You’re playing a single table tournament. You start the game with 1500 chips, and the blinds are 10 and 20 chips. There are ten players at the table. Clearly, you have time on your side, and there’s no need to play questionable hands – you can wait until you get cards that you want to play, and play them however you want to.

Fast-forward an hour. Now the blinds are at 100 and 200. There are five players left, and you’ve still got 1500 chips. So every five hands, you are going to lose 300 chips to the blinds. Every two and a half rounds, you are going to have lost 750 chips on average, and you’ll have to double through just to stay where you are. Now, time is against you. You can’t wait until you get a great hand, or you’re liable to get blinded out of the game. You have to make moves, whether you’ve got the cards to back you up or not. It’s a dogfight, and you have no alternative but to play a lot of hands that you wouldn’t normally touch.
In both cases, you’ve got the same number of chips, but somehow the chips that you’ve got have become less valuable as the game has progressed. The increasing blinds and falling number of players in a tournament mean that as the game continues, everybody has to play more aggressively, even recklessly, to stay alive.

M and Q

Paul Magriel is generally accepted to have created the M-value. M is the ratio of your stack to the total of the current blinds (and antes, if you’re playing them).

In the first example, the blinds add up to 30. You’ve got 1500 chips, so your M-value is 1500/30 = 50. Which is a lot – you’ve got plenty of time to play the game however you want to.

In the second example, the blinds add up to 300. You’ve got 1500 chips, so your M-value is 1500/300 = 5. This is very low indeed, and you have little choice but to act very aggressively, very soon.
M tells you how many more rounds you can play before the blinds wipe you out. It tells you how aggressive you have to be – but just as importantly, it tells you how aggressive other people have to be. There’s no point in trying to bluff a player out of some chips if they’ve got a low M-value – they simply can’t afford to lose the chips, and will call, even if they think they may be behind.

There’s a second number, invented by Dan Harrington, called the Q-value. This is the ratio of your chips to the average stack. At the start of the game, you’ve got exactly the same as everyone else, so your stack equals the average stack. As the game continues, this can change.

Consider again the second example. You have 1500 chips, but the table contains 15000 chips in total (1500 x 10 original players), divided amongst the five remaining players – an average of 3000 each. So you’ve got 1500/3000 = 50% of the average stack. So the other players aren’t in the same amount of trouble that you’re in. They have slightly longer to act, and can be more selective in the hands that they play. You can monitor this number throughout the tournament, and it’s particularly important in large tournaments – the blinds will probably stay relatively small compared to your stack for a long time. This means that you have time to act, but if you’ve got a low Q value, then you are losing ground, and you should probably step up the pace a bit (but don’t panic – you still have time to wait for the cards, if you have a healthy M-value). Note that every time half the players drop out of the tournament, the average stack doubles. So you should be looking to accumulate chips at that sort of rate, at the minimum.

Here’s one more example.

A tournament starts with 1,000 players, each holding 10,000 chips. After an hour has played, you have 12,000 chips, and there are 850 players left. The blinds are at 30 and 60. How are you doing?

The average stack is 10,000,000 chips divided by 850 players, which is 11,764. You have 12,000, so your Q-value is 1.02. So you’re very slightly ahead of the average stack. Your M-value is 12,000/90 = 133 – you’ve got plenty of time to play. Overall, you’re doing quite well, and you’ve got no pressure on you to play any differently.

Another hour passes, and now you’ve got 14,000, and the number of players is down to 530. The blinds are at 100 and 200. How are things going now?

There are still 10,000,000 chips, now divided between 530 players, an average of 18,868 each. You’ve got 14,000 chips, which means your Q-value is 0.74. Despite gaining chips, you’re falling behind. The M-value is now 14,000 divided by 300 = 47. You still have time on your side, but the clock is ticking, and you need to try to pick your game up a bit.

Another hour goes by, and now there are 90 players left. You have 27,000 chips, and the blinds are 750 and 1500. Is it time to hit the panic button?

The average stack = 10,000,000/90 = 111,111. You have 27,000, so your Q-value is 0.24. You’re a long way behind, and would need to double through twice just to get close to the average stack, never mind the leaders. The M-value is 27,000/2,250 = 12. Time’s short, and you need to really accelerate your play if you’re going to stay in the tournament.

The next hand you catch a lucky break, and triple through. Now you’ve got 81,000 chips, and everything else remains the same. Your Q-value is 0.72, and your M-vale is 36. You’re still behind, but the blinds aren’t threatening to eat you anymore, so you have some time to choose your hands and try to catch up.

