Poker Articles

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

1. Introduction

Ok, Ok so I missed last months article. My beautiful wife Michelle gave birth to our fourth daughter. I have 5 now, a full board. That's it - all over - no more missed articles. I've done my bit and am looking forward to the Poker Million.

The following article is brilliant; really interesting and it's going to cause such a furore (good word huh?) that I won't be able to walk the streets without being accosted and abused by irate poker players and Mike Caro. Ok, here's the essence of it :-

Gary Solomons was playing in a £250 competition at the Grosvenor Casino in Luton when the following happened :-

Gary S: "I was in the small blind with Ac As. I had 18,600 before the hand started.

The blinds were 300,600. Two off the button (largest stack by far est. 50k) makes it 2100 to go (raised 1500). I reraised 2000 more. He called.

Flop 9d Td 2c

I bet 8000

He reraised, I called All-in

He had Ad 4d and his flush came!"

2. Slow playing Aces?

In the above example, Gary's opponent was playing a lot of pots. As is the old Samuel method let's put him on one of the following hands :-

Table 1

nb. The second column is a count of how many ways that hand can be made! Now I use Mike Caro's Probe to give :-

Table 2

The 'P-Win' column is merely the probability (as returned from the probe over 10,000 hands) that our AA does not lose to that particular hand.

Now add a 'Fold' column that highlights hands that we reasonably expect our opponent to fold, should we go all-in before the flop.

Table 3

This gives the following :-

Table 4

i.e. only 7.69% of the time will we get a call to our all-in coup and furthermore, even if he does call us, 87.38% of the time we will still beat him.

This means that our all in bet results in a loss,
(100% - 87.38%) x 7.69%
= 0.97% of the time.

With the all-in bet Gary is a massive 102 to 1 favourite.

But he didn't go all-in.

Now averaging out the figures in Table 1 we derive that in just playing out the hand to the river, Gary and our Aces are a 7 to 1 favourite.

Now of course, Gary and many others will argue that the hand can (and probably will) be won far more subtly than a simple 'run to the river' but the essence of my argument will be the same.

We have swapped a 102 to 1 shot for something approaching a 7 to 1 shot!

Ok, Ok, let's look at this another way!

Given that Gary does not flop a monster (as was the case) what does he want to happen when he inevitably makes his bet?

The answer I suspect is :-
"Take the money and run"

Let's look at some monster flops :-

2.1 Axy

Gary needs his opponent to have one of Az, xx, yy otherwise he will not get any action.

2.2 3 clubs or 3 spades

To get action, Gary's opponent should have a suited KK; otherwise he will have a made flush or trips and thus be a favourite.

2.3 3 of a kind

Gary's will need his opponent to have a high pair to get any action.

You see; Gary is looking for a perfect situation to squeeze any more SAFE money out of his opponent! The inevitable conclusion is this :-

Gary was really playing for an extra 2000 (his re-raise). In most cases after the flop he wants to take that money and run. For an extra 2000 (the pot profit is 300 + 600 + 2100 before the re-raise), a fractional increase in pot profit, Gary has turned a 102 to 1 certainty into a much less favourable bet, approaching 7 to 1.

My conclusion is that this in no way can be justified and that Gary should have gone all-in or raised enough to make the increased risk worthwhile.

Lets face it even, if he calls an all-in bet Gary is still a 7 to 1 favourite to double through!

3 Conundrum

This is a question I pondered whilst playing 6 card Omaha hi-lo 8 or better at the Grosvenor Luton was:-

What is the chance of drawing 5 cards from a deck such that they give no possible low hand? You see I picked up AAKQJ double suited (in aces) playing the afore-mentioned game and wanted to evaluate its strength as a hi-lo hand!

Thanks for your attention,

Paul Samuel