Mike Caro poker word is Probability

Note: Not at the old Poker1 site. A version of this entry was first published (2010) in Poker Player newspaper.

One word that’s widely misunderstood is “probability.” Most people, including poker players, don’t fully understand how it works at the tables and beyond. They fail to grasp its importance. I’ll talk about that in this self-interview.

Question 1: What things does probability affect?

Probability affects everything. In fact, it governs everything.

The likelihood of anything happening can be precisely and confidently stated, provided there is enough information to perform the calculation. Often there isn’t.

We have enough information to calculate the exact probability of beginning with aces in hold ’em, assuming a deck of cards is randomly shuffled. It’s undeniably 220-to-1 against.

Although I prefer to express things in odds and percentages, mathematicians usually measure probability on a scale of 0 to 1, with 0 meaning impossible and 1 meaning certainty. On that scale the probability of aces is about .0045, but you won’t see me using that description very often.

More complicated

Unfortunately, most things that happen in poker and life are much more complicated. They can’t be calculated practically, even though they could be in theory. The ingredients that go into the formula are mostly beyond anyone’s ability to know, so there’s a lot of guesswork that goes into predictions.

That’s another misunderstood word – prediction. When experts predict that something will happen, they’re really not putting their reputations on the line, because all that’s really being predicted is the probability of something happening. If I correctly calculate that it’s 19 to 1 against any of a group of 50 professional poker players winning a given tournament, I might “predict” that none of those pros will win and state that it’s a 19-to-1 shot.

What if one of them does win? Then someone might blurt, “You were really wrong about that!”

Not wrong

But I wasn’t wrong. If I made that same prediction 20,000 times and no pro player ever won, you might be tempted to give great merit to my forecasts.

But in that case, my probability skills should be questioned. If my 19-to-1 calculation were correct, then there should have been about 19,000 times when my prediction came true and 1,000 times when it didn’t. Since my prediction always came true, I almost certainly miscalculated.

Even without math, the better you are at estimated chances, the more successful you’re likely to be in poker and life. Usually, if you go with probability’s flow, you’ll succeed; if you go against probability’s flow, you’ll be swept away.

Unfortunately, weird things happen in the short term or even for lifetimes, when governed by only a hundred or fewer key events. But probability still rules, and when you bet with it you’re much more likely to succeed than if you bet against it.

Question 2: Could you use probability to prove that your home poker game is being cheated?

No, you can never use probability to prove that. But you can use probability to provide overwhelming evidence.

If you correctly believe your results should be much better than they actually are, then the longer that trend continues, the more likely it is that something evil is happening and the less likely it is that you’re merely experiencing a bad run of cards.

That’s how probability works. We call the number of events measured the sample size. In poker, this could be the number of hands played. Small sample sizes are greatly influenced by luck, but eventually events tend to even out and fall close to their predicted probability.

Exact measurement

Remember, your advantage or disadvantage at poker (excluding factors such as rakes and tips) is an exact measurement of the difference between your opponent’s skill level and your own skill level.

Let’s make the skill scale 1 to 100 and assume that every point difference is worth $10 an hour. If your skill level is 97 and your opponent’s skill level is 99 – well, it’s a battle between world-class players, but you should eventually lose $20 an hour, on average. If your skill level is 70 and your opponent’s is 40, then you should eventually win $300 an hour, on average.

So, it’s not how good you are at poker that determines your probability of winning. It’s how your skills compare with those of your opponents.

You need to remember that and I’ll repeat it. The probability of you winning at poker has nothing to do with how skillful you are. It is a measurement of your skills versus those of the people you play against.

That’s why it isn’t wimpy or wrong to seek weak games. Weak games, relative to your own skills, are the only possible source of your long-term profit. — 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.


6 thoughts on “Mike Caro poker word is Probability”

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  1. Hi Mike.
    Great site I really enjoy it, but you should add an odds calculator.
    best regards Marc