You make it to the final table. There are ten players, and you have 1,300,000 chips. The blinds are 30,000 and 60,000. How aggressive do you need to be?

Your M-value is 14, and your Q-value is 1.3. You’re in good shape, but it’s time to be careful. There will be short-stacks, with low M’s and Q’s, who will be playing almost any picture card. Be careful that you only play against them when you have the better hand, but take every opportunity to take chips off these weaker players.

By understanding your M and Q through the game, you can change your play accordingly. By understanding other players’ M and Q values, you can anticipate their actions.

It’s important to make a couple of points here. Once your M-value falls below about 5, then the maximum raise that you can put in is less than five times the big blind. And betting any less than that will leave you pot-committed (i.e. you are better playing the hand even if the odds are against you, rather than folding, and leaving yourself with too few chips to make any meaningful moves).

Also, not acting when your M is still reasonable can cause you problems. If you bet half your stack with an M of 10, and win, then your M will go up to 15 (or more), buying you another five complete rounds of blinds. Going all-in with an M of 4 will risk your entire tournament, and only buy you 4 (or more) rounds of the blinds. Don’t let your M fall to dangerous levels, waiting for the perfect hand. It’s not a flag that reads ‘OK’ or ‘In Trouble’ – it’s a sliding scale of how aggressive you need to be.

Another thought is what happens to the importance of position, as games progress. Being last to act gives you information about your opponent’s hand. Have they shown strength, or weakness? Does their pre- and post-Flop play make sense, or are they bluffing? But once players have a low M-value, their bets tell you less and less about their hands. Players will play more aggressively with weaker hands, so you learn less about them from their activity. Also, if people are going all-in pre-Flop, then the betting is over before position even comes into play.

Playing At Different Levels

So, the Q-value tells you how you’re doing, and the M-value tells you how aggressively you need to play. Q is easy to understand – much more than 1, and you’re doing well – about 1, and you’re doing OK – much less than 1 and you’re in trouble.

M is more difficult – I’ve described it as a sliding scale, but for simplicity, I like the way that Dan Harrington advocates analysing your M-value.

He considers an M of more than 20 to be the ‘Green Zone’. You can play however you want, basically. Your strategy shouldn’t be influenced by the size of the blinds, which represent less than 5% of your stack.

Once your M drops below 20, then you drop into the ‘Yellow Zone’. He puts the lower limit of this at 10, and once you drop into this zone, you have to start playing more aggressively. With an M of 15, at a 6-handed table, you will lose half of your chips in 45 hands, so you need to increase your stack-size on a regular basis with other people’s chips. You can’t really afford to limp in with marginal, calling hands like suited connectors, or low pairs, as you will find that you can’t afford to pay the blinds on the frequent occasions when you miss the flop, while you wait for the less frequent occasions when you hit. Also, if other people’s M-values are falling similarly, they are more likely to raise, pushing you off your limping hand. Play lesser hands than you normally would (if you are typically conservative), but play them aggressively, to win the majority of the pots that you play.

From an M-value of 6 to 10, you are in the ‘Orange Zone’. If you want to put in a strong raise of five times the big blind, it’ll cost you about 1/3 to 2/3 of your chips – you’re either close to, or completely,
pot-committed. Now you need to win the hands when you raise – the EV of long-shots becomes far less important.

For example, if you think you have a 30% chance of winning a pot, but the pot-odds are paying 5/1, then normally you’ll make the play. But in the Orange Zone, you need to be more careful – if you lose 1/3 of your chips each time, you could easily go out chasing long-shots.

You also need to remember that you aren’t threatening your opponents as much with implicit pot-odds. If you are committing most or all of your chips to the pot, then the pot-odds could justify them calling with drawing hands, as they know they’ll get to see all the remaining cards for little or no additional cost.

With an M-value of 5 or less, you’re in the ‘Red Zone’, and in deep trouble. You can’t survive in the Red Zone for very long – get out, or you’ll be out of the tournament soon. Every bet needs to be all-in, as nothing less has a hope of chasing people away (even this isn’t usually enough once you’re M drops below about 3).

All-In Bets

Poker is all about The Fundamental Theorem – making the mathematically correct play, or forcing mistakes from your opponent.

The decision to call an all-in bet is only interested in the first of these, particularly in a cash-game. There’s no further play to be made by your opponent, so it comes down to doing the right thing according to the numbers. Logically, if you have a positive EV, you should call. If you have a negative EV, you should fold.

