Miller, Ed. Smallll Stakes No-Limit Holdem

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instead of 3bb on a steal, you lose an extra 1bb each time you fold to a preflop 3-bet.

Second, many opponents are almost indifferent to a 4bb raise versus a 3bb raise. You do not mind calls preflop since you have premium hands. You especially do not mind being called by weak aces and kings, because so often when they hit top pair you will have them beat. If raising to 4bb instead of 3bb won’t cause opponents to fold many of the weaker hands in their 3bb raise calling range, you prefer the 4bb bet.

Third, stack-to-pot ratio issues do not affect a decision between 4bb and 3bb in 100bb games unless 3-betting is common. You cannot get to a low SPR without a 3-bet unless stacks are short. If loose 3- bets aren’t common, ignore SPR when choosing a fixed bet size. If instead loose 3-bets are common, and the 3-bettor is indifferent between a 3bb and a 4bb raise, raising to 4bb is superior. A 4bb raise yields better SPRs for top-pair and overpair hands.*

What if the stacks are shorter? With 40bb stacks, it is criminal to raise to just 3bb with your strong range if your opponents will also call or 3-bet a bigger raise. For example, a 4.5bb raise yields an SPR under 4 heads up, whereas a 3bb raise yields far less attractive SPRs of 5–6.

Overall, with AA-TT, AK, raising under the gun to 4bb or 4.5bb is superior to raising to 3bb. If opponents will still play with you if you raise to 5bb, do it.

What if they just fold every time you raise to 4.5bb? Smile! You are making money. You win 1.5bb every time this happens. However, you can probably improve. You might raise to just 4bb instead, or exploit their tightness by adding a few hands to your opening range.

* With 100bb stacks, an open-raise of 3bb followed by a positional two-thirds- pot reraise to 8bb yields a pot of 17.5bb and an SPR over 5. If you instead raise to 4bb, these positional two-thirds-pot reraises yield a pot of 22bb and an SPR of 4 with 100bb stacks. An SPR of 4 is often easier and more profitable for playing a top-pair hand than an SPR of 5.

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weakness. He is not very observant, in part because he chats frequently while 12-tabling. This is a good situation for mixing up your bet sizes. When you hit, you might bet half the pot or less to induce a bluff-raise or a float. Fixed bet sizes are only a default. If you have good reason to vary your bet sizes, do it.

Situation 2: A Wider Range Under The Gun

Players at the table: 10

Effective stack size: 100bb

Your position: Under the gun

Your range: AA-22, AK-AJ, KQ

Preflop. Your opening range here is wider than in Situation 1. Should your standard bet size be higher or lower?

Lower! Adding 99-22 and AQ-AJ, KQ to the range changes things. Here is the breakdown:

Big pairs AA-TT: 30 combos (21%)

Other pairs 99-22: 48 combos (34%)

AK-AJ, KQ: 64 combos (45%)

This range is far weaker than the previous range. By our rule of thumb, weaker ranges deserve smaller bets. This is a medium-strength range, so in general we recommend a medium-sized fixed bet of about 3bb. But you may want to get rid of part of this range. Here’s why:

Your average equity with pairs 99-22 is much lower than with premium hands. With these pairs, you would like to steal the blinds as cheaply as possible, play a multiway pot for a small bet to maximize set value, or—barring that—get it heads-up against someone who will let you steal postflop. Overall, you don’t want much money to go in before the flop.

Big card hands AQ-AJ and KQ also have problems under the gun 10-handed. First, if they hit top pair or better, they often won’t be against another top-pair hand. And even if they do end up against a weaker top-pair, they won’t necessarily win much money. You want weaker top-pair hands to come in. A smaller raise size may encourage

that. Second, like all big card hands, AQ-AJ and KQ miss the flop most of the time. If you cannot steal effectively when they miss, you often want less money in the pot preflop and prefer a smaller preflop raise size. Third, if a tight player 3-bets in this 10-handed game, often you will have to fold AQ-AJ, KQ. When the risk of being forced to fold preflop is high, you prefer smaller raise sizes or to avoid the hands. All this suggests a smaller raise size.

If you are curious how often you will be dominated when you hold a big card hand or big pair, check out the following chart.

Table 1. Percentage chance of various hands being dominated.

Number of Opponents Remaining

This chart shows the percent chance a big card hand will face one or more dominating hands given how many players are left to act preflop. It assumes everyone up to that point has folded. For this chart, we define a dominating hand as one that has you beaten badly preflop or that often has you in deep trouble if you flop top pair. So

250 SMALL STAKES NO-LIMIT HOLD’EM

AK is dominated by AA and KK, TT is dominated by AA-JJ, and KJ is dominated by AA-JJ, AK, AJ, and KQ.

