Caro’s Peak Poker Theory explained

Mike Caro   ← Go back



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Poker is mathematical truth and psychological theory blended. If you correctly do math, you have an answer, not a theory. What’s known for certain isn’t theory.

Some might quibble with that statement and assert that answers change with time. But correct answers never change. Conditions might change, requiring new answers to different problems. But the previous answers remain correct. Maybe sometime we’ll discuss that important concept, but not today.

Theory time

Today it’s time to talk about Caro’s Peak Poker Theory. I know what many of you are thinking. Why does Mike Caro’s name need to be attached to so many things? In this case, I agree. It’s egomaniacal and unnecessary. I wish I had the authority to change it.

Anyway, the theory, which I’ve been teaching for decades, is derived from a simple mathematical certainty. Here it is:

Your career poker result is the sum of elevations for all new peaks above their nearest ancestors, minus the current distance below your most-recent new peak. So, what does that mean?

Meaning

When you start tracking results, you’re already assigned a peak. It’s the zero peak — your starting point. As soon as you finish a session higher than that, your career total (or campaign total, which I’ll talk about later) is the distance you are above the previous zero peak. The zero peak will soon be history and you’ll no longer care about it. But first, you need to discover whether this new peak goes any higher. Its summit hasn’t been found, but you know it’s above the zero peak. So you can add this new height, measured in dollars, to your new peak, because you’re already there. The difference between your current elevation and the previous zero peak represents your peak profit.

The first time you book a loss, the new peak’s height is established, becomes the target, and the previous one is meaningless. Until then, your peak’s height is a mystery. Got it so far?

How it works

Peak math is quite easy. You can only advance by reaching a new peak. And your total outcome is always exactly the sum of all new peaks above their last ancestors, minus the distance you need to climb to reach the the highest peak’s elevation. Mostly, you’ll be below that high peak, so you subtract the difference from the sum of high-peak differences. Sometimes, you’ll be on a new peak, but you don’t know how high it will be. You still add it to the sum of differences, making the temporary assumption that this is the summit. Climb, climb, climb! That’s your job when you play poker seriously.

It’s important to understand that you will only rarely reach new peaks. Months can pass as you climb up lesser peaks and descend the other sides. You will spend most of your poker career below your most-recent high peak. Get accustomed to that. You’ll usually be below that highest peak and were once better off than you are now. Cherish every dollar, every foot of elevation. Eventually, if you play winning poker, you’ll reach a new high peak again. The hike ahead of you always ends up higher in time.

The theory part

The reason I use Caro’s Peak Poker Theory when teaching poker lessons by Skype is that I believe students can relate to it. That’s the “theory” part. They can see that if you draw a very wide graph, entering each session’s end as a data point, then you could add a horizontal line marking the elevation of each new peak that occurs. You could measure the distance in dollars that new peak lies above the previous one. And you could add all these differences together and then adjust for your current distance relative to the reigning highest peak. That’s your net result up or down for all data entered.

And that would accurately represent how you’re doing overall. If you’re thinking that it’s easier just to keep a running total, you’re right. Your objection is interesting, but irrelevant, as you’ll soon see. Again, you can only win more money by reaching a new peak. But on the graph, most of your time is spent below your highest peak, thus not adding anything to your peak career profit. Realizing this keeps serious players from becoming frustrated. Or, at least, that’s my theory. They can see that peaks are rare, but the rest of the hike matters greatly. That’s because doing it well means they’ll be in easier striking distance of that future high peak — when they’ll finally be adding money again.

Imaginary sessions charted

Below is a simple graph to help you visualize your hike. It shows the imaginary results of sessions 1 to 14.

The labels on the peaks (or “negative peaks” in two below-zero cases) indicate where you stand overall, up or down from zero. Guide lines stretch from each label to the corresponding altitude on the graph. This is no different from how you might chart running totals without Peak Poker methodology.

Actually, the only data that’s essential to Peak Poker Theory is the lowest line of numbers inside the bordered box, right above the session numbers. That line uses ↑ and ↓ indicators after numbers to show standings relative to the previous high peak. That line is the most important, representing Poker Peak status. Above it is a line providing the actual result for each of the 14 sessions.

Poker1.com Peak Poker chart

Chart too small? Try Ctrl-+ (Cmd-+ for Apple) or zoom on mobile devices.

