Continuation Bet. A Lot.

Being the nerd I am, I have actively collected a lot of poker data over the years. A whole lot. In the past ten years alone, I’ve played well over a million hands combined of online Texas Hold’em, Stud, and Omaha. The majority of these hands and/or sessions were recorded either via automatic tracking software or manually in a long series of spreadsheets. I have also added other players’ hands to this database, actually going as far as purchasing blocks of data from various online re-sellers. All-in-all, I have data on over three million real poker hands that I have used to help evaluate and test theories, and prove (or disprove) specific strategies and tactics.

I’ve used this data for everything from helping put together preflop starting hand recommendations, to quantifying the power of position, to determining optimal bet sizing in different situations, and even to help me figure out the best times of the day and week to play that are the most profitable for my own specific LAggy style. As the old saw goes, you can’t improve what you can’t measure, and all this measured data I’ve collected has served to greatly improve my own game.

Lately I used these data to analyze flop continuation betting scenarios. This analysis resulted in an honest-to-goodness formula a beginning player can use to determine whether they should c-bet in any specific situation or not. The method itself is quite simple: you calculate your fold equity based on a point count system, then do the same for your pot equity, and finally just multiply the two numbers together and look at the result. Depending upon the number you get, you then either fold, c-bet, or slow-play your hand…

….ah, but all of this can really be boiled down to a much, much simpler let’s-cut-to-the-chase recommendation:

When in doubt, you should probably continuation bet

The simple fact is this: in small stakes games, if you were the preflop aggressor, you should be firing a continuation bet on the flop at a relatively high frequency. Depending on the number and type of villains in the hand and the texture of the board, this number can range from 60% to higher. Heck, against weak-tight nits on super-dry boards, you should probably be firing a flop continuation bet nearly 100% of the time.

This empirically-based conclusion of mine can be proved analytically by doing some simple algebra with a basic expected value equation. Setting EV equal to zero and ignoring any showdown equity you might have, one can easily see that Fold Equity = Bet Size / [Pot Size + Bet Size]. Here’s that relationship plotted out in X-Y fashion:

What this chart demonstrates is that you only need a villain to fold 33% of the time if you fire a half-pot-sized continuation bet on the flop. Given the fact that the villain is going to miss the flop around 35% of the time, this means a c-bet generally has a high percentage chance of working.

Now, the bad news is that actual (i.e, not required) fold equity will vary as a function of Hero's c-bet size, which is something we’ve ignored in this simple analysis. In other words, a small bet size may only need a small villain fold frequency to be break-even, but villains will fold significantly less frequently if they’re being offered good pot odds, which a small bet causes. At first blush, this argues in favor of c-betting less frequently on the flop, but the other thing we’ve left out of the analysis is that we have ignored showdown equity for all those cases when the c-bet doesn’t result in a fold. These two factors (more or less) cancel each other out, which means that roughly speaking, you should in fact be continuation betting a relatively high percentage of the time on the flop.

How high, you ask? My three million hands of empirical data suggests a continuation bet frequency around 75%. Said another way, you should be flop continuation betting as a bluff an average of three out of four times in small stakes games. Further, I suggest that your c-bet size be around 60-65% of the pot; this seems to be the optimal risk:reward sweet spot that applies enough pressure to the villain, while risking the least amount of the hero's stack if the villain calls.

Bottom line: Three million hands of data don't lie: continuation bet most of the time in small stakes games, and make your bet sizing to be around 60-65% of the pot.

Continuation Betting for Dummies

I haven't been posting here much due to crazy work travel, work problems, and, well, work, work, and more work. That said, in the limited spare time I have every day I have been making slow and steady progress on the ABC lessons with Le Monsieur. The latest one that I just uploaded to our shared Evernote lesson notebook was a big 3000-word treatise on when to continuation bet on the flop. (There are six additional lessons that accompany this one, btw...)

I thought this when-to-cbet lesson would be a snap to write, but in the end it took me nearly 3 weeks of research, errant thought, false-starts, and general noodling around to come up with a step-by-step instructional that a newbie can follow to determine whether they should c-bet on the flop or not. It also gives guidance on how much they should bet in each case.

Writing this lesson was a really fun--and sometimes aggravating--experience, but I think the end result is really useful. I also think it's kind of ground-breaking in a way; in fact, I've never seen this type of approach to c-betting addressed before anywhere in poker books, blogs, or in training videos. This is basically cutting edge stuff, folks.