As an example, suppose you are under the gun in a 6-handed game. Five players are left to act, so TT is dominated 9.5 percent of the time, and KJ is dominated 20.6 percent of the time.

There is no cookie-cutter way to use this chart. If you expect to play the hand out of position against good opponents, then as a starting point you might fold any hand that has a 20 percent or greater chance of being dominated. Under the gun 10-handed, this limits you to AA-TT, AK-AQ. Under the gun 6-handed, this would limit you to AA-TT (lower pairs are not considered here), AK-AJ, and KQ. However, as you approach the button, your chances of picking up the blinds with a raise increases. When the blind stealing equity is significant, it largely compensates you for the risk of being dominated.

We recommend you ignore this chart on the button. There is too much money to be made stealing blinds to worry about preflop domination.

Returning to the bet-sizing discussion, the hands 99-22, AQ-AJ, KQ comprise two-thirds of the new range. These additions work best with smaller open-raises. Therefore, the wider range in Situation 2 may work better with a smaller fixed raise size than in Situation 1. Also, you should consider dropping the weaker portion of this range in some games.

Try raising to 2.5bb or 3bb and see what works best.

Flop. Your range is much weaker than in Situation 1. Most of the time you will miss the flop. Consider betting smaller on the flop, like half the pot or a little less. The smaller bet size reduces your cost of c- bet bluffing.

This is only a starting point. Poker requires adaptation. If you find some opponents attack your small c-bets too often, adjust by betting half to two-thirds the pot instead. If that doesn’t work, consider tightening up from early position.

The only difference between Situations 1 and 2 is your opening range. Your range is the most important factor in determining a fixed bet size against thinking opponents. We considered the best preflop

raise size for each hand in the range then took roughly the weighted average. This works fairly well for approximating the “best” fixed preflop raise size for a range. To repeat:

Match your bet size to your range’s average strength. Then adjust it for the other factors.

Situation 3: A Shorter Stack Under The Gun

Players at the table: 10

Effective stack size: 30bb

Your position: Under the gun

Your range: AA-22, AK-AJ, KQ

Preflop. Your range is the same here as in Situation 2, but your stack size is different. How does that affect things?

First, as we said above, in tough 10-handed games you should probably drop some hands from this range.

Are you playing primarily to make the best hand with this range? With 30bb stacks, often yes. First, your opponents may mistakenly 3- bet you with a wide range. With a short 30bb stack, you are happy to see a light 3-bet so you can push. Second, if you can get all-in reasonably when you hit top pair or better with AA-22, AK-AJ, KQ, you profit significantly from making the best hand.

When stacks are small, stack-to-pot ratios play a major role in choosing an optimal fixed preflop raise size. Here the effective stacks are 30bb. If you raise to 3bb, heads-up pots will have SPRs around 4. If you instead raise to 4bb, heads-up pots will have SPRs around 3. This larger bet size can substantially increase expectation, even if opponents fold more often to the 4bb bet. When you are playing primarily to make the best hand and can achieve a good SPR against weaker ranges, raise enough to get there.

Your ranges in Situations 2 and 3 are identical. The only thing that changed was the effective stack size. With 100bb stacks in Situation 2 we recommended starting by open-raising to 2.5bb or 3bb. In Situation 3, effective stacks are 30bb. With 30bb stacks it is far easier

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to play for commitment with top pair hands. This dramatically changed our strategy. With 30bb stacks, we recommend playing for commitment and raising to 4bb.

When your range is weighted toward top-pair hands and stacks are short, SPR is the driving factor for choosing a fixed preflop raise size.

Let’s look at 6-handed games.

Situation 4: A Tight Range Under The Gun In 6-Max

Players at the table: 6 Effective stack size: 100bb Your position: Under the gun Your range: AA-TT, AK

Here your range is the same as in Situation 1, but you are at a 6- handed table instead of a 10-handed one. Does that affect things?

Yes. This range is way too tight. Add more hands. If you raise only these premium pairs and AK, then as with Situation 1, aim for a larger fixed bet size. But in general, if this is you, stop being a wuss and widen your range.

Situation 5: A Wider Range Under The Gun In 6-Max

Players at the table: 6 Effective stack size: 100bb Your position: Under the gun

Your range: AA-99, AK-AJ, KQ, and occasionally a lesser pair, suited connector, or small suited ace

Preflop. This is a strong range with a good balance of premium and non-premium hands. Let’s talk about choosing a fixed bet size.

First, how often will someone 3-bet? Suppose you expect many 3- bets. What will you do if that happens? If you will fold a good percentage of your range, in general you should open-raise for less or drop some hands from your range. (Sometimes a larger bet will deter some of the 3-bets and work better.) Smaller fixed raise sizes reduce the cost of folding to 3-bets. If you won’t fold to 3-bets often, feel free to make larger raises.

