Before we go any further, you need to understand the Expected Value (or EV) of a bet. This is the expected profit that you will make from your bet. Here’s a simple example.

You roll a dice. It costs you £10 if you roll 1 - 5, and if you roll a 6, you win £50.

In this case, there is a 1/6 chance of winning £50, and a 5/6 chance of losing £10. Your expected winnings are (1/6 x £50) + (5/6 x -£10) = £0.

So in the long run, you’ll break even playing this game.

In the above example, if you won £100 for rolling a 6, you’d probably be very happy to play, as you get a positive EV. In poker, you want to create a positive EV when you bet (so that you’ll win money on average) and a negative EV for your opponent if they bet (so that they lose money on average if they bet, and you win the pot if they fold – either way, you win).

This is actually a good indicator of whether you should be betting – will you be unhappy if you are called? Unless you’re bluffing, you should be trying to create win-win situations like the one above.

Here’s an example. You’re playing heads up (there are two of you left) and you’ve got

The pot’s got £100 in it, and your opponent’s got

The board’s showing the following cards:

You know that any Ace, King, Queen or Club on the River will give your opponent the hand. Since there are 3 Aces, 3 Kings, 2 Queens and 8 Clubs still in the deck, out of a total of 44 cards, what is the correct amount to bet here?

Your opponent will win 16/44 times, and will lose 28/44 times. So let’s do the sums. If you bet £50, then your opponent has to pay £50 to see the river. 16/44 times, he will win £150 (and keep his £50 bet), and 28/44 times, he will lose his £50 bet. Overall the EV is (16/44 * £150) – (28/44 * -£50) = +£23. Clearly, he should call this bet.

But if you were to bet £140, the EV would be quite different. Now, the EV is (16/44 * £240) – (28/44 * -£140) = -£2, so he should fold to this bet.

Looking at the situation from your perspective, if he calls the £140 bet, you will have an EV of (28/44 * £240) – (16/44 * -£140) = £102. If he folds, you just win the £100 in the pot. So from your perspective, you’ll win at least the value of the pot whichever decision he makes, which is nice.

You should also use this calculation when deciding whether to call somebody else’s bet.

Of course, this very simple example assumes that you know your opponent’s cards, that there is only one person playing against you, and that there is only one round of betting to go. In reality, the decisions aren’t as simple as this, as there are many factors to take account of, rather than just looking at your cards...

Implied Pot Odds

You understand pot odds, but in most betting situations, this is a misleading number. It assumes that you will see all the remaining cards if you bet. But if you bet on the flop, then you may have to bet again on the turn – and if you don’t get the pot odds the second time, then you’ll fold having seen only one of the two cards that could have made your hand.

Confused?

Remember our earlier example, and put yourself in your opponent’s shoes...

You’re playing heads up (there are two of you left) and you’ve got

The pot’s got £100 in it, and your opponent’s got

The board’s showing the following cards:

Your opponent bets £150, so your EV is (16/44 * £250) – (28/44 * £150) = -£4.55. So you should fold, right?

But what happens if you hit your card on the river? You’ll make another bet, which your opponent may or may not call. If you miss, then you’ll fold, so it won’t cost you any more. In our calculation, we never considered the possibility that you may win more money than the current bet. So what does this mean?

Well, depending on what card you get on the river, your opponent will be more or less likely to call a bet. For example, if a King or an Ace appears, he’ll probably know he’s beaten when you bet, and will fold. If a club comes up, he’ll feel reasonably confident, since the only way you could win would be with two clubs, and since you’ve been calling his bets to this point, they’d need to be big. He knows where the Queen and Jack are, so the only hands you’d be likely to win with are Ace-King clubs, or possibly Ace-Ten (and even that’s a bit shaky). What about a Queen? It depends on the player. Some would be so happy at completing their set (three of a kind) that they’d call almost any bet, and would even consider making one of their own (bad poker players, in other words). Others would notice that Ace-King would beat them, and be a little more cautious. Finally, the crown jewels here would be the Nine of Clubs – that would complete his straight and your flush – at which point, he’d call almost any bet.

