I've decided to record my progress in graph form so that it is easy to track, the page can be found here. Things continue to go well in my second attempt at the $20 + $2 level and after blowing my bankroll I'm actually back in the green overall. Clicking on the graphs will take you to a full sized image.

## Friday, October 8, 2010

## Tuesday, October 5, 2010

### The Two Most Important Concepts in Texas Holdem Tournament Play

Everyone is looking for a silver bullet when it comes to playing poker, this isn't it. This is an explanation of the two most important concepts in no limit holdem tournament play.

It's no secret that aggression is one of the keys to success, but why? The answer is fold equity. When you raise there is a chance that you will take down the pot right there, that chance is your fold equity - fold equity in tournament play reaches a premium as you close in on the bubble. Some players will only play the top 5% of hands at this stage which gives you 95% fold equity. So why not just raise every hand? The reason you shouldn't raise every hand (unless you have a massive stack) is that your opponent's fold equity reduces every time you raise because your table image changes.

This is a very simple concept to grasp and apply - simply work out the fold equity you have against the opponents left in the hand, take the lowest value and adjust it for position by removing 5% per player to act behind you. Once you have this value worked out - let's call it X - you can then profitably raise with the top X percent of hands. If you don't win the hand right there you will get a chance to make a continuation bet on the flop which takes advantage of the extra fold equity you gained by raising preflop. Heck, there's even a chance that you might have the best hand.

This concept is slightly less intuitive than the last, but it is far more powerful - I can credit the dramatic change in my results to an understanding of this concept. In a cash game the value of your chips is always known and the value of a single chip is fixed. However, in a tournament chips do not come with a particular value; the expected equity of your chips can be determined by working out the probabilities that you will finish in a particular place, then multiplying these probabilities by the prize money for that place and adding these values together. For example, if there are 5 evenly skilled players left and each player has 1000 chips there is a 20% chance you will come 1st, a 20% chance you will come second and so on. Your current expected equity if the payout structure is $90/$54/$36 (.5/.3/.2) would be (.2 x 90)+(.2 x 54)+(.2 x 36) =

Let me explain this concept further with another example:

9 man $20+$2 SnG

All players start with 1500 chips

All players are evenly skilled

The payout structure is 90/54/36

Your expected equity starts at

Suppose you win the first pot and now have 1600 chips. Your expected equity is now

You can clearly see that the expected value of your chips is not linear. The second 100 chips was worth 18 cents less than the first 100 chips. Each chip you earn will increase that expected equity by less than the last chip you earnt, in other words every chip you earn is worth less than the last. The flipside of this is that every chip you lose is worth more than the last.

Now, let's assume the game has progressed to the following situation:

4 players left

You have 1500 chips

All players have 3000 chips

Your expected equity is

Notice that even though you have the same sized chip stack as before, your expected equity has increased by over

One final consideration is this, you always stand to lose more than you can gain. Assume that there are 9 players, you have 2000, 7 players have 1500 and the last player has 1000. Your expected equity is

You're probably wondering how you are meant to perform these complex calculations at the poker table - the good news is you don't have to. Once you understand the concept of non-linear chip values you should be able to deduce the following guidelines to No-Limit Holdem Tournament play:

**1. The Raiser's Edge**It's no secret that aggression is one of the keys to success, but why? The answer is fold equity. When you raise there is a chance that you will take down the pot right there, that chance is your fold equity - fold equity in tournament play reaches a premium as you close in on the bubble. Some players will only play the top 5% of hands at this stage which gives you 95% fold equity. So why not just raise every hand? The reason you shouldn't raise every hand (unless you have a massive stack) is that your opponent's fold equity reduces every time you raise because your table image changes.

This is a very simple concept to grasp and apply - simply work out the fold equity you have against the opponents left in the hand, take the lowest value and adjust it for position by removing 5% per player to act behind you. Once you have this value worked out - let's call it X - you can then profitably raise with the top X percent of hands. If you don't win the hand right there you will get a chance to make a continuation bet on the flop which takes advantage of the extra fold equity you gained by raising preflop. Heck, there's even a chance that you might have the best hand.