It could be argued that if you are a good player, and have a nice, high M-value, then the mathematically correct play is to fold, even if your EV is slightly positive, since you could cripple your chances of winning the tournament if you lose, and the impact on your chances of winning the tournament won’t necessarily increase enough to justify the risk if you win.

Here’s an example. You’re playing a single-table tournament, with nine other players. You’re pretty good, and reckon that there’s about a 25% chance of you winning, another 25% chance of you coming second, and another 25% chance of you coming third, with you finishing outside the top three the remaining 25% of the time. You paid £10 + £1 to enter, and the prizes are £50, £30 and £20. So your EV from the tournament is (25% * (£50-£11)) + (25% * (£30 - £11)) + (25% * (£20 - £11)) + (25% * -£11) = +£14. Nice!!

Suppose early in the tournament, somebody goes all in, and if you call and lose, you’ll be virtually out of chips. If you call and win, you’ll have almost double the average stack. You estimate that your chances of finishing first, second and third if you lose this hand drop to 1%, 3% and 6%. If you win, your chances improve to 35%, 30%, 20%, with a 15% chance of you still finishing outside the top three. Your EV if you win will increase to (35% * (£50-£11)) + (30% * (£30 - £11)) + (20% * (£20 - £11)) + (15% * -£11) = £19.50. Your EV if you lose will decrease to -£8.40 (Yuk).

Assuming that the size of the bets involved here would make all other action almost irrelevant – so the pot-odds are more-or-less 1:1. If you have a 60% chance of winning, should you call? In a cash game, of course, you would – you have a positive EV for the hand. But in this tournament, whilst the EV in terms of your stack of chips may be positive, the EV for your prize in the tournament isn’t. Instead of winning £14 on average, you’ll win £19.50 half the time, and lose £8.40 half the time. So your EV would drop from £14 to (60% * £19.50) + (40% * -£8.40) = £8.34. Calling this bet, even though you are favourite, would cost you £5.66 of your winnings, on average.

In fact, you’d need over 80% chance of winning to call this bet. Basically, you’d need the nuts.

If you are a weaker player, with a negative EV, then the opposite is often true. Your best chance of making money in the tournament is to win an all-in gamble, as you don’t have the skills to grind out a result.
All-in bets turn the game into a crap-shoot – removing the betting from later rounds removes the advantage that a better player has over a worse player. Particularly early on it tournaments, you should be more inclined to make or call all-in bets if you are weaker, and less inclined if you are a stronger player.

Using the all-in bet, particularly before the flop, can negate the advantage of better players, and really annoy them as well! It’s no coincidence that the all-in bet forms the basis of David Sklansky’s ‘System’.

The story is that he was asked to teach a 21 year old rich girl how to play poker. She was entering the final event in the World Series of Poker. In a week. And she didn’t know how to play poker.
Seriously, you couldn’t make this up!

He realised that this was impossible, so he taught her how to play a very basic system that he had devised. There were two stages.

1. If somebody raises in front of you, go all in with Aces, Kings, or Ace-King suited.
2. If nobody raises in front of you, go all in with any pair, any suited Ace, any Ace-King, or any suited connectors, down to and including Five-Four.

Finally, he told her not to use the system in the first few rounds, as there wasn’t enough money in the pot to make it worthwhile – she should just move all-in with Aces here.

Imagine you’re her opposition. What would you risk your entire tournament (with a $10,000 dollar buy-in) with? Jacks? Queens?

So what happened? She stole a lot of blinds and quite a few early raises. Eventually, she ran into big hands, like Ace-King, Aces or Kings, but she’d stolen enough that she survived these hands (and of course, even here she had a chance).

She lasted until near the end of the first day, when she ran into a bigger stack with Aces, and lost. But the previous day, her father, who had been sceptical about the system, decided to test it in a $2,000 tournament. He placed 5th, and only got knocked out when he deviated from the system.

This strategy works, because players who were confident that they had better hands, were willing to wait for a better opportunity to come along than to risk their tournament on the turn of a card.

So, should you call an all-in raise?

In a cash game, decide based on the EV. In a tournament, it depends on what it does to your tournament EV. If you’re in the Red Zone, and this will push you into the Orange Zone, then the effect of winning the hand could be very positive, and the effect of losing negligible (since you weren’t going to win anyway). If you are in good shape, and it represents most or all of your chips, then why take the risk? If you’re a good player, wait for a better chance. Finally, if it represents a small percentage of your chips, make the mathematically sound play. If winning or losing makes little difference to your chances, treat it like any other bet.

