Julian Gardner looks at how to work out value, make value plays and avoid getting trapped by the pot odds

 You can use the concept of pot odds to communicate misinformation and overbet the pot to make it look like you’re weak

Expected value is a commonly used term in poker – and rightly so, as it should form the basis of most of the decisions a poker player makes. Expected value simply refers to the long-term return from a given bet. For example, if I toss a coin and offer you 3/1 on heads, it’s a great value bet. A coin will show heads on average one out of every two times it’s flipped, meaning that the true odds are evens. If you bet £10 on the coin showing heads at 3/1 you will win 50%of the time, but each time you win, you’ll receive £30 and each time you lose, you’ll only lose your stake of £10. The expected value of this bet is therefore £20 even though you’ll never win £20 as it would either be -£10 or +£30. But in the long run you can expect an average profit of £20 per bet – definitely odds worth taking.

In poker terms, the same principles apply to all the bets you make. Let’s say that you are hold A;-x; with a flop that gives you four to the flush, so your odds of hitting the flush on the turn are about 4/1. If the pot stands at \$200 and you need to call a bet of \$40 to play, this is a great value bet – the pot is offering you odds of 5/1 for your 4/1 shot. Although you’ll only hit your flush one in every five times, the \$200 you win each time outweighs the \$160 you spent the other four times. On average, your expected value for this bet is \$40.

### POT ODDS, IMPLIED ODDS AND VALUE VERSUS SURVIVAL

Of course, because most pots you play in hold’em consist of a series of bets, it’s more complicated than that. In limit, say, you can play pretty much like a robot, because the betting patterns are fixed, so you can have a pretty good idea of what one call will cost. But no-limit is much more complex. You must be aware that while you have good pot odds to call a bet, whenever you are active in the pot, there’s always the chance that you could call a bet for value and go on to lose all your chips later in the hand to an all-in bet that has you beat. This may not be such a problem in a cash game, when you can simply buy more chips and wait for probability to reward you in the long term, but in a tournament it’s no good making a play that’s likely to give you a small edge over time if it’s going to knock you out of the tournament right now.

As well as the immediate value of a bet, you also need to factor implied odds into your value calls. Implied odds are basically pot odds that take future actions into account and are an essential concept in playing poker. A good example of a standard implied odds play is a player calling in late position with a middle pair, such as 8-8, after three limpers have entered the pot. With three players already in, the pair of 8s would need pot odds of around 15/2 to mathematically justify a call here, but because of the implied odds of hitting a set the call is definitely justifiable. The thinking here is that you’ll have a strong, well-disguised hand that will win you a bigger pot after the flop,

However, many players use implied odds to justify poker suicide by calling long-shot bets in the hope that if they hit a two-outer, they’ll bust the other player. Pre-flop this can manifest itself with players choosing to enter pots with bad hands purely because the pot was large. In a freezeout tournament you have to be aware of the possibility that making a good-value call can leave you making a decision for your tournament life.

### CHIPS FIRST, SUMS SECOND

Your stack size to a large extent governs how much you can afford to make value plays. In the early stages of a deep stack tournament, you’re effectively playing a cash game. I’ll play any pairs, suited connectors and premium hands if the pot odds are offering me good value to get involved, just as I would in a cash game. I’ll happily limp with small pairs and suited connectors when I have position or am drawing to hands where the pot odds justify it, and get out quickly when I know I’m beat. Early on, it’s cat-and-mouse poker, playing for small pots. Whenever I do have a monster, I’m looking to slow play or trap my opponents into giving me a substantial portion of their chips and help move into a dominant position on the table.

But when the blinds rise and the antes start to bite, your priorities change. If calling a raise with a suited connector will cost you a fifth of your stack, it’s very difficult to justify this as a good long-term value bet when it’s unlikely you’ll last long enough to get paid off in the one time in ten you flop the nuts. If you’re low on chips your options are limited to using aggression to try to win pots right away. Being first into unraised pots is the key here – your cards don’t really matter.

### DON’T PLAY LIKE A ROBOT

If you read my article last month, you probably won’t be surprised to learn decisions I make in a tournament aren’t based just on the maths, but also on who is at the table. Knowledge of the types of players you’re up against will heavily influence your decisions to make value plays and affect your calculations of implied odds. For example, if I’m on the button and have Gus Hansen on my left, I won’t be calling a raise for value with middle pairs because I know that there’s no way Gus will let me see the flop cheap. If my initial call is likely to be raised, then the amount I’m going to have to bet just to have a 15/2 shot might be a substantial portion of my stack, and often it just isn’t worth getting involved, despite good implied odds.

Also, pot odds should never be used to justify staying in a hand when you know you’re beat – this is a classic mistake which will seriously shorten your tournament life. For example, at the recent WPT at Foxwoods, in one hand I had A-K, raised pre-flop and two players called. On the flop of A-10-3, the first player bet, I raised and the third player re-raised. At this point the pot was large enough to justify a mandatory call of the re-raise (with top pair and top kicker), but only if you were to look at a purely mathematical proposition. However, experience kicks in here and tells you that any pot where you have people prepared to bet at – and re-raise – a pre-flop raiser means that it’s highly unlikely your top pair is good, so I folded here – wisely, it turned out. One of my opponents showed a set of 10s, so I would’ve been calling according to pot odds in the hope of hitting a two-outer with the next bet likely to put me to a decision for all of my chips.

Value can work to your favour too, though. The beauty of no-limit is your ability to bet the right amount to make the odds good enough for someone to make a mistake by calling. But you must always be aware that if your bet is called by multiple opponents, it might build the pot to a level where someone on a draw gets the odds to chase you. I like to milk pots and trap like this early on, but, as I’ve said before, when you get to the business end of the tournament and the blinds and antes are high you should concentrate on taking pots down early.

One final point to be aware of is that if you’re generally making value bets and just pricing people out of pots by a small margin, an overbet into a pot can look like weakness. This can be used to your advantage; in one pro-celebrity tournament I was playing against a big-name sportsman who I had identified as an average, straight player. He’d been limping into a lot of pots and playing poker by the numbers. In one hand I picked up K-K and saw this sportsman make a small raise pre-flop. Knowing his style of play, I judged he had a hand he liked, but one that was not absolutely premium. Instead of making a small reraise or just calling, I overbet the pot, pushing in five times his raise to put him all-in. I knew he’d read this overbet as a sign of weakness and call me, which he did.

My K-K unfortunately lost as his Ace-10 made a flush, but the tactics I employed were right for this situation. If you know your opponents, you can use the concept of pot odds to communicate misinformation and, as in this case, overbet the pot to make it look like you’re weak when in fact you believe yourself to be way ahead.