So, how to use this information? Suppose you decide to bet another £150 on the river if you hit. Since the pot would be standing at £400 before you bet, you’d be offering him pot-odds of 3.67/1 to call – almost irresistible, even if you think you may have lost the hand. You need to assign a probability of him calling to each possible outcome.

The Aces and Kings are unlikely to get you a call – say 10% (he may think it’s a bluff).

The Queens are more likely to get you a call. The odds depend on your opposition – in this case, I’ll say 50%.

The other clubs except the Nine are also reasonable chances – I’ll say 50% again.

The Nine of clubs will almost certainly get you a call – 100%. Plus a possible additional bet from him – we’ll say another £150.

So you’ll stand to win...

10% * £150 6 times out of 16 (winning hands)

50% * £150 2 times out of 16 (for the Queens)

50% * £150 7 times out of 16 (the 2, 4, 5, 6, 7, 8 and 10 of Clubs)

100% * £150 + another £150 (for the 9 of Clubs).

Total = £5.63 + £9.38 + £32.81 + £18.75 = £66.56

Looking back at the original sum, now the pot is paying £250 + £66.56 when you win, so the EV is:

EV = (16/44 * £317) – (28/44 * £150) = +£19.81

So you call, and bet if you hit your card (and fold or check if you don’t).

Bad Beats

A Bad Beat is what people call it when they are ahead when they bet, but go on to lose the hand. For example, their opponent has only a few winning cards to draw on the River, but they hit one. They’ve made the correct decisions, read their opponents correctly, and lost due to luck.

It can be very frustrating, and can lead players to start playing emotionally (which is never a good idea!). But the way I look at it is this. You can only get a Bad Beat if you’ve played a hand better than your opponent. The better you are at poker, the more likely you are to get Bad Beats, and the less likely your opponent is (since you’ll be ahead more often than you’ll be behind).

A good poker player doesn’t mind Bad Beats, but if you find that you keep getting knocked out by them, it’s probably a reflection of a poor tournament strategy.

You will lose hands in a tournament, and every time you push all or most of your chips in, you’re risking your whole tournament on the turn of a card. This is very dangerous, and the best poker players don’t do it unless they have no choice. A better poker player will almost always beat a worse poker player if he keeps the pots small, and wins through attrition. It’s very tempting to push a lot of chips in if you’re in good shape, but it’s risky, even if you know your opponent will call in a bad position.

Consider this statistic. In the World Series Of Poker, the leader at the end of the first day has never won the main event. This is because they can only be in the lead by playing a lot of big pots. It’s risky, and sooner or later, it catches up with everyone. The eventual winner may only be slightly ahead, but he won’t have risked his tournament chances – you can’t win the WSOP on the first day, but you can lose it!

Expected Value And The Blinds

One interesting aspect of the EV is that in the long run, you’ll lose money on the blinds. If you are playing against opponents of roughly similar ability, then your EV on each hand will be about £0. But with the blinds, you are forced to make a bet, even with Two – Seven Off-suit (the worst hand in Texas Hold ‘Em). This outweighs any benefit of being in the Blinds (such as being able to disguise a strong hand as a bluff or an attempt to protect your blind).

You’ll see players making outrageous bluffs in the blinds to protect them (Dave Ulliott aka Devilfish is very aggressive, both in attacking and defending the blinds). But you have to bear in mind that with televised tournaments, you’re only seeing the highlights – you don’t see the hands being folded. This can give a skewed view on how to play poker, and I would strongly advise against anyone trying to learn strategy from the experts by watching them on television.

Also, bear in mind that what works against professionals may not work on a $5 table. On small-stakes online tournaments, bluffs are rarely respected, pot-odds are rarely calculated, and a large percentage of the players are relying on luck to get them through (even if they don’t know it).

