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StrategySit & Go

# Chip Value (4): The Risk Premium Concept

You already have a clear idea of how to understand the value of your stack and how it's possible to evaluate it. You also know how to evaluate your decisions.

To fully understand the process of chip evaluation and to be able to use it in all stages of SNGs – in particular on the bubble – you need to learn about the risk premium concept. In this lesson, you will learn what it is, how to use it and how it can help you to know the ranges you should play with.

## The risk premium is an extra equity

As you already know, the number of chips in cash games equals their value. This means that in cash games, every decision profitable in terms of chips (cEV) is also profitable in terms of money (\$EV). In SNGs, because of the principle of diminishing chip value, the situation looks different.

Since chips that can be gained in SNGs are not necessarily worth as much as the chips you are risking to win them, the equity that you need in terms of the cEV (chip equity) is not enough. This means that you need more equity in SNGs than you would in cash games in order to make a profitable play. This extra equity is what we call the risk premium.

Therefore, the risk premium concept can be defined as follows:

 Risk premium: extra equity that you need in SNGs in order to make a profitable play, in addition to the equity that you need in terms of cEV (chip equity).

Notation: In this context, you should understand a profitable play as the best one availble. In this lesson, the value of a given play is always calculated relative to the other decision available. For example, a call with \$EV = \$1 means that on average the monetary value of hero's stack after calling is \$1 higher than the monetary value of his chips after folding.

In general, recognising how high the risk premium in a given situation is depends on the size of the gap between the value of chips that you can win and the value of chips that you put at risk. In order to determine the size of this gap, you need to know how much your chips are worth in terms of their monetary value, so you need to refer to the ICM.

Imagine you are playing in a 9-man \$10+\$1 SNG with 50/30/20 payout structure. Blinds are 10/20 and there are still 9 players in the game.

Of course, it is a bit strange for a player to push all-in here, but on micro and low stakes it happens quite often.

Suppose MP2 has in range TT+ and AK.

Against this range, QQ has 52.37% equity, which means that in the long run you would earn about 96 chips on this call. This call is therefore profitable in terms of chips, meaning that it is +cEV.

Calculation Close spoiler Open spoiler

Chip expected value of your call (cEV) = chips you play for (stacks + blinds) * you equity - chips you risk (your stack)

cEV = 3010 * 52.37% - 1480 = ~96

Since the number of chips in cash games equals their value, in a cash game (for the sake of this example, let's assume there is no rake) you would have a clear call. However, in this SNG - under consideration of the ICM – monetary expected value of this call is negative, so you should fold.

Calculation Close spoiler Open spoiler

Monetary expected values of your stack in all possible scenarios calculated due to the ICM:
\$EV of your stack after fold: \$9.88 with 1480 chips
\$EV of your stack after call & win: \$18.30 with 3010 chips
\$EV of your stack after call & lose: \$0 with 0 chips

Monetary expected value of your stack after a call (\$EV) = probability of winning the hand * monetary expected value of your stack after call & win + probability of losing the hand * monetary expected value of your stack after call & lose

\$EV = 52.37% * \$18.30 + 47.63% * \$0 = \$9.58

\$EV of your stack after a fold = \$9.88 > \$EV of your stack after a call = \$9.58

\$EV(Call) = -\$0.30

In order to make a +cEV call, you need more than 49% equity here. Making a +\$EV call, however, requires at least 54% in this case. This means that your risk premium in this example is 5%.

Calculation Close spoiler Open spoiler

Equity needed for +cEV call (chip equity):
3010 * %Equity - 1480 > 0
Equity > ~49%

Equity needed for +\$EV call:
\$18.30 * %Equity - \$9.88 > 0
Equity > ~54%

Risk-premium = ~54% - ~49% = ~5%

Knowing how high your risk premium is helps you to adjust your range accordingly. Since with QQ your equity is 52.37%, whilst your equity needed for a +\$EV call is ~54%, you can clearly see that in order to make a profitable call, you need to hold kings or aces.

 In general, the risk premium depends on the gap between the monetary value of chips that you can win and those that you put at risk.

As you can see, knowing the monetary value of given stacks allows you to calculate your risk premium manually. However, you can also do this by using special programs. One of them is called ICM Explorer and is available here.

## Correlation between stack sizes and risk premium

A special characteristic of the risk premium is that you have different risk premium against every individual player at the table (unless some of them have equal stacks).

Take a look at the following bubble situation from a 6-man SNG with 65/35 payout structure:

Now what is your risk premium? Actually, you have one risk premium against Player 2, and a different risk premium against Player 1.

RP Hero vs Player 1: 3.9%
RP Hero vs Player 2: 15.9%

The fact that your risk premium against Player 1 is lower than against Player 2 is quite understandable, as you are 100 % in the money if you win against Player 1 and have still 900 chips left if you lose. However, against Player 2 you are not 100 % ITM if you win, and you are out with nothing if you lose.

As you can see, the gap between the value of chips that you can win and the value of chips that you risk is clearly higher when you clash with Player 2 than when you clash with Player 1.

From that example, we can derive the correlation between stack sizes and the risk premium, which looks as follows:

 Your risk premium is higher against bigger stacks (in particular bigger than yours) and lower against smaller stacks (in particular smaller than yours).

In lessons dedicated to bubble play, you will find more detailed information and strategies concerning this subject.

## Application of the risk premium concept

Although the risk premium concept – as part of the ICM-oriented evaluation of decisions – is included in calculations made by programs like HoldemResources Calculator or SitNGo Wizard, it is still important to be aware of it and to understand it.

First of all, it helps you to think outside the box and to fully understand the process of evaluating decisions and calculations that underpins the ICM programs. With this knowledge, you have a better understanding of how and when you should change your ranges and make other adjustments whenever you need to.

Furthermore, it improves your ability to evaluate intuitive decisions by helping you to understand the dependence between particular stacks. This approach might, in some cases, be more didactical than learning static ranges, as it applies to all possible scenarios (pushing, calling, repushing, etc.).

## Summary

In this lesson, you have learned that:

• Risk premium is an extra equity that you need in SNGs in order to make a profitable play, in addition to the equity that you need in terms of cEV (chip equity).
• The risk premium depends on on the gap between the monetary value of chips that you can win and those that you put at risk.
• Your risk premium is higher against bigger stacks and lower against smaller stacks.

## Next steps

#1 angel454g, 13 Oct 13 18:30

I would have like to seen how you calculated the risk premium.

#2 Ramble, 23 Dec 13 02:10

@#1 - It's in the 3rd calculation spoiler below the hand ranges graphic...

#3 kenpo189, 03 Mar 14 04:32

Increíble, excelente artículo

#4 Jaquare, 21 Jun 14 18:26

thanks for the article!! Another great one!!

#5 lcerebral18, 27 Jun 14 14:01

Hi, is there something I am missing but shouldn't RP Hero vs Player1 be 5.24% rather than 3.9%?

#6 mirth, 06 Apr 15 13:56

very interesting how much theory is involved. i have qq and he raised all in, i call. no, it is long-term not profitable. helps me realize why hellmuth folded kk to a preflop all in in the early rounds of wsop.

#7 RightMove, 29 May 15 10:25

Can someone explain how did you calculate RP hero vs player 1 and 2 please..

#8 ferrye, 30 Nov 15 12:46

Good stuff

#9 hassux, 25 Jan 16 21:38

#10 bubamarasr, 29 Jan 16 15:42