8s,QTo,Q9s,JTo

************************************************** *************************************************

2 off the button:

77,A9o,A5s,KTo,K9s,QJo,QTs,JTs


Happy Pokering,

Sitting Bull

I think if you go to abdul's positive ev sight (i think its one of the favorite links).


Short handed is alot more complicated than just a starting hand strategy. Look at that sight and reading the short handed section in holdem for advanced players would help also.

Against loose players headsup i think you should be calling preflop with hands that have a decent chance of flopping a medium or high pair, eg K3o is a fold, but J8 is a call, and if you have an A always put in a raise, and ofcourse with hands like Kq and Kj and the pairs u but in a raise too, then on the flop bet your strong hands and give them action while your medium hands should be check called unless u are sure that you are beaten. Don't try bluffing a lot, betting the river is the best bluff against loose players since they often call with anydraw they can find, but when they only have their high card or low pair they might fold. i Hope u will find this information, helpful.

In heads up, optimum strategy against a loose/extremely passive opponent would be to play just slightly more than half as many hands than he does. The same would be true against a loose/extremely aggressive opponent.


I'll explain more if interested.

This is not correct. You should play just about all of your hands against a loose extremely passive opponent.

If you assume your opponent will always bet, the optimum strategy is to play slightly more than half as many hands as he does. From memory the formula is (P-B)/2 I think, where P is the pot size, B is the blind, and the result is the percentile (e.g. .45 would mean play the best 55% hands). I'll post the derivation tomorrow if you're interested.


Note this is a theoretical observation, not a practical one. That is, this is assuming you're playing a moron who will always bet his hand.


By playing more hands than the above, your EV goes down because he wins a higher percentage of hands. By playing less hands than the above, your EV goes down because you lose too many blinds.

Oops! "That is, this is assuming you're playing a moron who will always bet his hand." should have been "That is, this is assuming you're playing a moron who will always call his hand."

My fear of the other 1-1 players breaking my knees makes me uncomfortable discussing this much further. His name is Erik123 because after he publicly explained a correct 1-1 turn play, he was left in an alley, counting the remaining fingers on his left hand in disbelief "1...2...3 1...2...3".


I will tell you, however, that whether or not that equation is right in some way, you are forgeting a few major factors and are analyzing the problem from the wrong angle. I am certain that you can play most if not all hands against a loose, passive player. Even against a loose-agressive player, 55% is far too few. Feel free to email me at inertpair@hotmail.com. I would be interested to see that proof if you have time to post it.


-Glenn

Let y = percentile of hands to play (.4 means play 60% of best hands)

Let x = percentile loose/extremely passive person plays (he always calls).

Let P = size of pot, B = blind.


EV is given by:


f(y) = P(y-x)(1-y) - By(1-x)

f '(y) = P - 2Py + Px + Bx -B


The max occurs when f '(y) = 0, which is when y = (1+x)/2 - B(1-x)/2P, which is slightly less than (1+x)/2.


This means optimal strategy against a loose opponent that will always call is to play slightly more than half as many hands as he plays. Playing too loose cuts down on profits by minimizing the Py term, meaning that you win a smaller percentage of pots (by playing cards that are less good).

"Let y = percentile of hands to play (.4 means play 60% of best hands) "


This makes no sense. Value of hands should be determined by average pot equity. The hand's rank is irrelevant. This is because the value of hands does not decrease linearly, and they are not evenly distributed around the mean. What I mean by this is AA wins more than 32 loses, etc...


"EV is given by:


f(y) = P(y-x)(1-y) - By(1-x)

f '(y) = P - 2Py + Px + Bx -B"


First of all there are math errors in this equation. If x is the number (%) of hands the loose player plays then x=1 so:


f(y) = P (y-1) (1-y) - B y ( 1 - 1 )


= Py - Py^2 - P + Py - 0


= -Py^2 + 2Py - P


and f'(y) would then equal:


= -2Py + 2P


which is 0 when y = 1.


so that doesn't help at all.


Caluculating the EV of a hand is nowhere near this simple. In your analysis you have completely ignored postflop play which is the main issue I was trying to get you to see in my previous posts. In a normal BB/SB structure, you are getting pot odds of 3:1 to call preflop from the SB and the same 3:1 to call a raise from the BB. This means you have correct odds to call with any hand that has at least 25% average pot equity. That is every possible hand. Postflop play changes the EVs (implied odds, reverse implied odds) so an arguement can be made that some hands should be folded, especially to a raise (which may give you information that your opponent holds a better than average hand, depending on the opponent).


Nevermind the wrong equations. Here's what you are missing completely. A weak passive player will check when you check and call when you bet. Therefore, there is a style of postflop play that will give you a +EV with any hand (bet when you have a better than average hand, check when you don't). Since you have correct pot odds to call preflop and your EV can only be positive postflop, you should play 100% of your hands.


When a player will actually bet or raise this changes of course, but it is never correct to play only 55% of your hands.