Assessing The Situation

It’s your turn to act, and it’s time to make a decision. What are you going to do? To make a decision, there are a number of questions that you have to answer. Some will push you in favour of betting, others in favour of folding. If you want to have any chance of making money from poker, just looking at the cards in front of you isn’t enough. You also need to consider the following:

1. What are the pot odds?
2. How many players are there at the table?
3. Who are you playing against?
4. How big is your chip stack, compared to the blinds and antes?
5. How big are the stacks of the other active players in the hand?
6. What bets have already been made?
7. How many players are left to act?
8. What’s the situation in the tournament?
9. What will your position be after the flop (if you are pre-flop)

Look at each of these in turn:

What Are The Pot Odds? Poker is all about the odds. If you have a 1/3 chance of winning a hand, and the pot is 4 times your required bet, then you’ll make money on average (have a positive EV). So what are the pot odds in this situation? Note that the Implied Pot Odds may come into play, but we’ll look into that later. Suffice to say, if the pot odds are longer than the odds against you winning, it’s a vote for playing the hand.

How Many Players Are There At The Table? The more players there are at the table, the less aggressive you should be in general. This is because the more players there are, the more likely they are to have a better hand to you. As a result, you should be looking to play fewer hands when your table is full than a few players have disappeared. And once you get down to two or three, it’s absolutely essential to be aggressive.

Who Are You Playing Against? Are they playing very aggressively (raising or reraising a lot of pots) or are they quite passive, flat-calling a lot? Do they play a lot of pots, or very few? If you raise, you need to know the likelihood of the players still to act staying in the hand, or even re-raising you. If you flat-call, again you need to know if the players left in the hand are likely to raise.

How Big Is Your Chip Stack Compared To The Blinds? If a large percentage of your chips are getting eaten by the blinds, then you can’t wait for the perfect hand to come along. By the time it does, it may be too late to help you.

How Big Are The Other Active Stacks In The Hand? Is somebody else in the hand, or yet to play, starting to run out of chips? If so, they may well play hands that they wouldn’t normally touch. On the other hand, if somebody has a monster stack that could eat yours for breakfast, they could wipe you out on a single hand.

What Bets Have Already Been Made? No hand other than pocket Aces is definitely ahead pre-flop. If there have already been a couple of bets before you, then you need to have a monster hand if you want to stay in the pot. Even then, you should certainly adjust your play accordingly.

How Many Players Are Left To Act? If you’re on the button, and the table has folded around to you, then a raise only needs to get past two players to pick up the blinds. If you’re first to act, with eight players after you, then there’s a good chance that your raise will be called, or reraised, by somebody with a better hand.

What’s The Tournament Situation? If you’re in the late stages of a tournament, looking at a money finish, then you may just want to hold on to your chips, and watch a few players fall out of the tournament. On the other hand, this often happens late on it tournaments, and if everyone else is being more passive than usual, be aggressive, and you may pick up a few easy pots. Watch how other people are responding to the situation – in general, doing the opposite is the best strategy.

What’s Your Position, Post-Flop? Most beginner poker players don’t consider this, but it’s an absolutely critical question. After the flop, will you be the first to act, or will you get to see what the other players in the hand do before you have to make a decision? Being first to act will generally put you at a disadvantage, as you have no idea whether the other player(s) have improved their hands on the flop. If you have a strong hand and raise, they can get out of the way. If you have a weak hand and check, they can force you off the hand. On the other hand, if you’re last to act, you can respond to their bet. If they bet, and you have probably got a better hand than them, you can call or re-raise them. If they check, and you missed your hand, you can either bluff, or take a free card. Note that there are times when you can cash in on an early position. For example, if you check a strong hand, somebody with a weaker hand may bet – either a bluff or a semi-bluff – and you can either call or reraised them (this is called a check-raise). But if they are playing the percentages, this won’t generally work, as they’ll check to get a free card. Had you raised initially, they’d probably have folded, and you’d have won the pot – they certainly wouldn’t be able to pick up a free card.

You can look at all of these things before you even look at your cards. Here are a few examples...

Example 1. It’s The Early Stages Of A Big Tournament, With Hundreds Of Players. Here’s The Table.

The action so far: C has been aggressive so far, winning a couple of pots with re-raises. G has yet to play a single pot.

The hand: A and B fold, C raises to 50, D, E and F fold, G re-raises to 120.

Before we look at your cards, let’s look at the situation.

