Hand analysis

Byron Jacobs

The following scenario is a familiar one for almost any limit hold’em player, especially those who like to play short-handed. Play is folded round to the button who is well known to you as a tricky player as well being an aggressive blind stealer. He open raises and you are in the small blind with a very decent hand – Ah-Qs. You know all about blind play and make the obvious and correct play of three-betting in order to put maximum pressure on the big blind. You are hoping to get heads up with the button as you almost certainly have the better hand.

The plan succeeds admirably. The big blind does indeed fold and the button declines to confuse the issue with any further raising. There are seven small bets in the pot and you are very happy with the progress of the hand to date. The arrival of the flop slightly dampens your enthusiasm because – as usual – it misses you completely. It consists of three random cards below ten and, for the moment, we will not worry too much about what these cards actually are. “Never mind,” you think, “I still have my two big cards and the flop probably missed him too. I must keep up the pressure.” Indeed you must, so you bet and the button dampens your enthusiasm for the hand still further by raising. There are now ten small bets in the pot.

With pot odds of 10-1 you have an easy call. Even if you are certain that your opponent has a pair, the overcards give you six outs (probably) and this makes you about 7½-1 to improve on the next card. Even if you downgrade your outs (your opponent may have an A-x or K-x hand where ‘x’ makes a pair; there is also the possibility of redraws on the river) you should certainly count them as being worth around 4½-5 outs and you still have value for a call.

However you know full well that your opponent is tricky and he could easily not have any pair at all – you may even have the best hand right now. Considering this you call and there are now 11 small bets (5½ big bets) in the pot.

The turn is another random low card. There is now no reason to bet, so you check and the button bets, bringing the pot to 6½ big bets. Now you have to decide what to do and there are various factors to consider.

  1. If you are 100% sure that you are just playing overcards, then you do not have pot odds to call and should fold.
  2. If there is a reasonable chance that your opponent – who is known to be tricky – is pushing a draw or even completely bluffing then you may have value for a call.
  3. 3) If you call the turn and the river is a blank then you will have to call again if the button bets the river. It would not be logical to fold, unless the board becomes really gross (however – if there is a reasonable possibility of this happening then you should probably be inclined to fold on the turn in the first place). By deciding to call on the turn you are making a clear assumption that there is a small possibility that your opponent is bluffing/semi-bluffing as you do not have pot odds to call purely on the value of your overcard draw.

So, now your job is to weigh all of this evidence and decide what to do. Some players take a rather simplistic view of this situation, deciding one of the following:

  1. I may well be winning the hand and I have outs even if I don’t. I am not going to be pushed off what is possibly the best hand. I call.
  2. It will cost me two big bets to find out if he is bluffing. That is just too expensive and does not represent good value. I fold.

If you always call here you will be making a mistake and if you always fold you will also be making a mistake. If the game is very short-handed (4 players or less) then you certainly need to call some of the time to prevent other players taking a shot at you every time a similar situation arises. So, what to do?

Dan Harrington has a excellent section in his No Limit tournament book (Volume 2) which deals with a topic that he calls Structured Hand Analysis. This is a method of estimating the probabilities of various outcomes in a hand and thus deciding upon a – hopefully profitable – line of play. Of course, the technique he decribes deals specifically with No Limit tournament situations (usually when someone has made a bet that will put you all-in if you call) but the method can be adapted to limit play.

Before we deal with the calculations we must be aware that in a live tournament situation where all your chips are on the line, no-one is going to object if you think for a minute or two before reaching a decision. However, in a typical online game you will only have 15-20 seconds to decide what to do, so we must try to keep the calculations simple, whilst ensuring that they do not become oversimplified and thus rendered useless.

The following line of reasoning is quick and dirty. It is a long way from being mathematically exact but I have tried to make it sufficiently simple that – with a bit of practice – it can be done in the 15 or 20 seconds that you typically get in an online game to make your decision. Okay, here goes. Firstly, we are going to work out how often we need to win to get value for our bets (well, calls to be precise) and secondly how often we will win when we play out the hand.

How often do we need to win?

The pot contains 6½ big bets. If we go on to win the pot then sometimes we will one more bet and sometimes not. So, let’s say the average result is a gain of about 7 big bets. It will cost us two big bets to see the hand through – one to call now and one to call on the river. So, we are risking two big bets to try and win seven. Thus if we win two times from nine, we will be at the break even point. Let’s turn this into a percentage. Two from nine is going to be a bit more than 20% but let’s keep it at 20% because sometimes the river card will be scary (although unhelpful to us) and our opponent will check the winning hand. So, we need to win 20% of the time to break even.

How often will we win?

We have two ways to win:

  1. We are behind but we win with our overcard draw. Now we need to decide what our overcards are worth in terms of outs. Clearly this is a maximum of six and possibly none at all if our opponent happens to have stumbled into a big hand. Much of the time they will be worth six outs, so let’s say four as a reasonable compromise. Four outs with one card to come is in the region of 10-to-1 and is thus worth about 10%.
  2. We are ahead and our opponent does not draw out on us. What is the chance that we are currently in the lead? With a tricky opponent this should be at least 20% and could be more. However, they will have outs and a reasonable estimate would be to give them ten outs – the equivalent of a gutshot draw (remember they can also win by simply pairing). Ten outs gives them about a 25% chance to improve and overtake us (I know this isn’t exact, but we haven’t got time to fiddle around with pocket calculators). Thus we need to downgrade our 20% chance of wnning to around 15%.

Now we are nearly done. Add the 10% and 15% and we get 25%. We needed 20% for a calling down strategy to be correct and we have exceeded that. Thus we call. This may seem surprising. After all, we know full well that a mere couple of overcards should not be worth a great deal on the turn. However, the pot – at 6½ big bets – is already quite large. With less earlier action and a pot size of 4½ big bets the previous line of reasoning remains valid, but now we need to win two times in seven to break even. This works out at about 29% and – in that case – we should be more inclined to fold.

This may see frightening complex but it isn’t really and it gets easier with practice. It is also a more satisfying way of determining your play rather than simply trying to decide if your opponent is bluffing or not.

Provided by Card Player, The Poker Authority

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