Miller, Ed. Smallll Stakes No-Limit Holdem

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What do you have? Many amateurs have only strong hands such as a range of AA-QQ, AK. This is way too tight. Blind stealing is a huge source of profit in online games. You want to make it at least a little expensive for the thieves to steal from you. The most potent way to punish a blind stealer is to 3-bet. At a minimum, you should 3-bet with a much broader range such as most of AA-99, AK-AJ, KQ, and some suited connectors. The suited connectors help because they form the bulk of your bluff hands and make it possible for you to hit any flop.

How about this line:

“Raise preflop, bet an ace-high flop.”

At first glance this doesn’t seem like much of an unbalanced line. But it is amazing how many weak players bet that flop 90 percent or more when they have an ace or three of a kind and check it half the time they don’t. If their preflop raising range is heavily skewed toward ace hands, such as AK-AT, KQ,-KJ, AA-TT under the gun, then on an ace-high flop with lower cards they have:

Preflop Range: AA-TT, AK-AT, KQ-KJ

Line: Raise Preflop, Bet An Ace-High Flop

Board: A♠9♥8♥

Suppose this player also has a common amateur habit. He habitually checks KK-TT when he hits second pair on an ace-high flop. This results in him checking when he has an underpair or no pair half the time. Since he also bets the flop around 90 percent of the time when he hits top pair or better, his flop check range looks something like this:

See the problem? When he checks the flop, a skilled opponent will bet to steal. The line is too unbalanced. For example, say the pot is 10bb and an opponent bets 6bb every time when checked to. If the checker folds all but top pair or better, the bettor wins 84.6 percent of the time for an immediate 7.5bb in expectation.* If the checker also calls with KK-TT, then he folds 48.3 percent of the time, and the 6bb bet returns an immediate expected profit of 1.7bb for his opponent.† Either way, it’s easy money for the opponent.

This can go the other way if you check top pair of aces too often. On an uncoordinated ace-high flop, it can be optimal to check when you hit top pair. This check shows weakness. It works best against opponents who like to bluff or call light on later streets once they sense such weakness. Suspicious opponents often won’t believe you when you bet the turn and river after checking the flop. But if you overdo it, say by checking top pair of aces and sets 90 percent of the time, then your c-bet line becomes unbalanced:

Preflop Range: AA-TT, AK-AT, KQ-KJ

Line: Raise Preflop, Bet An Ace-High Flop

Board: A♠9♥8♥

* He bets 6bb, making the pot 16bb. He wins 84.6 percent of the time. 0.846×16bb=13.5bb. Subtract the 6bb wagered to get the profit of 7.5bb.

† We say immediate because that is his expectation from winning the pot right then. Usually his overall profit is higher than that. This is because when he is called, the skilled bettor can sometimes win more by betting again on later streets or by showing down the best hand.

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These are the same numbers we saw before, but this time they are for when you bet, not check. In this scenario, an astute opponent just raises whenever you bet an ace-high flop.

There is no excuse for poorly balanced flop bets and flop checks. Early in the hand it is easy to balance ranges. For example, just by betting or checking 80 percent with top pair instead of 90 percent, these lines become reasonably balanced for $1–$2. All you have to do is make sure the percentage of good hands in a line is within several percent of the percentage of good hands you expect on a given type of flop. This is not perfect, but it’s tough to exploit.

Hunting For Unbalanced Lines

How do you find your unbalanced lines? In principle, it is simple:

Read your own hands.

Put yourself in your opponent’s position and ask, “What do I have?” If you don’t habitually read your opponents’ hands, this will be tough. But stick with it. Reading your own hands is a tremendously valuable exercise for defeating thinking opponents. It will also help you read others’ hands.

Using Brute Force/Counting Ways

We skipped the arithmetic when we talked about Bill’s “raise preflop, bet flop, bet turn” line. Let’s get your hands wet. Here is a recap of the problem:

Usually, when Bill raises preflop, the button floats the flop. Postflop, the button seems to know when to raise and when to fold.

