Poker players know that poker is not a game of chance. Sure, each hand originates from a deck of cards which is nothing more than a mechanical randomization device. But that no more means poker is based on luck than the fact that football teams flip a coin to decide who receives first means that football is a game of chance.
Seymour Flops
As the venerable Mr. Flops point out, In the long run, each football team will kick first and receive first about fifty percent of games each. It is their skill that determine who wins the most games/seasons/championships.
In the poker long run, each player will receive bad hands, meh hands, good hands and monsters about the same percentage of hands and it is the skill of the players that make the difference between winning and losing, profit and loss, earning and burning.
But there is a place for considering the effects of randomness in poker. That place is in the way we play similar hands against opponents who are trying to gain information on us. Against them, we should look for ways to deliberately and mathematically inject randomness in our play to make that information harder to get and less reliable for these observant villains.
Against skilled players, we do not want to make the same moves with the same hands in same spots 100% of the time. For example, we would not want to always 3bet premium hands and always flat call playable hands. Our game would be face up and our opponents would always know exactly how to play.
If you have pocket aces, you would probably like to 3bet and 4bet up to all-in ever time. You should, against unknown players because that is the best default strategy with aces.
Against observant opponents that you play regularly, you would need to mix it up. You do not want them to correctly assume you have a big hand every time you re-raise pre-flop, not do you want them to correctly assume that if you flat call pre-flop, you do not have a big hand.
So, with aces, kings and ace-king, a good strategy might be to play them hyper-aggressively sixty to eighty percent of the time and flat call the rest of the time.
By doing that, I give opponents just getting to know me a chance to see that I am capable of smooth calling big hands pre-flop. This gives them a factor to consider when I make frequent c-bets. It is important that either your flats of big hands and your re-raises with hands that you would normally call with be random or that they are perceived to be random. If you flat aces 20% of the time, but Villain is able to learn which spots you flat them in, your play would become more face up, not less.
How to randomize
The intuitive way is to tell yourself, ‘I’ll raise with aces three or four times and then flat with the and start the cycle over.’ The problem with that is that you will tend to be biased toward either one or the other, so you will not get the desired percentages and it will not really be random.
So, how to make your decisions truly random? You could bring a die to the table, a big colorful one. Use it as a card protector and randomizer. Rolling it as you look at your starting hand would be a good way to distract opponents trying to read your expression. If you get a big hand after one raiser, look at the die you just rolled with a plan to call if you roll a one or six and 3bet with two through five. Thus you would 3bet 66.6% of the time with a playable hand.
For hands you want to play with no raiser before you, you might still roll the die and raise unless you get a 3. Or you could raise the number of big blinds you roll with 1 being a limp.
Harrington, in Harrington on Cash Games, Volume 1, recommends using your watch as a randomizer. You would look at your second hand and tell yourself, for example, that if it is between 1 and 40, you will raise and if between 41 and 00 you will call. Watches are not as much of a thing as they used to be and neither are second hands. But you could keep your phone on the table if the rules allow it.
I suppose there is no reason you could not use the minute hand or minute digits to the same effect.
I would propose a better way of randomizing – one based on the suits of the cards in your hand. Suppose you want to raise with aces about two thirds of the time and call about one third. Of the six combos of aces, (AcAd, AcAh, AcAs, AdAh, AdAs, Ah, As), one is red, one is black, and four are different colors. You could plan to raise with mixed colors and call with the same color.
If you want to raise more often, such as 80% of the time, you could pick a color, red or black, and only call when you get that exact combo, red aces or black aces. That is one combo out of six so you would be raising 83.3% of the time, just over four fifths.
I like to use a kind of sliding scale depending on how well I think my opponents know me and whether I expect to play them again. Online at an anonymous site, I do not know them at all and do not expect them to get to know me. So I would 3bet aces about 100% of the time. Maybe late in a session if I’m up against an aggressive opponent, I might flat call expecting that opponent to keep aggressing post-flop.
Against opponents to whom I am new, but whom I expect to play more often, I would make it more sixty percent pure aggression and forty percent flat call. Aces are a hand you will frequently show down with, so a showdown with aces you flatted pre-flop will be noticed and remembered by observant opponents.
Then you can increase to about 80% raises. Especially if, before you get your next pocket aces, you have three bet with a hand like ace-face, suited connectors or small pair.
If you like my idea of making your calls more frequently with new players, \you could call with all three pocket ace combos that have your favorite suit. That would be half the time. Then slide the scale as the player get to know you until you are only calling with red aces, 16.7% of the time.
I would apply that thinking to all of the premium pairs, aces through jacks. Flat call the two monotone pairs and three bet the four two-tone pairs.
You could cut your combos of ace-king just about in half by flatting ace-king suited and ace-king off-suit monotone. That takes out six out of sixteen combos. Not exactly in half, but close enough. You really want to get precise, pick your favorite suit and flat with ace-king two-tone that has that suit.