When deciding whether to make an all-in bet, the logic is very similar. The only thing to add is that making a raise other than all-in is irrational, if it leaves you an unworkable stack. If a raise will leave you pot-committed, then you may as well go all-in, and reduce your opponent’s pot-odds (unless you want him to call, in which case the opposite is true).

The Bubble

The Bubble is the point at which there are a few more players remaining in the tournament than there are prizes. A few more people get knocked out, and the remaining players are all guaranteed a prize. How important the Bubble is depends on the situation. How big the smallest prize is, and how much time and effort the players have invested in the tournament will influence how people play.

Many players, at this point in the game, become very interested in survival, rather than accumulating chips. This being the case, it’s a great opportunity to start playing very aggressively, stealing blinds, and, if you’ve got a good stack, bullying the players with the smallest stacks – these players in particular will be trying to stay alive, and won’t want to make all-in bets against somebody with a big stack of chips.

Of course, the larger your stack is, the less important the Bubble is, as the chances of you being knocked out before the prizes are dished out diminish. So there will be players that you don’t want to attack, unless the situation made it appropriate otherwise.

If you’ve got a short stack, then playing weakly – folding good hands – is definitely not a good strategy. Whilst you may reduce your chances of missing out on the prizes by folding, if other players are doing the same, you may not help yourself very much, whereas playing hands where you believe you have a positive, or even slightly negative, EV will give you a chance of regaining a decent foothold in the tournament.

As a general rule, if other players are all playing to a similar strategy, the opposite strategy (if played correctly) is generally the most profitable. If everyone else is playing wild, aggressive poker, play only strong hands, and let others make the running, and you’ll get paid off for your good hands, without risking your chips. If, on the other hand, everyone else starts playing passively, as they may do on the Bubble, then there is a great opportunity to steal blinds and bully other players.

Going Heads-Up

There are two players left in the game, you and the other guy. The game has just fundamentally changed, and any hand that was previously decent just became a monster. Even if you’ve got a weak hand, your opponent may be weaker, or certainly not strong enough to respond to aggression.

This is a time for men (or women) to prove that they’ve got what it takes to run with the big dogs, or something like that!

Ultimately, the winner is generally determined by the cards. If you hit a big hand, and your opponent hasn’t, he’ll fold. If he has a big hand and you don’t, you fold. If both of you hit big hands, the chips all end up in the middle, and somebody wins.

Here are a few thoughts about different hands that you can get pre-Flop.

• Only 6% of hands dealt pre-Flop are pairs. Put another way, only one time in eight will either of you have a pocket pair – only one time in sixteen will your opponent. So generally, it’s going to be a battle of unpaired cards.
• This being the case, the bigger your cards are, the better. Ace with anything is favourite against any unpaired hand without an Ace. Suited cards only improve your chances of winning by about 2%, so focus on the numbers – the bigger, the better.
• If you’ve got a pocket pair, the chances that your opponent has a bigger one are small. You are at least even money against any other hand, even if you’ve got a pair of Twos against Ace-King. If you’ve got a bigger pair, then one of your opponents cards may be below your pair, and the chances of them winning are relatively slim.
• If both of you have unpaired cards, then the odds are quite close, unless one of you is dominated. Even if you’ve got Ace-King against Three-Two, you’re still only going to win about 2/3 of the time.
• The pot odds will make playing most hands compulsory. There are very few starting hands that you should fold in the small blind.
• Position matters. So if you’re on the Big Blind, be aggressive pre-Flop, and try to take the hand down quickly (before your opponent’s position helps him too much).
• If you’re in the small blind, then unless your opponent has been very aggressive, don’t throw any hands away. If your opponent has been aggressive, then throw away the weak stuff – you’ll be forced off it when he raises, and you can make more money with your good hands.
• Raises don’t need to be as large, particularly pre-Flop. If you have a strong hand, and your opponent does too, the chips will probably end up in the middle anyway. If you have a reasonable hand, then all you need to do with a raise – in fact, all you can do with a raise – is to indicate strength. A raise of 2 – 3 times the big blind is plenty to do this.

There is a large element of luck in heads-up play, particularly when both players are good. If you run into a weak player, then bully them mercilessly – raise their big blind every time, and watch them fold. If they try to limp in from the small blind, then attack them.

Unless you are sure you are playing somebody weak, don’t get carried away with the situation. If your opponent indicates strength, and you’ve got nothing, then accept what he says. Just remember that the more he indicates strength, the weaker your hand needs to be to fight back.