Session by session

In the session list below, notice that until the sixth entry, everything seems obvious. The total result is the same as the Peak Poker status result. But on the sixth session, you lose 605, rapidly descending the east slope of your new high peak. That takes you from +551 to -54. But now the PP status doesn’t match. It’s not -54, but -605. That’s because the measurements are relative to the previous high peak and until now that was the zero peak.

When you understand that, you’ve grasped the essence of Caro’s Peak Poker Theory. We’re always measuring PP status in comparison to the previous highest peak.

  1. -230
    230 below peak — the zero-peak starting point.
    Sessions above peak: 0 | Below peak: 1
    Total: -230 | High-peak: 0 – 230 below peak = -230
  2. -85
    315 below peak and not off to a good start.
    Sessions above peak: 0 | Below peak: 2
    Total: -315 | High-peak: 0 – 315 below peak = -315
  3. +490
    175 above peak and climbing a new one. Profit comes now.
    :Sessions above peak: 1 | Below peak: 2
    Total: +175 | High-peak: 0 + 175 above peak = +175
  4. +174
    349 above peak. Still climbing — at least, potentially.
    Sessions above peak: 2 | Below peak: 2
    Total: +349 | High-peak: 0 + 349 above peak = +349
  5. +202
    551 above peak. How high is it? Try to climb some more.
    Sessions above peak: 3 | Below peak: 2
    Total: +551 | High-peak: 0 + 551 above peak = +551
  6. -605
    605 below peak, since that’s how far you must climb to recover
    Sessions above peak: 3 | Below peak: 3
    Total: -54 | High-peak: 551 = 0 – 605 = -605
  7. +100
    505 below peak and winning overall again
    Sessions above peak: 3 | Below peak: 4
    Total: +46 | High-peak: 551 = 0 – 505 = -505
  8. +255
    250 below peak and still cimbing
    Sessions above peak: 3 | Below peak: 5
    Total: +301 | High-peak: 551 = 0 – 250 = -250
  9. +62
    188 below peak and still climbing
    Sessions above peak: 3 | Below peak: 6
    Total: +363 | High-peak: 551 = 0 – 188 = -188
  10. -240
    428 below peak, oops, a setback, who cares?
    Sessions above peak: 3 | Below peak: 7
    Total: +123 | High-peak: 551 = 0 – 428 = -428
  11. +890
    462 above peak, rapid climb
    Sessions above peak: 4 | Below peak: 7
    Total: +1,013 | High-peak: 551 = 0 +462 = +462
  12. -400
    400 below peak and that one didn’t go any higher
    Sessions above peak: 4 | Below peak: 8
    Total: +613 | High-peak: 1,013 = 0 – 400 = -400
  13. +222
    178 below peak and a possible easy climb to a new one
    Sessions above peak: 4 | Below peak: 9
    Total: +835 | High-peak: 1,013 = 0 – 178 = -178
  14. -403
    581 below peak, but still determined to climb
    Sessions above peak: 4 | Below peak: 10
    Total: +432 | High-peak: 1,013 = 0 – 581 = -581
Peak ratio

As soon as high peaks are above zero, the notation changes, as it does in line 6: “High peak: 551 = 0 – 605 = -605.” I did that to emphasize that the only thing we’re targeting is the most-recent high peak. It’s 551, but for our purposes it’s zero. Thus, 605 must be won to reach that previous best level. The PP status is -605 now, not -54, which is the overall result.

The last part seems silly — “0 – 605 = -605.” This format is the same for each new result thereafter: zero plus or minus some number equals that same number. Repeating: I did that deliberately to emphatically reinforce the core concept each time. Your Poker Peak status is always relative to the current high peak, and the height of that peak doesn’t matter.

Notice that out of the 14 sessions, 10 closed below peak and four above. This 10-to-4 ratio will probably get much worse as time passes! As I said, it’s not abnormal to close more than 90 percent of your sessions below peak. I want you to realize that hard fact, so that you make the most of the majority of time you’ll be playing below your high peak, knowing that you were doing better at some point in the past.

Understanding that puts your hike in perspective and makes it much less likely that you’ll play poorly between peaks. Again, that’s the “theory” in this method’s name.

Why bother?

It’s true that your current profit is always the same as it would be if you just measured it against zero. You’re either up or down from zero — either winning or losing overall, or perhaps breaking even. So, why bother with peaks?

You bother, according to my theory, because you’re always in pursuit of the next new peak. It gives you a certain goal at all times. You’re either on a new high peak, exploring whether it goes even higher, or you’re below your last high peak and are climbing.

