Optimal Mode of Play

Introduction

In this Article

• What is the optimal mode of play and how do I find it?
  
• What are the typical characteristics of the optimal mode?
  
• What are the effects of playability?
  

The majority of poker encounters are concerned with winning the maximum amount from bad players. The goal might also be to exploit the weaknesses of such an opponent as much as possible. But what if the opponent is an excellent player? Many tricks that are effective against weak players are counterproductive in that situation. Thus, against a good player it's less about exploiting his weaknesses – he hardly has any – rather, it's about playing in such a manner that we don't give him a toehold.

Part I: Playing against tough opponents - The theory

Jack is loose-passive. He calls the flop with almost every hand – regardless of whether he's hit anything or not. On the turn, though, he becomes tight and folds a lot.

So with Jack, we'll bet the turn again after making a flop bet, and he'll often fold. If he raises the turn, we know that he has a strong hand and can usually make good laydowns after that.

Joe is an acquaintance of Jack and a tough player. He watches our game against Jack and when Jack no longer wants to play, Joe jumps right in for him. We assume, incorrectly, that Joe plays the same as Jack. Joe is a tough player, though. He uses our tendency to bet the turn after betting the flop by playing call flop, raise turn without mercy. On the turn he often raises as a semi-bluff, so that what were good laydowns are now fatal mistakes.

To sum it up: Joe is extremely good at identifying our weaknesses and exploits them optimally. Whereas our mode of play is highly profitable against fish like Jack, it turns out to be very costly against Joe.

We will later see that there are modes of play that are nearly free of weaknesses, which is why even very good players cannot exploit them. If you strictly adhere to these “optimal” modes, though, you will not win the maximum amount against fish. However, they are theoretically at least break-even against *any* opponent, but, as no one's play is completely flawless, usually at least slightly +EV against any opponent.

An optimal mode of play is colloquial for a mode of play without weaknesses. Even the best poker player in the world, one who knows exactly how we play each hand and knows our ranges exactly, cannot gain an edge against an opponent playing optimally.

The optimal mode is purely defensive. We are not looking for weaknesses in the opponent that we might exploit, rather we assume that our opponent is a perfect player, and that any deviation from the optimal mode will be punished by him.

If you play strictly optimally, then the reads and stats about our opponent no longer matter. We play the same against every opponent and are at least break even against every opponent. In fact, we are a little plus since no opponent plays entirely free of mistakes.

It is clear, however, that we won't make the maximum. To do that – as in the example against Jack above – we would have to deviate from the optimal mode to exploit particular weaknesses in our opponent.

The maximum mode is based on the weaknesses of the opposition. The fewer weaknesses the opponent has, the more the maximum mode will approximate the optimal mode.

The two modes will be identical against an perfect opponent, that is, one without any weaknesses at all.

Of course, we try to get the maximum out of all opponents. Against fish, the optimal mode would be +EV but we would give up a lot of value.

Against good players, though, the optimal mode is often very close to the maximum, so playing the optimum game already yields the maximum value, in some sense. But the optimal mode has a decisive advantage: it is independent of any reads or stats. We cannot be "wrong" and cannot be tricked by the opponent. No matter what the opponent does or how good he is, we are at least break even, but usually almost always +EV by default.

Typical characteristics of the optimal mode

The optimal mode is the maximum mode against perfect opponents.

Imagine our opponent is perfect. He has seen through us completely and knows our strategy entirely. The only thing he doesn't know are our cards. But he knows our raise range. He knows how we play draws, made hands, and so forth.

This opponent doesn't exist? Au contraire! We imagine simply that we're playing against ourselves, only we don't know our cards – "our" ranges are still known to us.

Sequences like bet/fold with marginal hands will be easily turned against us by good opponents. A bet/fold is only to be considered if our hand really has no showdown value in the situation. Bet/fold value bets should be avoided.

Mathematically, a difficult poker decision occurs when the opponent puts us in a position where our EV is near 0. This can be the case with thin value bets on the river with marginal hands when the opponent raises (see above, bet/fold lines). Clearly, if the opponent seldom raises then the bet/fold line is very strong. It's a good weapon against passive fish. But with it we would give a tough player a chance to cause great difficulty for us. 

Another formulation: the optimal mode shoots for a minimum risk. It is about maximizing the minimum EV.


The minimum EV of check/call is "+" in the example above, the minimum EV of bet/fold is 0, however. Thus, we play check/call even if bet/fold is potentially more profitable.

As we said, we assume a perfect opponent who knows our strategy. Imagine we play monster hands heads-up OOP without initiative in the following way: check/call flop, donkbet turn. This line works wonderfully against typical LAGs. Assume further that we only use this line when we have a monster hand.

Now this strategy would be fatal againt a perfect opponent who knows about it already – he can easily make good folds against us. Hence, this mode is non-optimale.

