Wednesday, November 28, 2012

#5: How to calculate pot-odds

Since we're quite a bit on the mathematical tour, we're going to continue this before going to discuss some other big aspects. It's all pretty logical stuff, but you do need to know it in order to become a winning poker player, especially since the games are pretty hard nowadays anyhow.

So. We are dealt QhKh under the gun in a 6-Max, rakefree, game, and we raise it up to 3bb. Btn who has a small 25bb stack makes a 3Bet to 10bb. Blinds fold, we call and see the flop Ah3h9c. We check to him, and he ships his remaining stack of 15bb.

But can we make a profitable call?

-We quickly estimate our equity (previous article) to 4*9 = 36%
-The potsize:
   Preflop: 1.5bb (blinds) + 10bb + 10bb = 21.5bb
   Flop: 15bb
   So the potsize is 15 + 21.5 = 36.5bb

We need to call 15bb to win a 36.5 + 15bb = 51.5bb pot

This gives us the following pot odds: (15/51.5) * 100% = 29.1%

Since the pot-odds are lower then our equity, we can make a profitable call. Said in words: The reason why we can make a profitable call although we have approximately 36% equity, is because of the money we allready invested in the pot.

How much $$ do we make with our call?

Now we came so far, it's pretty easy to calculate the so-called Expected Value of calling his flopbet.

Percentage equity - Percentage pot-odds = Edge in %
36.0% - 29.1% = 6.9%

Multiplie this percentage by the size of the pot.
6.9% * 51.5bb =  3.55bb

We win 3.55b on average by calling his flop bet.

#4: How to calculate Equity in NLHE/PLO

Count Your Outs: In order to calculate your equity (your odds of winning the pot), you need to first know how many outs you have to make your hand. This becomes quick and simple with a little practice and a little memorization.

A very important given in Poker is:
  • When you're drawing OTF (on the flop), every out you have gives you roughly X(amount of outs) * 4% equity. 
  • When you're drawing OTT (on the turn), every out you have gives you roughly X(amount of outs) * 2% equity.
When you've got more then 13 outs OTF, you're required to use a different formula:
  ( X(amount of outs) * 3(%) ) -9% = Total Equity 

It's important not to forgot to move the cards that aren't outs. For example:
  • Hero holds QK
  • Villains range is narrowed to AK 
  • Flop = TJK
So our outs are:

No King (we're still outkicked)
No Queen (makes straight)

That'll give us (3+4) * 4 = 28% equity.

We'll go to Pro Poker Tools to check it up:

Hold'em Simulation ? 
95,040 trials (Exhaustive)
board: TcJsKd

Which says we're close to matching, which is pretty cool since we can do these kind of calculations while playing.

The stronger a read you get, the more accurate your equity calculations will become, which will obvious will maximize our profits.

#3: Preflop Betsizing in NLHE

Probably the most important aspect of Poker is betsizing. We want to get maximum value when we have a hand with lots of showdown, and we want to get off with bluffs cheaply; Minimize or loss when someone calls our bluff. Non of it is rocket science. It's just logical thinking.


Preflop you can pretty much hold on to these standards:
Openings raise in early position: 3x
Openings raise in late position: 2.5x
Opening raise on the button: 2.25x

The reason you want to lower your raisingsize when you're in late position, is because you'll be opening wider, and thus with a wider range, so you want less money in the pot when you're weaker in general. You should ignore this if you're a superbus player postflop in position! But start out this way.

As A 3bet I'd recommend just use a standard raising size of 3x~3.5x the original raise, depending on if he's likely to 4bet a smaller 3bet, if he folds lots to Cbet etc. For example:

6 Max Game, Hero = Btn
CO opens 3bb (folds to a lot of Cbets)
Hero 3bets 10.5bb (we 3bet quite big because he folds a lot to Cbets)

We Cbet the 2KKxxy flop 2/5th Pot and he folds.

#2: Simple Opening Chart

I would like to add some Opening Charts to this Blog in sequence to the previous blogpost.

Raise First-in
Facing one Limper
Facing Three Limpers
Facing Raise Early + Late Position
Raise + 1 CC
Raise + 2 CC
Facing 3bet / 4bet
Credits to Leader from the twoplustwo forums.