Second, how often will you take down the blinds? This can play a significant role in 6-handed games. For blind stealing, you want to raise just enough to get the job done. For example, a raise to 3bb or 3.5bb might be plenty.

How about postflop stealing? If you can steal many pots postflop, you like more money going in preflop and so might raise more. However, under the gun against tough opponents, most players cannot steal enough postflop pots to justify a larger raise.

Overall, we recommend raising to 3bb for starters, then adjusting from there.

Flop. This works similarly to Situation 2.

Situation 6: Open-Raising From The Cutoff

Players at the table: 6

Effective stack size: 100bb

Your position: Cutoff

Your range: 30 percent of hands

22+,A2s+,K9s+,Q9s+ JTs-87s, J9s-97s A2o+,KTo+,QTo+,JTo

Preflop. Choosing an opening bet size from the cutoff can be tough because it depends so much on how the button and blinds play. If they are tight, you play to steal the blinds. Here your range is 30 percent of starting hands. It’s a good start for a stealing range. You might widen or narrow it depending on how tight the three players to your left are.

As usual, when your range is wide and weighted toward steal hands, aim for smaller fixed bet sizes. Bet just enough to get the job done. If you match your bet size to your range’s average strength, a raise to 2bb or 2.5bb would be best. But that is only a starting point, and it can break down here. In the cutoff, you’re trying to get three players to fold, and the button has a major incentive to play. In general, in current online $1–$2 games, raising to 3bb or 3.5bb from the cutoff works better.

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If the button plays a lot of hands well against you, tighten up. If he 3-bets frequently, ask yourself how often you will take it down postflop. If the answer is “often,” you want more money in preflop. If the answer is “not often,” you want less money in preflop.

Situation 7: Open-Raising From The Button

Players at the table: 6

Effective stack size: 100bb

Your position: Button

Your range: 51.4 percent of hands

22+, A2s+, K2s+, Q8s+, J7s+

T9s-54s, T8s-53s, T7s-85s

A2o+, K9o+, Q9o+, JTo-54o, J9o-75o, J8o-85o

Opening on the button is a special situation requiring a multipronged approach. Here is the key question: Will most of your profit come preflop or postflop? Typically most profit comes from taking the blinds preflop. When that’s the case, bet the smallest amount that gets the job done. If instead most of your profit comes postflop, you don’t mind building the pot and should raise more.

Preflop. Let’s say the blinds play roughly AA-22, AK-AT, KQKJ, some suited connectors, and the occasional suited ace, suited onegapper, and unsuited connector. This is about 20 percent of hands. Preflop, stealing is extremely profitable. You might be used to making a pot-sized 3.5bb opening raise on the button, but you want to bet the smallest amount that will get these tight blinds to fold. In practice this is typically 2.5bb or 2.25bb.

Small open-raises lay the lowest price to win the blinds. They also reduce the cost of folding to 3-bets.

When the blinds play only 20 percent of their hands, you should open-raise half your hands or more from the button. This assumes that the blinds don’t loosen up and that you won’t spew money postflop. If they don’t and you won’t, you have found a gold mine. You can expand your button open-raising range up to 100 percent of hands if the blinds don’t adjust. It’s free money. Don’t be afraid to open-raise

60 percent or more of your hands from the button, especially against tight blinds.

Against looser blinds that play, say, 30 percent of their hands and 3-bet with 10 percent of them, you must take down a few pots postflop or tighten up preflop. Against blinds who play 30 percent of their hands, you steal the blinds roughly half the time you raise. If you are open-raising for 2.25bb or 2.5bb, you usually only have to take down a modest percentage of the postflop pots to show an overall profit. This assumes you don’t spew for stacks or routinely pay off when your opponent hits.

Flop. Say you open-raised preflop to 2.25bb from the button. One of the blinds called. The flop comes, and the blind checks. Most of the time you will c-bet here. How much should you bet?

Your range is strongly weighted toward weak hands. Most of the times you bet, you will be bluffing. The best c-bet size here is the smallest bet that will get your opponent to fold frequently. You might start with betting a third to half the pot. Amazingly, some opponents fold about the same number of hands to a third-pot bet as they do to a half-pot bet. Against such an opponent, it is foolish to bet half the pot. The smaller third-pot bet achieves the same result at lower cost.

If you are lucky enough to face an opponent who will fold frequently to even smaller c-bets, bet less.

Against tough opponents in $1–$2, larger flop bet sizes tend to result in the most profit. Consider c-betting two-thirds the pot and adjusting from there. Rounded off, after open-raising to $4.50 or $5 and getting called by one blind, this means betting $7 or $8.