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Book Excerpt: Analytical No-Limit Hold ‘em (Engels)

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Book Excerpt: Analytical No-Limit Hold ‘em

  by Thomas Bakker

Perceived Ranges

We constantly ask ourselves what the ranges of our opponents are, but our opponents will be doing the exact same thing! So in order to effectively plan ahead, we will need to analyze what our opponents think our range is, which to them is our “perceived range,” and how they will respond to it. If it’s strong, our opponents will be cautious; if it’s weak, our opponents will be confident about their hands.

Let’s analyze how our villain perceives our range in our main hand.

TABLE LAYOUT:

UTG: $895
Hero (CO): $1,752
BTN: $191
SB: $2,755
BB: $1,103

Blinds: $5/$10 Pot: $15

Hero’s hand: QcJh

Action: The first player folds. Hero raises to $35.

We are the cutoff and make a pot-sized raise. Since our villains think we are good and aggressive, they will assume we have a wide range here. So a range of approximately 36 percent of the hands would not be far off:

22+, A2s+, K3s+, Q6s+, J7s+, T7s+, 97s+, 87s, A4o+, K8o+, Q9o+, J9o+, and T9o

Action: The button folds and both blinds call the $35 raise. The pot is now $105.

Flop: Td9s5h

Action: The small blind checks.

At this point, the small blind will check with most of his hands as discussed in “Continuation Betting” starting on page 119. But how does this flop hit our perceived range? From quickly looking at our range on paper, it seems like our range hits the flop with many hands, but a lot of the weaker hands, such as ace-rag and king-rag have completely missed. And if we analyze the exact numbers, the results are:


Hand Type
Probability
No Pair or Draw 47.1%
Any Pair 43.1%
Top Pair 12.7%
Second Pair 12.7%
Open-Ended Straight Draw 5.6%
Set / Two Pair 4.2%
Overcards 22.6%

Recall that we earlier calculated that the probability the small blind had a hand of absolutely no value was 8.8 percent. That is, over 90 percent of his hands made something.

So the small blind’s range is much stronger than our perceived range. This means that, on average, the small blind will be somewhat confident about the strength of his hand.

Now that the small blind has realized all of this, plus he’s probably thinking about his perceived range as well, understanding that it’s quite strong, it’s his turn to act.

Action: (After the small blind checks) the big blind also checks. Hero bets $60. The pot is now $165.

Our continuation-bet is relatively small. The small blind will notice this and try to interpret its meaning. Why do we bet $60 here? With what hands would we bet more?

He most likely understands that we realize that many of his and the big blinds hands contain a straight draw of some sort. So if we were trying to protect our hand against their draws, we would probably have bet more, trying to make them fold. Thus the fact that we did not bet big gives the small blind a clue (but in no way a guarantee) that our hand is either a complete bluff, a draw (such as our actual QcJh), or an extremely strong hand which here would be a set, or a pair of jacks or queens which both block many straight draws.

The fact that we did bet even though we knew our opponents’ ranges were strong, could tell the small blind that our hand has equity. Recall the formula we used to decide if continuation betting would be good showed that the expectation of a $60 bet was $170.71.

$170.71 = (0.559)(0.541)($105) + {1- (0.559)(0.541)][(0.384)($675) - $60]

Most of this information, except for our equity when called (and the probabilities that they fold are a bit different to him since he does not know we have queen-jack, making hands that contain a queen or a jack less likely in the small blind’s and big blind’s ranges), is also available to the small blind. So in theory he could solve the above formula for an unknown range and calculate the equity that makes a $60 bet more profitable than a bigger bet. This would give him an idea what the strength of our hand is because we decided that $60 was the most profitable bet.

Of course, nobody will ever make these profitability calculations at the table, let alone make them for someone else to find out what their equity is, but it’s interesting to realize that this is possible. With or without these calculations, the small blind probably deduces that we have at least some kind of hand on this flop, so he can further narrow our range to something like the following:

55, 99-AA, A5o, A9o+, K9o+, Q9o+, J9o+, T9o, A5s, A9s+, K5s, K9s+, Q8s+, J7s+, T7s+, 97s+, and 87s

Manipulating Your Perceived Range

All of the above is correct when everyone plays in an honest, straight-forward way. However, sometimes you will want to represent a different range than you actually have. This is essentially the idea behind bluffing. But there is also another type of bet that is somewhat related to a bluff. Let’s call it overplaying your hand, and these two types of bets are listed below:

  • Misrepresenting your range
  • Overplaying a hand that is in your perceived range

For example, consider the following board:

TsTc5dAd9s

On this river, our opponent checks and we make a bet. Now, if we have thus far played our hand extremely aggressively, we are representing a range with a lot of tens and maybe a pair of fives, but no weaker hands. If we do not actually have a ten but instead are betting ace-king, we will have misrepresented our range. And since our hand does have value, we are hoping for a call by an opponent who does not believe we have the hand we are representing, but still holds a hand we beat. In this case, he might call with a weaker ace or even a pair of kings, queens, or jacks. This is an example of misrepresenting your range.

Now, consider the following board:

Td5s4sAd9s

If we have been playing our hand as either an ace or a flush-draw, and in fact do have an ace, our bet would be an overbet if we were strongly betting this river. However, when our bluffing hands are in our perceived range, it’s easy for our opponent to realize that we might be bluffing. But in the hand above, we are representing a completely different range than our actual hand, so it’s much more difficult for our opponent to guess our hand. This is an example of overplaying your hand.

Now, let’s look at this board:

5d4h3sJdAs

If we have been slow-playing a flopped straight, either by check/calling or in some other way, our perceived range will be weaker than our actual hand, allowing us to value-bet and get called lighter. This is another example of misrepresenting your range. Nonetheless, by slow-playing, we pretended to have a weaker range than we actually had, but are still, as in the first example, hoping for a call. However, now we beat virtually any hand that calls, where as before that certainly was not the case.           

» SYNOPSIS

Poker has changed immensely in the last few years. While once played only in casinos and home-games, it’s now immensely popular on the Internet and has taken on a completely different aspect in terms of winning strategy. Not too many years ago, the best players still played somewhat intuitively and used strategies which were effective in tricking some of their poor playing opponents into making mistakes. But today it’s different.

Poker, especially on the Internet, is now dominated by players who have spent a lot of time studying the details of the game, and to make money in today’s modern poker climate, it will be necessary for you to do the same. Analytical No Limit Hold ’em provides the tools and theory needed for tough mid-stakes short-handed games, specifically those played online.


From Analytical No-Limit Hold ‘em, by Thomas Bakker. ©2010 by Thomas Bakker. This material appears with the express permission of the author and Two Plus Two Publishing.

Analytical No-Limit Hold'em, by Thomas Bakker as well as other titles from Two Plus Two Publishing can be found in bookstores, and is available online both at Amazon and the Two Plus Two Store.