**2. The Non-Linear Value of Tournament Chips**This concept is slightly less intuitive than the last, but it is far more powerful - I can credit the dramatic change in my results to an understanding of this concept. In a cash game the value of your chips is always known and the value of a single chip is fixed. However, in a tournament chips do not come with a particular value; the expected equity of your chips can be determined by working out the probabilities that you will finish in a particular place, then multiplying these probabilities by the prize money for that place and adding these values together. For example, if there are 5 evenly skilled players left and each player has 1000 chips there is a 20% chance you will come 1st, a 20% chance you will come second and so on. Your current expected equity if the payout structure is $90/$54/$36 (.5/.3/.2) would be (.2 x 90)+(.2 x 54)+(.2 x 36) =

**$36**. Simple when the chip stacks are even. Let's mix it up a bit by keeping 5 players but varying the chip stacks. Now it gets complex - with stacks of 2000, 1000, 750, 750 and 500, without going in to the math too deep the expected value for each stack is**$58**,**$38.5**,**$30.9**,**$30.9**and**$22**. The thing to note is that the second players chips haven't changed - he has 1000 chips in both examples yet the value of those chips did change.Let me explain this concept further with another example:

9 man $20+$2 SnG

All players start with 1500 chips

All players are evenly skilled

The payout structure is 90/54/36

Your expected equity starts at

**$19.8**Suppose you win the first pot and now have 1600 chips. Your expected equity is now

**$21.17**- those extra 100 chips made your chip stack worth**$1.37**more! Now suppose you win the next hand worth another 100 chips, your expected value is now**$22.36**- only an extra**$1.19**cents more.You can clearly see that the expected value of your chips is not linear. The second 100 chips was worth 18 cents less than the first 100 chips. Each chip you earn will increase that expected equity by less than the last chip you earnt, in other words every chip you earn is worth less than the last. The flipside of this is that every chip you lose is worth more than the last.

Now, let's assume the game has progressed to the following situation:

4 players left

You have 1500 chips

All players have 3000 chips

Your expected equity is

**$24.93**Notice that even though you have the same sized chip stack as before, your expected equity has increased by over

**$5**! The expected equity return from 1500 chips increases as the number of players gets lower.One final consideration is this, you always stand to lose more than you can gain. Assume that there are 9 players, you have 2000, 7 players have 1500 and the last player has 1000. Your expected equity is

**$25.81**, the small stack goes all in and you call; you stand to either gain 1000 chips or lose 1000 chips so you should be happy with a coin flip right? Wrong. Those 1000 chips you stand to lose are worth**$12**in expected equity and the 1000 chips you stand to gain is only worth**$10.7**in expected equity despite the fact that you one player closer to the money.You're probably wondering how you are meant to perform these complex calculations at the poker table - the good news is you don't have to. Once you understand the concept of non-linear chip values you should be able to deduce the following guidelines to No-Limit Holdem Tournament play:

- Because you always stand to lose more than you will gain you need to adjust your normal pot and implied odds calculations. Play tighter and chase less.
- Call less and raise more. This is re-enforced by the Raiser's Edge concept discussed above. Most players will make calls with negative expected returns because they don't account for the non-linear value of tournament chips.
- The players with the most to lose are medium stacks playing against big stacks, as a medium stack you should avoid this without premium holdings. As a big stack you should play aggressively.
- If you believe you are more skilled than your opponents, your chips are worth even more in expected value. Treasure them.
- As a big stack it can be beneficial to allow a small stack to hang around so you can beat up on the medium stacks for a longer period of time.
- Never forget that you always stand to lose more than you gain when getting involved in a hand so you need even more of an edge than you normally would in a cash game. Only play from position, only play when the implied odds are worth it, only play when you think you have the best hand.

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