However, randomizing your play of premium hands is only part of the picture of achieving balance. If you were to three bet only premium hands and three bet them every time, your HUD stats would show that you 3bet 3% of hands. If you balance by flatting them one third of the time, your 3bet percentage would be 2%. A knowledgeable player with enough hands on you in his HUD could recognize that.
He could be confident that when you do three bet, you have a premium. He would likely assume you had cut either ace-king out of your three bet range or that you had cut queens and jacks out. Either would deduct about 1% from your three bet range.
So you would want to balanced by three betting hands whose strength alone do not merit a three bet. Pick hands such as big suited connectors, middle and small pairs and ace jack that you would normally flat-call hoping for a favorable flop and add them to your three bet range.
If your goal is only to bring your three-bet percent back up to three, you will have to be careful. There are a lot of combos of suited connectors, suited aces and small pairs. If you wanted to merge your range of value three bets and balance three bets, you could add tens (six combos), nines (six combos), plus ace-queen suited (four combos).
That’s about 1.05% of combos. Now your total 3bet range 3.05, almost exactly what it would be if you were three betting premiums always and exclusively.
That sounds like a lot to remember at the table. Easier to remember and giving roughly the same results would be flatting ace-king suited (four combos) plus same color premium pairs (8 combos) while three betting ace-queen suited (four combos) and tens (six combos).
When You Do Not Need to Randomize
Against non-observant opponents, all of this randomization is meaningless. What matters is whether they will interpret your three-bet as a strong hand they should fold to or a weak hand that is bluffing.
There is no point in trying to balance against opponents like that. Simply 3bet all you strong hands and if you see that this villain always folds to 3bet, start adding bluffs to your 3bet range unless and until he catches on and then take them out. I do not recommend that you slow play premium hands against a beginner who you suspect will fold to a re-raise.
If you have a premium pair, especially aces or kings, you should 3bet knowing that you will almost always either pick up the pot or be called by worse. Being called by the same hand with a big pair is very rare, but like everything rare in poker, it happens:
Merged Versus Polarized Ranges
Adding those relatively strong hands to your value three-bet hands gives you balance. It could also be said to add bluffs with a merged range. it is merged because you are merging the top of your non-three bet range with your now reduced value three-bet range. Another approach would be to polarize that range.
I advocate a merged range pre-flop and a polarized range post-flop. Pre-flop, I like to get in strong, especially if a three-bet is to be called, bloating the pot and reducing stack to pot ratio (SPR). Showing down after a three bet with a middle pair or ace-queen sometimes will increase the likelihood that I will be called on later three-bets.
Post-flop bluff and balance is about your image and also about exploitative play. If you see the flop with two broadways, your default may be to continuation bet anytime you are against one opponent. Your adjustments might be to cbet against any two or three opponents whom you know to frequently call pre-flop and then fold the flop. Or you might take bluff cbets out of your range if you know that the players now in the hand rarely fold post-flop.
Cbet bluffs would be more polarized. Most often your hand either improved to a value hand or strong draw or it did not. If your ace-jack made top pair/top kicker, or higher cbet as a default. If your ace-jack flopped ace-high, one over-card, cbet to fold out any one player who does not have top pair or better.
Adjust that default based on information. On a table full of players who like to see the flop but always fold if they miss, a cbet frequency of 100% can be profitable. A half-pot cbet bluff need only get through one-third of the time to break even.
Four-bet Bluffs
Really?
Yes. Four-bet bluffing is something you should be doing so that villains do not assume that every four-bet is aces or kings. The GTO-ish value to bluff ratio is 2:1. Easily achieved by one of two methods.
You could default four-bet aces and kings (12 combos)always and add ace-king offsuit two-tone (6 combos). Alternately, you could pick another pair and add it as your bluff four-bet range (six combos). Which pair to use?
I would argue for jacks, rather than perfectly merging that range by “bluffing” with queens. Queens are more easily playable than jacks post flop since overcards to queens do not come as often as over-cards to jacks. Against a Villain who three-bet, ace-king is well within the range, so if an ace or a king flops, and prompts aggression, the laydown should be easier, absent information that this Villain is bluffy.
Four-betting only aces, kings and jacks is still only 1.36% of combos, a very tight range. A range that tight will induce folds by hands like ace-queen and king queen that would be coin flips against jacks.
I think a case could be made for an even wider range, especially on a tight table. I would add ace-king offsuit to that four-bet range and I would shove all in so long as stacks are not above 100BB. This invites a coin flip with a pair, likely a pair below kings since you block aces and kings.
In an upcoming article, I will argue that coin flipping is profitable with ace-king and that you should default invite them and accept them. I also talk about the math and psychology of the ace-king coin flip in the book, Poker Beginner to Poker Winner in 1,000 Hands.
This book is available in .pdf here.
Frank Reese is a public school math teacher with a degree in psychology who found in poker a way to combine both fields for fun and profit.