-Glenn

f(y) = P(y-x)(1-y) - By(1-x) would reduce to

f(y) = Py(1-y) - By if x played every hand, in which case x would be 0 (not 1).


Of course the equation is rediculously simplistic, but that's always the case whenever you try to model something complicated. The maximization was done on the assumption that you would always bet. While the equation is simplistic, I don't think it's incorrect.


Your statement on pot equity is correct, but too difficult to model, hence the simplifying assumption regarding the relative strength of hands.


What you're suggesting is to play the same number of hands as the opponent, and then outplay him after the flop. My suggestion involves playing better cards and winning on the basis of the cards. I like your suggestion.


Regarding playing hands. You wrote, "In a normal BB/SB structure, you are getting pot odds of 3:1 to call preflop from the SB and the same 3:1 to call a raise from the BB. This means you have correct odds to call with any hand that has at least 25% average pot equity. That is every possible hand."


Since this doesn't depend on the opponent, you appear to be saying that you should always play every hand. Did I understand you correctly?


BTW, thanks for your responses.

I still have no idea what you're trying to do. You said that x is the percentage of hands your opponent plays, that is why I used 1.


Modeling heads-up play with the assmption that you will always bet is useless. The idea that:


"the equation is rediculously simplistic, but that's always the case whenever you try to model something complicated"


is wrong. I was just looking at the derivation of Black-Scholes today and it is not simplistic. It is simpler than the actual chaotic process, but not simple.


"Your statement on pot equity is correct, but too difficult to model, hence the simplifying assumption regarding the relative strength of hands."


It is not difficult to model this at all. If your pot equity is greater than the amount of money you voluntarily put in the pot divided by the total amount of money in the pot, then your expectation is positive. For a given structure you could easily find the cutoff percentage.


"you appear to be saying that you should always play every hand. Did I understand you correctly?


Preflop pot odds say you should play every hand. Due to reverse implied odds and the value of information, this is not always correct in practice.


Here is a proof of correct preflop play against a loose/passive opponent.


Assumptions:


1. Your opponent will never bet.

2. Your opponent will always call a bet.

3. Normal bet structure, SB = s, BB = b.


Correct preflop play:


Your EV is positive when:


average pot equity of your hand > (b-s)/2b


In a 1/2 blind structure, this is .25

In a 1/3 blind structure, this is .333

In a 2/3 blind structure, this is .167


Since your minimum postflop EV is 0 (you can always check with every hand), you definitely should complete the SB with any hand that passes the above test, or you are giving up money.


Now we can determine what hands to raise with preflop:


This is pretty much trivial. You should raise with any hand that has more than 50% average pot equity. The ROI for a raise is:


(average pot equity * 2) - 1


Any time this is greater than 0, your EV is postive. Therefore, you should raise with any hand that has more than 50% average pot equity.


For reference, 32o has 32.3% pot equity preflop. The second worst hand, 42o has 33.2% and is the only other hand that you have incorrect pot odds to call with preflop in a game with a 1-3 blind structure. The small loss you will take preflop by playing these hands should easily be overcome by your postive postflop EV, however. J5s is the cutoff for raising hands with a preflop equity of 50.0%.


Obviously, your postflop EV should be very positive, since you should only be putting money in the pot in +EV situations. Anytime you have better than a 50% chance of ending up with the pot with your hand, the current board, and your opponent holding 2 random cards, you bet, otherwise, you check. It requires serious analysis to know excatly where the cutoff point for a given hand/board is, but your postflop EV would be positive if you bet only when you held the absolute nuts.


-Glenn

Thanks Glenn! This is a very nice post with good food for thought.


"I still have no idea what you're trying to do. You said that x is the percentage of hands your opponent plays, that is why I used 1." I wrote that x was the percentile, and gave an example that .4 would mean that x would play 60% of the hands. This is why when the answer comes to (P-B)/2 that translates to slight more than 50% of hands rather than 50% less.


I wrote "the equation is rediculously simplistic, but that's always the case whenever you try to model something complicated". This was overstated. I should have written that simplifying assumptions are commonly used, which is what I was trying to do. What the above question answers is what % of hands you should play if you play a game where your opponent plays the best x% (or y, whichever I used) of hands.


1) You can choose to fold or play pre-flop

2) If you choose to play, you must bet, and your opponent must call.


It would also work if 2) were

2) If you choose to play, your opponent must bet, and you must call.


A follow up question. What hands should you call a pre-flop raise with? The pot odds are still 1 to 3, but there's a couple of things working against you.

1) Your not calling against random hands, but hands good enough to raise (say J5)

2) Your out of position for future rounds.


Thanks for any comments.

You should call a raise with most hands. If your opponent plays well, you should call with less hands than if your opponent is a supermagoo because your implied odds are less and your reverse implied odds are greater. I don't think it could ever be correct to fold more than 20-25% or so, however. The specifics really depend on how you and your opponent play postflop, but you definitely shouldn't be folding very often if at all.