Welcome to the most difficult street to play in poker. The river bet is the largest and often the trickiest to nail down. This is when you have to compute for the most factors, hand read through the most cards, and make the most expensive decisions. Prepare to treat the fifth card with respect and you can change the tide of a tournament. Misplay this street and you will walk back to the rail wondering what could have been.

We’re first going to look at triple barrel bluffs because they are the newly important component to our river game. In the past, a player could make good money hardly ever launching a triple barrel. Those days are largely gone. People hold on much more when it comes to the turn bet, which is a great play if you’re never going to fire the river, as 80%+ of players are prone not to do. Your goal is to become the 20% who have that third bullet chambered. Because of the huge discrepancy between what people call the turn with and what they call the river with the triple barrel can be the most profitable bet in the entire hand. Yet I repeatedly watch players shy away from it.

Value betting is also intensely important, yet the bulk of players are more content to check down and not risk being outplayed. These are the largest mistakes you could make as you enter the high-stakes world, and mastery of the principles will give you a huge leg up at any final table, where the pressure causes people to make needless calls and, worse, folds.


Let’s begin with the bluffs, as they are the most exciting. Many people stare and wonder when a seasoned veteran of the felt jams on the river, only to look nonchalant as his target mucks his hand. People see this as wizardry or balls of steel. Yet, for many professional poker players, the bluffs are a simple matter of mathematics; they do not evoke fear in the same way the government does not fear that someone will win the lottery.

To make some of these really sick plays we’ll have to turn back to our old friend Flopzilla. Let’s take a look at one of the more interesting boards someone could launch a triple barrel bluff on. I played the hand shown in Figure 99 a couple years ago during a larger buy-in WCOOP event. I had 10-9o on the button. A good player opened from the hijack. During that day he had been flatting a number of raises and not getting the better of me on the flop. Sometimes, the game opens up, and you start reading better.

I felt in that zone, so I 3-bet semi-bluffed with my 10-9o, relying on my opponent to be in an awkward spot on most flops with his stack size (Figure 99).

Here I was risking 738 to win 1,413, so my bet needed to work 52.23% of the time. As we can see by looking at the number next to the initials “F3” on my HUD, our opponent folds 60% of the time to a 3-bet. He folds 60% of the time to all 3-bets, including the 3-bets when he’s able to call in position. It’s likely he is folding more to a 3-bet when he is out of position.

Still, people get testy in these 6-max tournaments, so I’m not doing this play with a complete bluff. The 10-9 offsuit is a great semi-bluffing hand because the hand is not good enough to call with but it has considerable postflop value. Therefore it’s a great hand to take to war when we 3-bet bluff, as opposed to a complete bluff or a hand which would be more profitable as a flat.

My opponent ended up calling, as I expected would happen a large percentage of the time. Since he was opening up his game a bit I gave him a slightly wider range in my mind, one that I thought looked like the range shown on Flopzilla in Figure 100.

Note: I had him 4-betting with A-Qo, A-Js, 9-9, and 8-8 occasionally, which is why you see those bars underneath the hand rankings. Those indicate that a certain percentage of the time the hands are 4-bet, thus not giving all of the combinations to his flatting range. You can see the exact percentages to the right of the starting hand category. We now go to the flop, which came out to be 3♦- 3♠-2♠. He checks to me. I bet 818 (Figure 101).

We are now risking 818 to win 2,639; 818/2639 = 0.3099. Our bet needs to work 31% of the time here in order to show a profit. To prevent us making money from any two cards, our opponent needs to call or raise with 69% of his hands.

If our opponent just calls us here with 69% of hands he’s still not making a profit, because we get a free shot at hitting the turn. If he jams 69% of the hands we break even. He would have to shove 69.1% of the hands in order to make a profit in the bluffing war.

So, let’s enter this flop in Flopzilla, and decide what we think our opponent is defending with. My guess is he’s going to play ace high or better, any pair, any flush draw, and any open-ended straight draw. Let’s enter that first by putting a filter next to every part of the range (Figure 102).

He needed to defend with 69% of his hands, and even if he’s defending with his ace-high gutshots here that only adds up to 53.3%, so he’s folding 46.7% of hands when we only needed him to fold 31% of the time. Our play has considerable prowess here. However, he calls our bet.

If we thought he was only calling with his entire range we’d be prepared to enter a turn card here on Flopzilla. However, he is likely check-raising some of his combinations. His statistics say that he check-raises 18% of the time, which is a healthy number. Unfortunately, he didn’t show down any of those hands. We need to put a filter icon next to everything that is check/calling in order to compute the turn card more effectively, so we need to cut out whatever we think is check-raising.

