Poker Articles

A Bit of Maths
By Paul Samuel
(The UK's answer to Mike Caro or Lassie)

Introduction

I have recently become a much much better poker player and it happened very suddenly after a short break from poker whilst my wife and I had a:

This is in addition to the three I already have, Joseph, Lara and Abi, "the flop" (pictured right). Piper (pictured above) is "the turn." By the way, my wife is already talking about the river! Now lets talk poker!

I was always a good technician. I always had a good scientific understanding of the game but was missing something. Friends of mine would tell me I played too tight, but I know now that this is just how the problem manifests itself to the outside world.

So now, for all you avid students of the game constantly frustrated by long runs of bad cards and not getting any action when you do hit them, I am going to reveal all. Well, nearly all.

Now lets talk about cookery! Yes! I said cookery. Bear with me, there's a point to this.

I am a really good cook. No I don't mean I cook the steaks when the BBQ comes out. I don't mean I do a really good fried breakfast. I mean I REALLY am a really good cook, like you know, restaurant standard. Bread, cakes, biscuits, ice cream, soufflé, homemade pasta... yes, the lot. Ask Gary Solomons (he writes here, too) -- he'll tell you.

Did I get good overnight. Well, in a way, YES!

Take bread for example. I spent weeks and weeks creating floury horrors until one day my results matched my technique. My scientific understanding or my internalization of bread-making was great. Matching that technique with the actual realization happened suddenly!

What most "would be" cooks do is pick up a book and get stuck in. Sometimes things come out well and sometimes they don't. That's because these people don't understand the background techniques! Occasionally someone just gets stuck in and seems to be just naturally talented. This happens only very, very occasionally, and because their technical understanding is cellular (I won't go into that).

Your route to cookery or poker mastery is far more likely to be a slow plod through technical mastery and then BINGO! You will become talented!

I am actually going to illustrate this today with a simple example. But first, the answer to the last article's conundrum.

Answers to Last Conundrum

The conundrum was, what's the probability of flopping a rainbow (i.e. 3 different suits). Here's how you work it out:

52 x (52 - 13) x (52 - 26)
--------------------------
         52 x 51 x 50

           or

(52 - 13) x (52 - 26)
---------------------
         51 x 50

You can choose anything for the first card (52/52), but you cant choose the same suit for the second ((52-13)/51) or either of two suits for the last card ((52-26)/50).

This gives your answer of 39.76%. Is that what you would have guessed ?

The Science of Intuition

I was playing in a £50 ($80) pot limit hold 'em rebuy event at Roy Houghton's excellent poker room in London. The blinds were 100, 100, 200 on the button when I picked up an AK in middle position with about T2000 left.

No one had called before me so I made it 800 to go. The button (with about T3000) called and all others passed.

The flop came down rainbow and raggedy. Something like T72. I checked and the button bet the pot 1900. I passed. I showed my cards and Mike Magee, a very well respected professional, gave me a telling off!

Now, my scientific friends, I will tell you why he was right, and I won't give you any airy-fairy gut feel/experience/card sense explanation. I will give you the famous Paul Samuel 'CSE' (see below) explanation.

First, what will the button call with in this spot?

Now, I understand that are a number of variables here, especially those concerning the type of player he is. In this case, my opponent was a conservative, experienced and quite tough sort of player. No fool, but no Doyle either!

In this spot, this type of player calling will almost certainly have one of AA, AK or maybe, just maybe, an AQ (with a swing to suited). He may even have a KQs. With position, I'll give him that.

Now a real tricky or loose player may call with all sorts of stuff with a view to outplaying me on the flop but most guys (and this guy in particular) aren't that tricky or that loose. Most guys will either call with one of the above or will re-raise with something else, like KK, QQ or JJ.

So you see, this raggedy old flop is actually a very good flop for me. I should have lead out. If he's got the AA then good luck to him, but there are just three combinations of AA. There are nine of AK, 12 of AQ and three of KQs. This means I like (or in the case of AK, don't mind) 24 out of 27 hands. Those are good odds!

My check on the flop is really really weak. If he did defy our logic and call with some real garbage then we've given him a free card.

If he has one of the genuine hands we mentioned we are a huge 8 : 1 favourite to have flopped the best hand. (i.e. 24/3 : 3/3). If he called with a non-genuine hand and hit the flop, that's too bad, but also very unlikely. If he called with a non-genuine hand and missed (more likely), then a flop bet will surely scare him off!

So despite our fears (which as you know are traitors), our flop bet has at worst a 1/9th chance of being called by the best hand!

You see what we did ? We reduced Mr. Magee's intuition to a probability. It's just "a bit of maths."

Recently, I started doing the right things in such situations. This happened recently and suddenly.

THAT FRESH BAKED BREAD SMELLS REALLY GOOD!!

Corrections to Previous Article

I just missed a few boards! Just a few. It could happen to anyone! Just for being mean to me, I'm not going to tell you what they are. It barely affects the results, just a few tiny adjustments here and there. The principal conclusions remain the same.

What's the CSE?

It's the "clever swine explanation."

Epilogue

I played in a £250 +1 Rebuy last night (10th July), and I had a disastrous night. I had to tell you that because I would have felt dishonest if I hadn't.

Finally, Another Conundrum

In hold'em, given a flop with three different value cards, what's the chance of a player having flopped a set? Take nine cases, two to ten players and guesstimate or calculate each one.

Thanks for your attention.