How? That’s not an easy question to answer, since it depends on Bill’s opening range, his betting tendencies, and the flop and turn. It is so complicated, in fact, that most successful high-stakes players analyze the problem intuitively rather than mathematically. From experience and memory, they develop a keen sense of their opponents’ betting lines. Once a weakness is found, they exploit it. They also analyze their own play to avoid the same problem.

But what do you do if you don’t have that intuition? Count the hands. A program like Flopzilla is the easiest way. But for old schoolers, you can find an Excel version for Bill’s “raise preflop, bet flop, check turn” line on a K75 rainbow flop at

http://smallstakesnolimitholdem.com/K75_Line_Balancing.xls

This is brute force counting. The chart lists every hand in Bill’s opening range. It gives the preflop betting action or range of actions for each hand. Namely, Bill raises to 3bb with every hand he plays. Then, on a given flop, it shows what Bill has and what he does with each hand.

From these columns, you can add up the ways Bill can have, say, top pair or better when he takes a particular line. Divide that by the total number of combinations for that line and you have the percentage of the time Bill has top pair or better.

This chart tells only part of the story. To better understand his weaknesses, Bill will have to repeat the exercise for other flop types, such as an uncoordinated ace-high flop like A♣T♥4♦, low boards like 6♥6♣4♦, and perhaps a couple other board types. He should look for 90%/10% lines first and correct those right away. Then he should ask whether he needs to tweak his 80%/20% turn lines against certain opponents.

Summary

Line balancing takes time. First you have to find unbalanced lines, then you must figure out how to fix them. Further, if the flop and turn

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change dramatically, you could end up with a quite different set of betting and checking frequencies. It gets complex quickly. But the value in doing the exercise remains. You’ll find leaks and plug them.

Any time a betting line results in an easily exploitable frequency of good vs. bad hands, mix it up. We recommend that when you find a common hand situation that causes you trouble against your tougher opponents, do this exercise and see if the problem is an unbalanced line.

Bankroll Requirements

You need way more than you think you need. You need way more than the successful pros say you need. You need way more than the statisticians say you need.

You need a lot.

Let’s talk basic stats first. Pretend you are Seo Awsum, a solid poker pro. Seo plays online $1–$2 6-max for a living. He plays eight or nine tables at a time, buys in for a full stack of $200, reads stack sizes for every table before entering a pot, knows the regulars, analyzes stats, does not play too many hours at a time, and rarely tilts. Seo played a million hands last year and averaged $12 per 100 hands with a standard deviation of $200 per 100 hands.

If Seo plays another million hands this year and plays the exact same way in the exact same game conditions, he can expect (with 99 percent confidence) his total winnings at the end of the year to be anywhere between approximately $70,000 and $170,000. That is a difference of $100,000 due purely to randomness. And Seo’s winnings over any given 80,000 hand sample—about a month’s worth of work—could be anywhere between approximately –$5,000 and $25,000 (again using a 99 percent confidence interval). His monthly income can vary by as much as $30,000. That’s a monthly difference of 150 buy-ins due to chance alone.

Now let’s talk reality, because you are not Seo Awsum. If you are an online poker pro, your situation is likely worse. For starters, your winrate may be lower than $12 per 100 hands. Also, you may not have the stamina to play a million hands in a year. And most importantly, we haven’t yet discussed one of the biggest threats to bankrolls.

We calculated Seo’s variance numbers using basic Stats 101 formulae. To predict bankroll requirements, statisticians have traditionally taken this approach of using a player’s historical winrate

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and standard deviation and plugging them into these formulae. Some also then make estimated adjustments for stepping down and other factors. These adjustments tend to be optimistic in that they typically assume you won’t tilt and will step down when you should. But there is a far bigger problem. Stats 101 calculations assume that in the future you will play in similar games. This is called sampling from the same distribution. Reality is vastly different. Games change.