Let’s have him check-raise getting it in with nut flush draws and any over- pair 8-8 or greater. We would first need to augment his flush draw range by right clicking it, putting red Xs on the ace-high flush draws, and closing it again (Figure 103).

We hit the accept button at the bottom and we’re ready to go. Some of you are thinking, “But I think he’s probably check-raising a few more of those combinations, especially the open-ended straight draw and flush draw.” That’s great. However, later in the hand we’re going to see that we are helping him here on the flop by giving him so many flush draws with which he’s check/calling.

As always, when we’re bluffing we want to make our opponents monsters. If our strategies beat the cyborgs they will likely beat everyone, so they should be applied with regularity. The 5-4s and K-x flush draws are appropriate combinations to add in because people get a little more coy with these hands, whereas the nut flush draw almost always seems like a snap check-raise all-in hand.

If you’re noticing the “edited” filter next to gutshot as well as flush draw that’s because I cut out offsuit 6-high gutshots but kept in the ace-high ones. We now edit the over-pair section the same way to remove 8-8 and 9-9. We’ll have our opponent calling down with worse pairs. Figure 104 shows what the final product looks like.

You’ll notice that the filtered percentage is now a smaller number at 48.4%. You’ll also note that we have villain trapping with quads, full house, and three of a kind. That strengthens his range. If he played fast with any of those hands it would give us more reason to keep firing at him.

The virtual dealer slides our opponent’s chips to the middle, burns, and turns. Fourth street is a Js. He checks to us. We fire half the pot, assuming we’re threatening his full stack. He is unlikely to believe we are bet/folding when we would get such a good price (Figure 105).

We are risking 1,865 to win 5,322 here; 1,865/5,322 = 0.35043, so our bet needs to work 35.04% of the time. Our opponent needs to defend 64.96% of the time in order to ensure we can’t bet with any two cards here.

Let’s click the button near the filter and make sure it’s green (I already did it in the previous figures) and add the turn. Under statistics now we will have a breakdown of all our opponent’s turn combinations, which should look like the breakdown shown in Figure 106.

As you can see our opponent needed to defend 64.96% of the time and he’s defending 68.4% of the time. We’ve made an unprofitable bet, right?

This is where things get tricky. Look at everything there is a filter next to in this analysis. He has to call you with any pair, including the twos. He cannot fold them ever. He has to call you with every open-ended straight draw. If once he looks at five-high with a flush draw on the board and folds he’s not defending enough. He has to be trapping with every full house, quads, and three of a kind. He needs to be flatting instead of check-raising you on the flop with most of his flush draws. And even when all of these stars align he is barely ahead of your bluff by a couple of percent.

This encapsulates what professional gambling is. When we make this bet on the turn we do not know what exactly our opponent is playing back at us with. We don’t know exactly what they called with. We do not know what they call with this on the turn. We’re gambling against him finding the right solution.

The right solution here depends on six or seven items coming together. Gambling on that occurence by checking back and giving up the pot seems stupidly risky. Gambling on him not finding the right safe combination in 30 seconds or less seems like a much better gamble. However, neither is perfect nor foolproof. In the hand our opponent called.

Now we get to where things got really interesting (Figure 107).

Our opponent called fairly quickly, and my read was that he’d gotten exasperated with me. I’d been making these kinds of plays for an hour, and my guess was he wasn’t too happy about it. Strangely he left himself 2,489 in chips in a 7,187 pot. You would think he would not want to leave himself so few chips for any kind of decision on the river, but when you get fed up with a player you

occasionally forget to ask yourself these things. The river came a 5♠. He checked to me. I moved all-in for his final 2,489 in chips. He’s now getting 4 to 1 on the call, which means he only has to be right 1 in 5 times in order to turn a profit (Figure 108).

Why would we do this, when it’s so obvious we’re going to get called so often? We’re risking 2,489 to win 9,676; 2,489/9,676 = 0.257234, so we need our play to succeed 25.72% of the time for us to turn a profit. While that sounds like not much it doesn’t seem doable at first blush. Won’t our opponent call with everything getting odds this good?

What do we think a frustrated player calls the turn with? We’ll give him the hands he’s trapping with. Full houses, three of a kind, quads, flushes, and the like. We’ll also give him the pocket pairs 4-4, 5-5, 6-6, 7-7, because our opponent has shown previously that he understands we like to bet scare cards, and a jack is an unlikely card in our hand. He also knows we could be double barreling with a flush draw of our own. Speaking of which, we’ll give him the nut flush draw. We’ll have him folding the 2-x combinations. That turn continuation range should look like the hand shown in Figure 109.

Now, if we put the river card we will see what our opponent’s range looks like on that street (Figure 110). This is where the real magic happens.