By “climbing,” I mean trying to climb. Obviously, this won’t always happen and you’ll have to hike down a slope before reaching one that goes up. The theory is that you’ll be unlikely to lose your footing and fall to a lower altitude than necessary, because consciousness of peaks makes you realize how much longer a poorly managed hike could become before reaching the reward of a new peak.

I’m not telling you to be obsessed with peaks. In fact, I teach that you should make quality decisions and never care about outcomes — either for a hand or for a session. But new peaks will happen, whether you care about them or not. And by being aware of them, your climb becomes psychologically simpler. You understand that most of your sessions will occur below a previous high peak. Instead of being annoyed, you focus on the next high peak, even one that might be far away. This focus makes your hike productive and pleasant.

Caro’s Peak Poker Theory is really a motivational concept built on fundamental math. And it works.

Peak Poker status

You only track two things: (1) The value of your most-recent new peak relative to zero; and (2) The distance you are from that most-recent new peak, called Peak Poker status or simply PP status. If you’re currently climbing a new peak, you still measure its altitude above the previous one until its height is established by your first descent. At that point, the just-visited peak becomes the target, and you can forget about the previous one. Conceptually, this peak (and any new one that follows) becomes a fresh zero-peak. All Peak Poker distances are zero based, plus or minus, relative to the current high peak.

Of these two things, only the second is important in Caro’s Peak Poker Theory — PP status, representing the distance you are from your previous new peak. The first tracked thing (value of most-recent new peak) is just for convenience, whenever you want to know where you stand overall. My theory is that if you focus on your PP status — thing two — you’ll magically self-motivate to build your bankroll. Note that occasionally you might have twin peaks, each the same height. That’s not a problem. Your PP status is exactly zero, because you’re neither above nor below the established high peak. Just use the most-recent of the twin peaks as your target — although it really doesn’t matter.

For convenience, you’ll usually refer to your Peak Poker status as “above peak” or “below peak,” with the assumption that you mean the previous highest peak and not any sub-peak below it. So, if you tell me, “I’m $480 below peak,” I’ll know what you mean.

Does Peak Poker Theory work for losing players?

So far, I’ve assumed that players have long-term winning expectation. What about players who don’t? The math still is accurate. The practical difference is that losing players might never climb above their initial zero peaks. If they do, it will likely be early in their hikes, when a few lucky wins can put them temporarily into new-high-peak territory.

But the formula still holds. Even for losing players, results are always the sum of the gaps between all new peaks and their new-peak ancestors, plus or minus any current distance above or below the targeted high peak. So, if a player descends from the get-go, then the sum of new-peak gaps is zero minus the current deficit. So, yes, the formula applies to losing players.

Application of Caro’s Peak Poker Theory might even help losing players to realize that their game plan isn’t working. Once it becomes clear that a new peak probably is out of reach, they may decide to improve or to save money by decreasing poker play or quitting entirely. That’s not good news for the winners, but it’s unlikely that losing players will be adopting this or any other serious poker advice.

Career vs. Campaign

I teach that it’s okay to temporarily stop tracking your career peaks and declare a smaller campaign with its own zero-peak starting point. Why?

It may be because you’ve learned new things about poker and you believe you’re a much different player now. So, Peak Poker that. Or you may want to start fresh for a new year. Peak Poker that, too. Whatever your reasons, if declaring a new campaign helps motivate you, do it. You might even give the campaign a name.

Just don’t forget that your lifetime results still have informational value. That information is always accessible. It’s simply the sum of all your campaigns, the failures and the successes, and career segments that weren’t part of campaigns.

Advice

Never worry about where you are now relative to where you used to be. Doing that will make you feel negatively about your status, since you’ll spend most of your time below your highest peak. In fact, the majority of your sessions will be attempts to return to easy climbing distance of a new peak. That’s poker.

Fight for every dollar. Don’t let frustration make your often-tedious climb more difficult. If you do, you’ll waste much time before arriving at your next new peak — or may never reach it.

Final words

That’s it: Caro’s Peak Poker Theory math married to psychological trickery, forcing you to focus on the next new peak. Clearly, it can be applied to other life endeavors, not just poker.

Try it. I’m betting that you’ll focus more clearly on long-term poker goals and enhance your results. At least, in theory. — MC

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Mike Caro

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Known as the “Mad Genius of Poker,” Mike Caro is generally regarded as today's foremost authority on poker strategy, psychology, and statistics. He is the founder of Mike Caro University of Poker, Gaming, and Life Strategy (MCU). See full bio → HERE.

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