Let's start with some quick definitions. When I say a continuation bet on the flop, I mean that you bet the flop after having raised preflop, the flop has missed you, and no one else has bet. For example, you raise with A-K, miss the flop and bet your A-high hand, hoping to win the pot. When I say value bet on the flop, I mean that you hit the flop and are now betting your hand for value, not simply to take down the pot.
Consider the following example as an illustration of Harrington's claim. The pot is $2 on the flop, after my preflop raise with A-K. I've missed the flop. Let's say this happens 10 times and, on each occurrence, I continuation bet $1, and take down the pot four times, winning $2 for those bets, which totals $8 (4 x $2). Six times, however, my bet fails to win the pot and I lose the hand. My total losses on those six bets is $6 (6 x $1). Thus my profit is $2 ($8-$6). This is what Harrington is talking about. Over time, as long as my continuation bets of half the pot are more than 1/3 successful, I will show a profit.
If we focus only on the flop, then certainly, conventional wisdom (and Harrington) is correct, but let's expand our focus to the entire hand. When looked at in totality, I need a much higher than 1/3 success rate with my continuation bets to show a profit. If you take a look at your Poker Tracker stats, you'll see that it shows net profit/loss by hand, not by street. Your net winnings include the entirety of the hands that you play, not one street. I will show you in what follows that continuation bets appear to lose money on their own, but are definitely worth the loss so as to provide cover for value bets. That is, continuation bets are the price we pay to win more in other hands. Conventional wisdom looks at bluffs in a similar fashion. You lose money on bluffs, but this will win you more when you actually have a hand.
Read simply, the conventional wisdom might lead one to think in the following manner. "I am raising A-K. I could win the blinds, but someone may call. If I get a caller, I may hit the flop and get more money by betting for value. If I miss the flop, I'll still make money if my half pot continuation bet is successful just over one-third of the time." That last bit is what troubles me. You will make money only if you are successful far more than one-third of the time. I'll demonstrate this claim through a few scenarios.
First, let's consider some heads up scenarios. We'll say that I hold A-K and have made a preflop raise of four times the big blind, and have one caller. Let's start rather simply and just talk about the success or failure on the flop. The pot is eight big blinds; thus a half pot continuation bet is four big blinds. Now if the traditional wisdom is correct, then I should show a profit if just over one-third of my bets take down the pot.
Let's say this situation arises 100 times and my bets win 34 pots, but lose 66 (which would be just over one-third of the time). Now here is where we shift our focus. I lose 66 times while betting four big blinds before the flop and four big blinds on the flop for a hand investment of eight big blinds in each of these losses. That's a total loss of 528 big blinds. On the flip side I win 34 pots. Again I invest eight big blinds in each, winning the eight big blinds in the pot; but wait, half of that pot I contributed with my preflop raise, so my actual profit is only four big blinds for each hand. That's a total winnings of 136 big blinds. I lose 528 big blinds (8 x 66) and win 136 big blinds (4 x 34). Am I showing a profit? No, I'm showing a big loss, 392 big blinds. Like Lucy, conventional wisdom has a lot a ‘splainin' to do.
What say we up that success rate to 50%? Conventional wisdom is conservative, anyway. Half the time my continuation bet wins the pot, half the time it doesn't. Now what figures do we get? Fifty times I lose eight big blinds for a total loss of 400 big blinds. Fifty times I win four big blinds for a total win of 200 big blinds. Still not showing a profit, but at least my net loss is only 200 big blinds now.
Let's try again, this time with a 67% success rate. Sixty-seven times I win four big blinds for a total of 268 big blinds. Thirty-three times I lose eight big blinds for a total loss of 264 big blinds. At last, success! I win four big blinds over 100 hands if my half pot continuation bet is successful just over two-thirds of the time. A two-thirds success rate is quite a bit more than just over one-third of the time, double in fact. Conventional wisdom seems to be way off.
Let's consider two questions. First, why is my analysis so far from conventional wisdom? I'm looking at the preflop and flop investment, whereas conventional wisdom looks at only the flop. There are good reasons behind the conventional analysis. Once you put money in the pot, it is no longer yours. It is simply part of the pot. You have no claim on it; thus ignoring what happens preflop makes quite a lot of sense. On the flop there is X amount of money to be won, and you have Y amount in your stack. It seems perfectly reasonable to simply ask what sort of bet at this point in time will prove most profitable relative to your current stack. If we want to analyze an entire hand, however, which is what ultimately matters to your bankroll, then we need to consider total investment and total winnings/losses.
Second, my analysis doesn't consider all the possibilities, shouldn't we consider what might happen on the turn and river, before concluding that a continuation bet cannot be profitable? This is certainly correct. The continuation bet is quite often a semi-bluff. If I have A-K, and the flop misses me, then I have at least six outs (assuming I'm not up against a set, which I will be two out of every 17 flops in which a pocket pair calls me). I'll expand my analysis to try and take this into account. Thus far, I only want to show that the conventional wisdom may lead you to think that a continuation bet is profitable when, properly considered, it isn't.
By including further factors, the success rate needed to break even becomes lower, but not all that much lower. There are too many factors and possible situations to include them all in a full analysis; thus, while I am expanding the analysis to consider improvements on the turn, I can't consider everything. I only hope to get us closer to concrete play. Let's again consider our above half pot continuation bet scenario with a 50% success rate on the flop, but we'll now look at what happens with an improvement on the turn. With six outs, my chances of hitting the turn, are 12.8%. Let's plug this back into the half pot continuation bet scenario with a 50% success rate on the flop. In 50 hands I will fail to win the pot on the flop, but improve 6.4 times on the turn. (Things get complex now. Sometimes that improvement will give you the best hand, but sometimes it will get you into trouble. For simplicity, let's just assume you win the pot with a bet on the turn and that furthers wins and losses cancel out.) After your half pot bet on the flop and a call, the pot now has 16 big blinds. Eight of those big blinds are yours, so the 6.4 times you improve on the turn you only win eight big blinds each hand for a total winnings of 51.2 big blinds. Now if you recall from above (or if you just scroll back up there) under this scenario we had a net loss of 200 big blinds. Again, our half pot continuation bet succeeds 50 times and wins us four big blinds each time for a total of 200 big blinds. It fails 50 times, but now (under the expanded analysis) 6.4 of those failures will turn into a total winnings of 51.2 big blinds. We lose eight big blinds 43.6 times for a total loss of 348.8 big blinds. This comes out to a net loss of 97.6 big blinds (200 bb + 51.2 bb - 348.8 bb). This is much better than the previous loss of 200 big blinds and shows the semi-bluff potential of a hand like A-K.
Against conventional wisdom, I think I have shown that not only is a one-third success rate far from break even, but also it appears that a continuation bet may not even be profitable. Of course, if looked at in the traditional way, then a continuation bet is profitable, but realize that the traditional way of looking at this situation exaggerates your actual winnings. You will indeed be making money on the flop if just over one-third of your half pot continuation bets are successful, but your bankroll will be moving down. In Part II, I will examine varying continuation bet amounts and the needed success rates to show a profit with these bets.
Part 2.