When we put the filters next to everything we think that is calling we can see that if we have our opponent calling the river with any three of a kind and any flush he is still only calling 69.4% of the time, so he folds 30.6% of the time. Our bet needed to work 25.72% of the time.

This kind of math used to be incredibly difficult to do. Ranging a person through so many streets is an exhausting process, especially when you consider the different numbers of combinations each hand represents and how they are affected by new community cards. Having Flopzilla to range easily through multiple possibilities allows us to realize some generalities. One that’s easy to discover if you do a number of board run-outs like this one is that people generally do not have a good flush in their hand when the board comes four to a suit, especially if they were calling with a number of pairs on the turn.

Now we need to try this kind of work on a variety of boards: when over- cards come, when they do not come, when the three-flush comes in, when a one- gapper straight hits, when the top card pairs, and so on. When we try to do them on similar boards we get many exciting findings. It is beyond the scale of this book to go into every category of board run-out, mostly because what your opponent calls down with varies so much, thus making the variety of answers extremely diverse. However, with this $30 piece of software and 30 minutes a day you can start taking notes and jotting down your findings. You can run the numbers on any bluff you attempted. Then you will possess information that nobody in poker held until a few years ago.

It cannot be overstated how calming this kind of study is. When I was younger a number of successful professionals heavily criticized my play, which cost me some lucrative backing deals. Without any prowess in math I was forced to explain that I’d come to my conclusions simply watching millions of hands take place, which had cost me years of my life. The wise children from atop the “I won a live tournament once” mountain “tsked tsked” at me, and went on their merry way to wherever it is demigods spend their time.

Years later I tried a huge bluff at the final two tables of the PCA that was very similar in nature to this one. Actually, it was a much better bluff. The number of pairs my opponent could have was six times the number of combinations our paltry pocket pairs gave here. I raised huge on the river versus what looked like a block bet and ran into the nuts (oops!). I later busted the tournament, after having the chip lead with a few tables left. The announcers of the tournament got their quips in, much to my mother’s chagrin. A number of professional players, who apparently had nothing better to do that day, started approaching people who had invested in my tournament run. They asked them what the hell was wrong with them. “How could you support such an awful player?”

Privately I did work such as this for my investors, and then did it four more times to check I was right, targeting varying ranges. You do this by removing the river card on Flopzilla and editing the turn range again. If you want, you can even go back to the flop and make some changes there. Then you run it through to the end again and see how the ranges were affected.

Sometimes you find the play wasn’t profitable versus certain ranges. For example, if we have our opponent folding 4-4, 5-5, 6-6, and 7-7 in our hypothetical turn range his river range looks like the range shown in Figure 111.

He’s now defending 77.9% of the time, so our bet is only succeeding 22.1% of the time, when we needed it to function in a quarter of the trials. You want to create a number of possible ranges, assign them a probability of likelihood, and then look at the varying results. If you find you would turn a profit versus the vast majority of potential opponent ranges then your play was profitable.

I was able to do work like this to quiet my guilty conscience. I did not want to lose a great opportunity for my investors, who were and remain great people. Through doing work like this and showing them how I came to my answers I was able to let them know I didn’t fire my chips in blindly. They understood then that they had invested in a player who had prepared for his big day, regardless of what the results were.

I was even able to turn some of my former adversaries into allies. During an open webinar I was criticized again by someone for this play, and I showed my logic for it. I asked if any of my observers could show me my erroneous approximation, because if I had made a mistake I wanted to know it. A young man came forward and showed me a way I could improve my method. It didn’t change the answer, but it did show me a bad bluff I made in a smaller tournament. In my mind I had been defensive without reason, and had labeled him as a “hater”. In reality, he had been trying to learn from me, and I had arrogantly ignored his potential input. Creating an open dialogue aided by these tools is the first step to vast improvements in high-stakes poker. My only regret is that I do not have time to do this more often.

One note before we move on to the next tool that we can use: expect to make mistakes. That is why you need a good group of friends to review your work. Early on the analysis is basic enough for you to find the mistakes, but as you move into higher stakes and the problems become more complex you’ll need to find some colleagues. Since you shouldn’t be trying to get into higher stakes when you’re not already a professional I’ll assume you’re at the tables constantly and working within a training site or forum.

Host many “interviews” for players who can help you. Casually chat them up over Skype, show them a hand, and ask “What do you think?” If they show you some new angles make sure you stay in touch. If they ask for a day or two to watch a tutorial to learn the software, and then they hit you up to check their own work, keep that hard worker in your network. If he goes, “Lawl, who cares?” or “So-and-so doesn’t even use a HUD, and he’s #4 in the rankings” find other personnel.

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