#1: Intro & Preflop Hand Selection


As a sequence of the PLO Blog ( I decided to also make a 6-Max Texas Hold'em (No limit) blog. Obvious there's just a shitload No Limit Hold'em Information available at this moment, so in order to get me some followers I needed to do something special. I decided to make some basic content first, but then go indepth about Poker Pro Tools. The most valuable tool for a Cashgame grinder. And after all, we all want to grind cash, right? Right?

I'll start of with a basic 6-Max opening Chart, and quickly follow up with the rest of the basics.

Hand Groupings:


These are monster hands in any 6-max game and should almost always be played with the most aggression possible pf.


These hands are very strong and should generally be raised or 3-bet pf. If it’s 3-bets cold to you, you may fold depending on the conditions.


These hands are also strong and should be raised from any position if there has not been a raise. The better of these hands can be 3-bet against overaggressive players or late position raisers. They should generally be folded for a raise coming from early position.


These hands should generally be folded UTG and MP with the exception of A9o, A8o, K9s, KTo, and JTs, which should be raised in MP. If there's a limper, these hands should be played either for a call or a raise depending on the exact hand and the likelihood of a raise making it heads up to the flop. All these hands should be raised in opened from late position and the small blind.


These are hands that you should open from the CO, BT, and SB, but should generally fold otherwise unless both your hand is suited and there are at least two limpers.


These are hands that should be opened from the BT or SB but should be folded otherwise unless both your hand is suited and there are at least two limpers.

Suited Cards

Any two suited cards can be played if there are two limpers to you in the SB or if you are in the BB and there is a raise and two callers. Most suited cards can be played with one less limper or one less caller simply avoid hands like 74s, J3s, and 83s in this situation.

Big Blind Defense

Big blind defense is critical to your success in short-handed limit hold'em. You will play more hands in the big blind then in any other position. These hands will mostly be in small pots were you will be OOP. It's critical that you play them right. You should typically defend the following hands vs. a stealer:

All pocket pairs, Axs, Axo, Kxs, K6o+, Q6s+, Q8o+, J7s+, J9o+, T7s+, T8o+, 97s+, 97o, 86s+, 87o, 75s+, 76o, 65s, 65o, 54s

Heads up versus a lone late position raiser, you should 3-bet:

77+, A9s+, ATo+, KJs+, KJo+, QJs

Against a late position stealer and one caller, you should defend all of the above and Qxs, J6s, T6s, 96s, 85s, 64s. With two callers, you should defend also defend any two suited.

If you are in the BB and a solid, passive or unknown early position player raises, you must play significantly tighter. Heads up versus this player, you should defend:

66+, Axs, A8o+, K8s+, KTo+, QTs+, QJo, J9s+, T8s+, 98s, 87s

You should 3-bet with:

99+, AJs+, AQo+, KQs

Against an early position player and one cold caller, you should defend:

Any pocket pair, Axs, A9o+, KTo+, Q7s+, QTo, J8s, JTo, T7s+, T9o, 98s, 87s, 76s, 65s, 54s

Against an early position raise and two or more callers, you should defend the above and:

A7o, 98o, 87o, any two suited

In both of the above cases, you should 3-bet the same hands as you would heads up the raiser.

Call-C/R Big Defense

When you have a hand worthy of 3-betting and are HU, you have another line you can take to deceive your opponent. You can just call pf with the intention of c/r'ing nearly every flop. If your opponent bets every flop, then you are in a nearly identical situation after c/r'ing the flop as you'd be if you were to 3-bet and lead every flop. The main purpose of this tactic is to trick your opponents hand reading ability into believing that you have a far weaker hand then you in fact have. For example:

CO raises, BT folds, SB folds, Hero calls with AhKh

Flop: Kd7s2c

Hero checks, CO bets, Hero raises

If CO has KQ or KJ, he likely believes he has the best hand even after our c/r. He will likely raise again either on the flop or on the turn. If we had 3-bet pf and bet the flop, CO would likely question whether he has the best hand and may elect to call down rather then risk a punishing re-raise from Hero.

This tactic works well in some situations but poorly in others. Let's review some of the considerations.

* If your opponent is very passive or very aggressive, tend to avoid this tactic. In the case of the passive player, you are not likely to get any extra action through your deception and he may check through the flop. In the case of the over aggressive player, you are likely to get extra action anyway. Therefore, you do not want to deprive your opponent of the chance to cap a worse hand pf.

* Contrarily, the ideal player to use this tactic against is a good, but not great, tight and slightly overaggressive player. This type of player will almost always give you extra action as he will attempt to read your hand and will give you extra bets.