1. What are the Pot Odds? It’ll cost you 120 to see the flop, and the pot is offering 200 (or 1.67:1), which are good pot odds, but not great. Play only if you have a big hand
2. It’s a full table. Be cautious. Fold.
3. Who are you playing against? Too early to tell much, but the re-raiser hasn’t played a hand so far, so he may well have something. Fold.
4. You have plenty of chips. Time is on your side – be cautious, and Fold unless your cards are strong.
5. Nobody had a particularly large or small stack. No help there.
6. There’s already been a bet and a re-raise. Fold
7. Two players left to act – potentially a five-way pot. Fold.
8. The tournament’s just started. You don’t need to play marginal hands. Fold.
9. You are last to act. This would normally be good, but with C playing in a very aggressive manner, he may well bet the flop even if he misses. So the advantage of position may be very limited here.

It’s looking grim, and you haven’t even seen your cards yet! I would fold anything except AA and KK here – the least you’re likely to be playing against is an Ace-King, or a good suited pair.

You look at your cards – they are

It’s not a good enough hand to call a raise and a reraise. Even if you hit the Ace, you may well be behind, so it’s an easy hand to fold.

Example 2. Late on in the same tournament. You are at the final table, but your chips are running out...

The action so far: Things have been going pretty well, but a couple of bad-beats have left you short on chips. Given the size of the blinds, you’re going out soon unless you can pick up some chips! G has been erratic, playing some hands well, but throwing chips away on others. Most players have become cautious, trying to climb the prize ladder.
The hand: A, B, C, D, E and F all folded. G raised to 25,000. H and the small blind folded.

1. The pot odds. You’ve already put 10,000 into the pot (as the Big Blind), so it’ll cost you 15,000 to see a flop, with 40,000 already in it. That’s pot odds of 2.67:1. Play
2. It’s a full table, but all but one have folded. Play
3. G hasn’t been consistent, and you shouldn’t read too much into his raise.
4. You are short-stacked. If you don’t act soon, your stack will be so small that even doubling through won’t help. You really can’t afford to lose your big blind here. Play.
5. G is running out of chips as well, and may be trying to steal the blinds using his late position. Play
6. Only one bet, from an erratic player. Play
7. Nobody left to act. It’s one against one if you bet. Play
8. It’s late in the tournament, and things have become very passive. Be aggressive. Play
9. You have position on G. Play

I’d consider playing a wide variety of cards here. Even if I miss the flop, I may be able to take G off the hand by outplaying him on the flop.

Your cards are:

and you play. The flop comes down:

G checks, you bet and G folds. You win the hand.

You Have 30 Seconds To Act

You’ve seen some quite complex mathematics here. If you’re concerned that you can’t do the sums that fast, don’t worry – very few people can (although I hear tell that Chris Ferguson is one who always knows the odds when he’s playing).

In reality, experience will give you a good feel for the EV. In the above example, just over 1/3 of the cards will complete my hand, and I know that if I do, there’s about a 50% chance of a call on the river. So 1/3 of the time, I’ll win (£250 + ½ of £150), or £108.The other 2/3 of the time, I’ll lose £150 (so £100 on average). So there’s a small positive EV. I’d play it if it represented a small percentage of my stack, or I was low on chips, but otherwise, I’d probably fold and wait for a better opportunity.

You’ll learn to do quick calculations like this, and whilst the exact answer may not always be right, you should be close. What really isn’t optional is knowing how many Outs (winning cards) you have if you are drawing to a hand, or you opponent has if you are ahead.

Not Playing The Odds

The Fundamental Theorem of Poker states that you will gain if you play your cards the way that you would have done if you could see your opponents’ cards, or if they play differently to the way they would if they could see your cards.

You may interpret the first part to mean that you should never deviate from the most mathematically-sound way of playing. But you can’t read one part of the theorem without the other. There are times when you should play a hand differently, in order to induce an incorrect decision from your opponent. An example of this is bluffing. If you have a poor hand, you should logically throw it away. Playing it will lose you money, if your opponent knows that your hand is weak. But if you can convince them that you have a strong hand, then they will misplay their hand – by folding a hand stronger than yours – and you can win money (by using the second part of the theorem).

There are a number of times and situations when you should vary your play – here are the main ones.