To make our mode of play optimal, we must balance our bet sequences. The opponent must not automatically know, for a given sequence, whether he is ahead or behind.

Let us take the viewpoint of the opponent for a time. He raises on the button, we call in the BB. The flop is Jh 8h 6s. We check, he bets, we raise.

Our opponent knows our strategy. Which hand do we have?

• group 0: pure bluffs
• group 1: draws: T9, 75, XXh
• group 2: weak made hands: X8, X6, etc
• group 3: weak made hands mit draw: ......
• group 4: strong made hands: XJ, etc
• group 5: monster: 66, 68, etc.

As we see here, the knowledge our opponent has about our strategy hardly has an advantage. He cannot effectively guess our hand. Our strategy is therefore balanced. With this hand range, the line check/raise flop, bet turn, is game theoretically sounder.

Now, in some situations, we would rather play check/call on the flop. This is the case in way-ahead-way-behind situations.

Say the opposition raises us out of MP3 and we call from the BB. The flop is A22 rainbow. We check, the opponent bets, we call.

Which hand do we have? Typically, we would have an A with a weak kicker or a small pocket pair,

i.e.

• group 0: A7 - A3
• group 1: 77-33

If we play all other hands in this situation check/fold, we have a problem: the opponent knows our hand range and this range is also homogenous: he now knows how to play hands like AK – A8 and also KQ, KJ, etc. perfectly. Because of this advantage of information, we might as well show our enemy our cards. This means that in this form, the line check/call is unbalanced.

We now have two possibilities:

• 1. Eliminate the check/call line completely
• 2. Mix some deception into the check/call line

The first option would be a shame, since the check/call line is somewhat better than check/raise. For this reason, we'll examine the second option. How do we add deception to this line? We diversify our groups:

• group 2: OOP bluff call. (Goal: check/call Flop, check - check Turn, bet - fold River)
• group 3: Monster. (Goal: check/call Flop, check/raise Turn)

In this way we can play our main groups 0 and 1 for maximum value without divulging unnecessary information to the opposition. We have balanced our line. 

This point is extremely important to dispel a common misconception. Balancing the strategy doesn't mean that you just play differently than you normally would here and there all willy-nilly. Such things constantly crop up in poker books: "I normally raise AA pre-flop, but here I'll limp for deception." This is exactly how you must not think and act.

It must be absolutely clear to you from the start how your strategy looks and how it is balanced. For example, the axiom: raise or fold first-in already leads to a perfectly balanced strategy – the opponent cannot guess our hand from our action since we raise every playable hand – regardless of it's strength. Limping strong hands opportunistically would be very counterproductive.

The same is true of typical flop situations: if we are OOP on the flop in the BB without initiative and play either check/fold or check/raise, there is no reason for extra deception. To build in a check/call here and there would be counterproductive because the opponent would notice that something is rotten in the state of your hand. You already have enough deception by playing check/raise with both playable made hands and playable draws.

Even if you told your opponent exactly how and on what boards you play what hands, he can hardly use this information if your strategy is theoretically optimal.

A classical example is the following:
The pot on the river is 8 BB. The opponent tells you that he has a bluff catcher. You tell your opponent that you either have the nuts or you are bluffing. You even tell him that 90% or your bets mean nuts and 10% are nothing more than bluffs. Actually, you have the nuts in 20% of cases, so 22% of the time you'll bet the river.

You bet. The opposition now has 1:9 odds on his calls. If he calls, 10 BB are in the pot. He wins in 10% of cases, so the EV for his call is 0. It's the same with the EV of a fold.

Your EV is then +9 BB in 22% of cases no matter what the opponent does. But by mixing 10% bluffs into your strategy, you can bet the river 2% of the time as bluffs and the opponent can do nothing about it. Your average EV is therefore .22*9= 1.98 BB. Without the 10% bluffs it would be only .2*9- 1.8. And a bluff quota for more than 10% for all your bets would cause your EV to sink since the opponent would have a +EV call.

The point is that even though your opponent knows exactly what you are doing, he cannot use it to his advantage. Your hand has an EV here of at least +1.98, no matter what your opponent does.

In practice – how do I find the optimal mode?

We raise pre-flop from the SB with Kc8d. A tough player calls from the BB.

Flop: 9h 8h 2s.
Hero bets, Villian calls.

Turn: Ah
Hero ???

Now, we are playing against ourself. We know that we will often raise for a free SD or as a semi-bluff in this situation if the opponent bets into us.

We also know that, with many made hands on such a board we would play call flop, raise turn – since we know that we often bet the turn again on a draw heavy board after a flop bet with a made hand.

Furthermore, we also know that he will usually call the turn with a 9 and an 8, but usually not fold.