  2. Hey Mike S., Thanks for responding, it’s nice to talk of this stuff.
    I agree that poker is based on important decisions that takes study and application. And there are those that do it better than others and we say they are “great players” But my point is how much more important pure luck is than what we are made to believe from the poker community. For ex. “All In”s that gets a fold is not counted on an “All In” succes measurement, rather on a tactic succes measurment…..and We agree that you will have to go “all in” at least a few times to win a tourny. And just as ICM is less imoportant at the beginning of a tourny, luck, on the other hand, is more important in the short term and supposedly evens out so that 54% vs 46% plays and pays correctly…some day. However as ICM becomes calculable near the end of the tourny, luck, on the other hand is NOT calculable in the long run….how long will it take your 57.5% edge to pay off? And ICM doesn’t give you a better chance to win by the way…its just a better place to risk going broke. In fact luck is so vague that small and medium percent advantages barely even matter in the short and medium term and maybe long term as well. For Ex: if I told you you had 20 years to live…or 10 ….would you still put alot of stock in odds? As I said: how long will my 70% “loss while ahead” record take to pay off positive. No one knows so the discussion of odds pales in comparison to the reality of luck. Of course big pairs against small pairs have such great odds and A9 vs K9 as well. However, I’ve been beat very often when the K has fallen…..a 3 outer. I just finished a game, a guy went in with J9 and got called by 69…flop: 626…lol.
    I believe most players ignore or are ignorant to the real importance of luck on poker. They believe wrongly that their “better” decisions equal out the luck. This is due to the “bizness” of poker. That’s what I am saying. Poker is like running through a rock slide. You can train and those who train and run faster have a beter chance but there is no acounting for where or when the rocks will fall ! If you are less lucky than I…you won’t make it even if you are faster.
    Again, real great to converse about this. Peace out.

  3. Yo Mike,
    Great stuff. Sometimes I get lost in your writings and forget what I am supposed to do that day…. I’ll work on it!

    Here’s the thing: Poker, to simplify, I think we agree, is basically getting it all “in” with the best hand. Now in a tourney I think you will agree, that you will be obliged to go “all in” a few times in order to win. So the ultimate importance on luck is enormous as no matter how skilled you are, let’s say you are 70% better than your opponent, you will inevitably give him a shot at you at 55% when going “all in”. This is why, and is my point, I believe that poker sites and the pro community being businesses, need us to believe that we can improve and can eventually beat the game. This generates income. I believe the truth of luck is not perpetuated by any professional format…except maybe you!!!
    I kept track of my “all in” record for this last year. You ready??? For “all ins” when I am ahead I lost 70% of the time. Now I don’t care what people say there is no way this can be linked to my skill as I did what is supposed to be done……“get it all in”. By the way my record when “all in” behind was 85% loss. So the old luck “suck out equality theory” does not hold.
    I believe that luck is not equal. Some people are lucky in love (like me) and some are lucky in finances and in cards. Luck is not even and it does not equal out as the “professionals would have us believe. How long will my 70% loss record take to equal out?
    People like me are being duped by misinformation by the pro control of the game. This keeps us coming back for more. I know I have leaks but nothing like 70% of my game, if you get what I mean.
    I agree that roulette and craps are more luck-oriented games and poker has decisions. But skill in poker has no way near the importance as we are made to believe. And the site sponsoring of pros is creating an even more unbalanced view of the game. If I were paid to travel around and play tourneys for free I too would “make a living playing poker”. I believe many people would. As this takes out the money loss factor for these players and percentages don’t even matter anymore.
    This recent epiphany has really hurt as I do love the game but no matter how I play, i.e.: meta game, loose, tight, aggressive, weak, avoiding flips, pushing always….. It all still ends up a dice roll and everything equals out. I believe Ivey and some of those guys are truly luckier in cards than me (not in love though!!) Hell, Roland Dewolf says it himself; that in games of pure luck he can’t be beat.
    I just wish the pro element that possesses the business of this game would be more responsible to the simple layman and stop pumping up this idea that with training we can beat the game. In fact someone should create a luck test whereby you must score in the 60% range in order to be allowed to play on line as luck is the true heart of this game and no amount of skill will beat that.
    Love to hear your thoughts Mike.
    Take care, and G O O D L U C K

    1. In your all in calculations did you count the times that you pushed all in and your opponent folded? If you didn’t, wouldn’t this be similar to the mistake that people make when calculating a win with a bluff when they were in fact bluffing with the best hand?

      I have no doubt that luck matters. Alas, there is no course on getting lucky. You can’t teach luck. Just like football coaches can’t coach speed.

      That being said I believe that chance favors the prepared mind and the harder you work, the luckier you get.

      Also, based on some of Mike’s other writings, I don’t think that he thinks poker is getting it all in with the best hand. I think that’s a gross over simplification. It’s about making sound decisions. And he has written several times about instances where getting it all in when you have the best of it is the wrong decision. Some guy smarter than Mike Caro (hard to imagine, I know!) once said that you should make things as simple as possible, but no simpler. I think that applies in this case.

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