Anyway, you'll have to wait for the app to come out for the full step-by-step version, but here's the TL;DR Cliffs Notes version of cbetting:

1. First determine your fold equity (FE) in the hand. You have to estimate what the likelihood is that the villains who saw the flop with you are going to fold if you bet. I've touched on this before in this blog, like in Bug's Poker Tip #7 and Tip #17 before, but not nearly to the extent I did this time around, nor did I quantify each effect, nor have I put in a sequential, step-by-step process. Long story short, the significant level-1 factors that influence your FE include: number of villains, board texture, type of villains, stack sizes, preflop action, position of the players, and the hero's image. I've spent hours wading through poker tracker data to actually determine the approximate weightings and importance of each of these, and I now have a solid and easy means to accurate estimate FE in a poker hand. In a nutshell, my method uses points that you assign for, say, the number of calling stations left in the hand, or who has position on whom preflop, etc.  You total the points and end up with a FE estimate. It's pretty cool stuff if I do say so myself-- oh, and dead simple to do.
2. Second, determine if you want the villain to fold or not, which of course hinges around your own hand strength, or pot equity (PE). This seems simple on the surface, but again, when you're teaching level-1 poker to a newbie, and you're trying not to inundate them with hand reading, poker stoves, leveling, etc., it's surprisingly challenging to actually determine whether your hand is strong enough or not to want a call. Again, I spent a lot of time sorting and analyzing real poker hand data, and now have come up with another simple point count system that does a reasonably accurate (and conservative) job of determining your pot equity in a hand independent of villain's range.  Related to this is a method of determining if your hand is vulnerable or not to getting out drawn on the turn and river. And yes, once again, this is not as easy as it sounds to do, but I think we have a very innovative and simple method figured out.

Okay, so after you have the FE and PE's of a situation estimated, the third and final step is to plot them against each other on a 2-d chart. Here's a simplified version of the graph, and if you've done a reasonably good job estimating your fold and pot equities, this type of chart actually can go a long way toward helping you a) decide to if you should c-bet; and b) determine how much you should bet:

Researching and writing these lessons continues to be extremely fun and educational. I also think it's going to result in a really powerful training aid for beginning and intermediate poker players. And, oh yeah, it also helps offset all the work, work, and work that my day job insists on dumping on me lately. 

All-in for now...

-Bug

A Little Math: Fold Equity

Q: You're on the button in a $1/2 NL cash game with full 100bb stacks. The action folds to the player in the cut-off, who open raises to $6. You know he has a very wide range here. You decide to 3bet (re-raise) to $18 and see if you can just take down the pot (i.e,. bluff). Both blinds muck their hands. Ignoring the rake, how often does the villain have to fold to your 3bet to make this a profitable play?

A: Okay, first things first: We have not said what our actual hand is. If the villain calls (or reraises), we would have to factor in our hand strength equity against his range, but that's not what the question asked. We're simply trying to calculate how often we need the villain to fold to take down the pot such that we show a profit over the long run with a bluff here. In other words: How much fold equity do we need to make this a plus EV play? Here's how it's calculated:

You're risking $18 to win $9 (i.e., the villain's $6, plus the $3 in dead blind money). 

Said another way, you're giving yourself odds of 9:18, or 1:2.

This means that to break even we need to win 2/(1+2) = 2/3 = 66.6%

If the villain folds at least 2 out of every 3 times in this situation, the play is +EV and you should always re-raise with any two cards in this situation.

All-in for now...

-Bug

PS. Note that if the villain folds less than two out of every three times, this may still be a profitable play to make. Our hand will have some equity against his range and might in fact win outright at a showdown. We'll also we'll have position, which gives us an edge to try to out play him on the flop, turn, and/or river.

Thinking In Terms of Equity

Waaaaaay back on January 1st of this year, I posted my Poker Resolutions for the upcoming year (re-read it: here). Number #17 on the list was "Think of poker decisions in terms of Equity and EV."

Recently I received an email from a reader that said, in part:

You've explained equity to me at least 10 x if not 100. I see it on stove. I see it in ICM. I read it in Miller. P 110. 

But I am unable to explain it. Please help.

Okay, so what is Equity? And why does it matter?

In simple terms, Equity is your share of the current pot at that moment in time. In more complex terms, it's, well, a little more complex to explain. Let me try.

There are essentially two types of Equity we're concerned with in poker: Pot Equity (sometimes called Hand Equity), and Fold Equity. Your Total Equity in a hand, therefore, is simply your Pot Equity plus your Fold Equity. Let's look briefly at each:

1. Pot Equity. Let's say you're dealt AKo and your opponent holds JTo. Using PokerStove, we can see that before a flop is dealt, your (Pot) Equity is 65% vs. your opponent's 35%. People frequently assume this means your chance of winning the hand at that moment in time, and while this is a reasonable way to think of the situation, it's not technically accurate. What the 65% number actually represents is your theoretical "share" of the current pot at that instantaneous moment in time. If the pot was $100, then $65 of it "belongs" to you in the long run (i.e., if you were to run this scenario out a few thousand times). If the flop came out J-T-4, however, your Pot Equity on the flop would plummet to just 21%, because your opponent flopped top two pair; your share of a $100 pot at this point in the hand is now just $21. If the turn brings a Queen, your Pot Equity is now back up over 90%. And when the river drops another Jack on the board, your Pot Equity, or rightful share of the pot, is now a big fat goose egg, i.e., Zero.
2. Fold Equity. The layman's explanation for Fold Equity is simply the probability that your opponent will fold if you bet a certain amount. The more technically accurate definition is that it represents your share of the pot given the propensity of your opponent to fold to a bet of a given size. In the aforementioned example, your Pot Equity was zero on the river. But let's pretend that the Queen, Jack, and Ten on the board were all of the same suit. Let's also assume that the Ace in your hand is also of that same suit. Alas, your King is not, so you're still beat in the hand. Your opponent doesn't know that, however, and suspects that there is a possibility that you have a straight flush. If you bet big here, there is a chance a paranoid opponent may fold. How big of a chance? Well, unlike Pot Equity, there is no handy program like 'Stove we can employ to spit out the answer. Instead, how much Fold Equity you have depends on less tangible factors, like the emotional state of your opponent, what he perceives your range to be, and so on. It also (obviously) depends on your bet size. In this example, we might say that your Fold Equity on the river is nearly zero percent if you bet small, but might be as much as 10-20% if you bet a very large amount and made your opponent believe you could have the nuts.

So why does knowing what your Total Equity is matters? Because, as you will recall, there are two ways to win in poker: 1) show down the best hand (i.e., have big Pot Equity); or 2) get your opponent to fold (i.e., have Fold Equity).

Note that in the vast majority of poker hands we play (i.e., if we don't have total air or the nuts), we're somewhere in between, trying to win, with a combination of both Pot and Fold Equity. This is where things like Show Down Value hands and Semi-Bluffs come into play. Here's a simple graphic I ginned up to hopefully explain better:

Your Total Equity in a poker hand is the sum of your Pot Equity and your Fold Equity.

Finally, I'll leave you with an Equity rule of thumb that is often repeated by professional players: If you think you have more than 50% Total Equity in a hand at any given time, you should bet. I'll leave it to the reader to figure out why this is true....

All-in for now...
-Bug

Missed Fold Equity

I played in my monthly 45-man $25 live tourney last night. A big fraction of the gang showed up, including Flyboy, Raster, Solar Ted, 'Copter Bob, The Tash, and even my son. Good times were had by all, and Raster sent an email out this morning that said he took third place. Woo hoo! Gotta love it when one of the crew monies!

Ah, but that's not to say all was good. The very fact that he had to send an email with the good news is just another way of saying that none of us were still there to witness the score. Instead, we all popped out early like zits on the morning of a teenager's prom, yours truly included. Worse, I busted in the worst way possible: I screwed up.

 I can take coolers.

 I can handle bad beats.

 Hell, I can even deal with losing to luck boxes that thrive on suck outs.

 The thing I hate, however, is busting because I made a stupid mistake. Here's what happened:

Blinds were T500/T1K and I was sitting with a stack of around T16K. We were down to three tables, and my image was fairly snug. Table was relatively good, with me having position on the better players, and some weak-tight players on my left.

I was dealt A♥3♥ on the button, and the action folded to me. The small blind was a nit, and the big blind was a relatively tight player, too, and had been folding to my steals more often than not. The few times I was called by him, he turned over face cards, and the one time he reraised me, he turned over a pair fours. I had also seen him fold a turned top pair face-up to a big re-reraise.

Anyway, back to the hand. After it folded to me, I raised to T3K. The small blind folded, but the big blind called. With little to go on, I put him on face cards, Ax, or suited connectors. He had me slightly covered in chips.

The flop came out J♠-4♥-7♥, which gave me the nut flush draw, an over card, and a backdoor straight draw. Perfect for a c-bet when the BB checks to the raiser....

 ...ah, but the BB decided to donk out for T3K into the T6.5K pot. I was getting over 3:1 pot odds to call. I probably had 9-12 clean outs twice to the flush and/or an overpair. I did the math in my head and called. 

Arghgh.

 Yes, I was getting the right pot odds to call and see two cards, but why the hell I didn’t just shove is beyond me. In other words, I calculated I was getting enough odds to see the turn and river, so I had mentally committed to seeing the turn and river. And if I’m planning on seeing the turn and river, why not add fold equity into my arsenal as well?

 The turn came a blank. Pot was T12.5K, and I had about a T10K behind. The villain led again for T5K. Which left me in a terrible spot.

Do I call and then shut down on the river if I miss? If so, my M is in horrible shape, but o the other hand I won’t be quite dead.

Do I reshove here? If so, the villain will be getting great odds to call with top pair, so my fold equity is basically nill.

Do I fold? If so, what the hell am I doing in the hand in the first place (remember, I said I mentally committed to seeing two cards). Ugh.

In the end I reshoved. The villain thought for a relatively long time, but then called. Of course he turned over KJ, and then of course held on the river. I was sent packing.

I repeat: Arghghg.

Seriously,  I don’t mind missing my draw, but what I do hate is how I missed the fold equity opportunity. 

Sigh.

But at least Raster scored.

All-in for now…
-Bug