If we did that, we would give our opponent the perfect opportunity to exploit our game. If he raises, we won't know where we stand. Mathematically, this is equivalent to a +- 0 EV decision. This means we are giving the opposition the chance to steal all the EV from our hand.

What is the alternative? Check/call turn. This doesn't even give our opponent the chance to shove us into an undesirable situation.

For comparison: against poor players, a turn bet is often stronger here. A passive player will often fold a heart and not semi-bluff, but will raise his strong hands. Against such a player we would have an easy game using bet/fold. A good player, however, will turn those bet/folds against us.

Look at your hand histories without looking at your own cards. Knowing your own strategy, try to guess your own hand ranges from your bet sequences. Check whether your ranges are mixed enough so that a perfect opponent cannot get a perfect read on you.
If you find bet-sequences that you play only with a certain group of hands (e.g. strong made hands), you must either eliminate these or add deception to them. Always remember the following axiom: the sequence will naturally be determined from the main group of hands. This means that you should not suddenly play all your top pair hands weakly for deception, but instead you should play a small portion of your drawing hands as you would play top pairs and vice-versa.

You play heads-up against somebody who knows you, ideally for play money or small amount. But agree beforehand exactly how your bet sequences with which hands will be played, meaning you make no ad-hoc changes to your game. After a time you should be able to recognize whether a particular bet sequence is too transparent and must therefore be mixed with other hand groupings.

Summary

The maximum mode of play is the mode that exploits the weaknesses of the opponent to maximize our EV against this opponent.

The optimal mode of play is that which has no weaknesses itself and therefore leaves no point open to attack by a strong opponent. The optimal mode is not based on reads or stats.

The optimal mode is at least break-even against every opponent, but is de facto +EV against nearly all opponents since opponents give us +EV through their mistakes.

How, then, should we play? Against weak opponents, we will look for exotic and calculable bet-sequences to extract the maximum value. These opponents are incapable of turning these strategies against us.

Against good opponents we will approximate the optimal mode as nearly as we can. This will yield no weak point for him to attack and we will at least break even against him.

In this way, we extract the maximum value from the fish without giving it right back to the good players at the table.

Prognosis

The optimal mode does not require reads or stats and is at least break even against every player. It is, by default, slightly +EV against good players and solidly +EV against fish.

This opens the following possibilty to us: if you master the optimal strategy, you should be able to play 10 tables – even at the highest limits – on autopilot and still make guaranteed profit. You won't hit the fish for the most possible, but it will give you more time for multi-tabling. This strategy is used by Senorpata on PartyPoker, amongst others.

Sklansky, Theory of Poker, p. 179 - 190

Chen und Ankenman, [0,1] game part 1 - 8, rec.gambling.poker

Williams, The Complete Strategyst

Part II: Pre-Flop Fine Tuning

We all know the pre-flop equity principle. We also know that in pre-flop play, the playability of the hand and also the post-flop strength of the opponents play a role.

Now ask yourself the following question: is it possible to unite these three factors (equity, playability, opposition strength) so that we discover the actual strength of the hand?

How do the playability and equity of a hand fit in with it's EV? Can playability be calculated in the equity?

To test this we present the following: we take two hands with the same EV heads-up. One of these hands has excellent playability and the other very bad playability.

A2o has an equity of around 55% against a random hand and bad playability.
The EV of A20 from the SB heads-up is -.09 according to PokerRoom EV stats.

98o has an equity of around 48% against a random hand and very goodplayability.The EV of 98o according to PokerRoom EV Stats is also -.09.

The difference in equity between these hands is around 7%. This means we modify the equity of a hand using the playability as follows: depending on the playability, each hand gets plus/minus 3.5% equity.

This means the following: suppose we have A2o in the BB and a TAG from MP2 raises. He's playing roughly according to the ORC. We have an equity of around 35.5% against his range and extremely poor playability. We discount our equity by 3.5%, giving us a "true equity" of 32%, and therefore a fold. A hand like 65s has an equity of 34% here. Because of it's usable playability, we increase this by 1%. Thus, we have a "true equity" of over 35% and therefore a call.

This effect is very difficult to quantify. We know that a bad player can make up to -5 BB/100 and even more in extreme cases. This is .05 BB per hand. The AVG pot in heads-up is around 5BB. So for a call from the BB we count de facto not 1 SB but .9. This means that instead of 35%, 35%*.9 = 31.5% is sufficient equity, an advantage against fish of 3.5%. We have not yet considered, however, that we'll still have the sub-optimal hand on the flop, turn and river. Our advantage against the fish on the full 5BB is only 1%. I think a middle value of 2% to be realistic.

This means: against extreme fish, we can add a maximum of 2% to our equity.

Hence:

True Equity = Equity plus/minus up to 3.5% for playability plus up t0 2% against weak opponents