* It is best to use this tactic with your strongest 3-betting hands until you have a good grasp of the effects of this play on how your opponents behave.

* Similarly, it's best that you avoid this tactic until you how players will react to a flop c/r normally so that you avoid missing bets or spewing.

* You do not have to c/r every flop. You should c/r most though even if you miss. The reason is two fold. First, if you have a hand like AK that has missed the flop, your hand is often best but vulnerable. You must avoid giving cheap cards or allowing your opponent to take a free river. Second, c/r'ing when you miss mixes up your game well. You're opponent will likely be very confused by your play and will often adjust by playing looser and more passively in the future.

Note that this line of thinking also applies when you raise and are left HU with a 3-bettor. In fact, you should be more likely to just call with strong hands in this situation because a cap significantly narrows your range to a thinking opponent.

Small Blind Defense

When defending the small blind, you must be significantly tighter then in the big blind because you are not closing the action and you have less money committed to the pot.

Against a lone late position stealer, you should defend with a 3-bet the following:

66+, A8s+, A9o+, KTs+, KJo+, QJs

Against an overaggressive late position stealer, you should also 3-bet:

55, A7s, A8o, K9s, KTo

And call with:

QTs, JTs-J9s, T9s, 98s

Against a lone early position raise, you much again be tighter. You should 3-bet:

99, ATs, AJo, KQs

As long as the raiser isn't passive, you should call:

KQo and KJs

If there is one cold caller and big blind is a loose player, you should also call with any pocket pair. If big blind is not loose, there should be two cold callers.

Cold Calling

You should very rarely cold call in short handed limit hold’em. There are exceptions though. As we’re already seen, certain hands should be cold called in the small blind when an overaggressive player raises. We’ll now examine when a more typical player raises and others have cold called.

If there is a raiser and one other cold caller, you should also cold call in the small blind with:

88-77, KJs-KTs, KQo

If there are two cold callers, you should cold call:

99-22, KTs, QJs-QTs, JTs-J9s, T9s-T8s, 98s

on the button. You should add:

A9s-A8s, ATo, K9s

in the small blind. With three cold callers, you can call many more hands in the sb including:

99-22, A9s-A2s, ATo, KTs-K8s, KQo-KJo, QJs-Q9s, JTs-J9s, T9s-T8s, 98s, 87s, 76s

Blind battles

As with all heads up situations, blind battles are heavy influenced by how your opponent players and how he sees you. Because you will be out of position the whole hand, you must be careful if your opponent is aggressive. If your opponent 3-bets when you raise with a weak hand, you will very rarely win no matter what he has. Fortunately, most players are far too tight and passive in this situation. Therefore, you should raise a large range of hands until you have a read that your opponent is aggressive. You should open the following in the SB:

Any pocket pair, any Ax, Kxs, K4o+, Q5s+, Q8o+, J7s+, J9o+, T7s+, T8o+, 97s+, 98o, 86s+, 87o, 76s

When you face a raise from the small blind, you can reasonability defend almost any hand especially if small blind is an aggressive player. However, many of these hands are difficult to play post flop. Therefore, until you have a good understanding of limit hold’em you should restrict yourself to the following:

Any pocket pair, any Ax, Kxs, K4o+, Q5s+, Q6o+, J6s+, J8o, T6s+, T7o+, 96s+, 97o+, 85s+, 86o+, 75s+, 75o+, 64s+, 65o, 54s

If small blind open limps, you are in a very advantageous position. You will have position for the rest of the hand. Small blind is very likely to have a weak hand. In this situation, you should raise regardless of your cards. This may seem strange at first, but keep in mind how hard it is to win a hand when you miss the flop out of position. Your opponent will miss the flop about two-thirds of the time with unpaired cards.

Taking advantage of loose passive tables in early position

A table where most pots are limped three to five way to the flop gives you opportunities to open limping with marginal hands in early position. Specifically, you should consider limping pocket pairs, suited aces, and suited connectors through 87s.

Open limping on the button

Open limping on the button is often seen as a cardinal sin in poker strategy, but there are exceptions to almost every rule. Here the exception is when both blinds are very loose. In this case, you have little chance of stealing the blinds. With certain hands in this situation, you will benefit more from a small post flop pot in which your opponents will make bigger, more frequent post flop mistakes. Hands you should consider open limping on the button include small pocket pairs, small off-suit Aces, off-suit connectors, and medium suited and off-suit kings.

Credits to Leader from the twoplustwo forums.