Games change. It’s as simple as that. Past results do not dictate future performance. Or, in statistics terms, the underlying distribution can change quickly. One day you’re playing against Andy, Bill, Caroline, David, and Eric with a 3bb per 100 hands winrate and a standard deviation of $200 per 100 hands. The next day, two major events happen that lower your winrate. Andy figures out that when you raise the turn, you are more likely than an average opponent to have a real hand. He exploits your flaw by folding more frequently when you raise. It’s a subtle difference, maybe one extra correct fold every 600 hands, but if that fold costs you 12bb you now win 2bb per 100 less. Meanwhile, Eric is replaced by Felicia. Felicia reads hands a little better, which impacts you in a few ways. She is less likely to lose chips to David, the weak player in the game. Also, she occasionally makes a thin value bet against you that Eric would not have. Again it’s a subtle difference that costs you 2bb per 100 hands.

Overnight your win rate has gone from 3bb per 100 to –1bb per 100, while your standard deviation remains around $200 per 100 hands. You are now a loser. You just won’t figure it out for tens or hundreds of thousands of hands.

The fact is, games can change quickly, and small changes can kill your expectation. This fact dramatically increases bankroll requirements.

You will, as a professional player, experience downswings you probably never thought were possible. In preparation for this book, Sunny played several hundred thousand hands of $1–$2 6-max. He took the gig seriously, regularly analyzed his play, tilted minimally, and achieved an excellent winrate. Yet, at one point he suffered a downswing of 40 buy-ins. Forty! That’s $8,000.

You may have read stories about successful pros who rose to the top on 30or 40-buy-in bankrolls. Well guess what? It’s selection bias. They got lucky. Literally hundreds of players who could have been just as successful did the same thing and went broke. If you play on 30 buy-ins, it’s only a matter of time before you too bust out.

So what can you do? First, assume solid 6-max pros almost never suffer 30 buy-in downswings due to chance alone. This is not true, but it’s a great assumption. If you find yourself in a big downswing, ask how much you are tilting and stubbornly sticking to tough games. Then ask whether the game has changed. And don’t forget collusion. This is one of those delicate topics that all the “in” people don’t like to talk about. But the fact is, if Andy and Danny get on instant messenger and play best-hand against you, you will take a major hit right in the winrate.

The best way to deal with a small downswing is to tighten up a little while you determine whether you have played well. Run hands by your poker friends, your coach, or the online forums. Review stats like VP$IP, PFR, 3-Bet Percentage, and C-Bet Percentage, and analyze them by position—not just as averages—to help figure out if you are making consistent mistakes.

The best way to deal with a big downswing is to take a few days off. Relax, exercise, sleep, and get your head back in the game.

After a few losses, you should step down. There comes a point in a downswing where you may be playing badly and not know it. In general, after losing 20 buy-ins, not only should you take a break and analyze your recent game, you should also seriously consider dropping down a limit or two.

So how big a bankroll do you need? Clearly—and perhaps surprisingly—it is more than 40 buy-ins. But what is the magic number for an online pro who doesn’t have much room to move down and still make a good living? This number depends on a great many factors, such as how much you think games might change, how aggressive you are, your risk tolerance, your winrate, your living expenses, how much you tilt, and how good you are at stepping down. It also assumes you don’t have a job or a trust fund to replenish your

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bankroll. No matter how you slice it, it’s just an estimation. No one can know your true number.

But who are we to deprive you of our recommendation? If forced to give you a specific bankroll number, ours is:

100 buy-ins

You may not like that recommendation. That’s okay. Our goal with this book has been to challenge you to see situations in new ways—to see all 64 squares if you will—and to help you survive and thrive in the online poker world. If this recommendation sways you to keep 60 buy-ins in your bankroll instead of 30 buy-ins, then we have done our job. We have increased your chances of survival dramatically, and even more importantly, we have made you think.

Best of luck to you!

Ed, Sunny, and Matt

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