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Introduction

In this article

• Why pot odds can be deceiving
  
• How to play against a range
• What to pay attention to when making an odds call
  

As you may already know, the value of your chips in a SnG varies throughout the tournament. And according to the ICM, a chip won is worth less than a chip lost.

This means the amount of equity you need against given ranges and with given pot odds also varies greatly from one situation to another.

The problem with pot odds

A lot of players make uncouth mistakes in SnGs simply because they place too much emphasis on the pot odds when making their decisions. This would, of course, be a good strategy in the early phase of a MTT or in a cash game, but this article will show you why doing so often leads to poor decisions in SnGs.

The biggest mistakes are made when the Big Blind is confronted with an all-in before the flop and has to decide between calling and folding. According to a wide spread theory, you should always call when the pot odds are 2:1 or better.

The reasoning is as follows: You are getting 2:1 pot odds, which means you only need to win in a little more than 1 of 3 times for a call to be profitable. And since 32o has 34% equity against AK, you should call with any hand. This is referred to as an "odds call."

This argumentation, however, proves to be wrong, even in cash games. The reason: You are playing against a range, and not against a certain hand. 32o only has 32% equity when your opponent's range includes every possible hand, which is why you should fold.

Assume your opponent's range includes 100% of all starting hands. Which hands could you then call with? The Equilator shows you all the hands that have at least 34% equity against a 100% range.

The result: every hand except for 42o and 32o (a range of 98.2%). You can use the Equilator to find all hands with a given equity against any given range.

You can determine which hands have at least 34% equity against an opponent's (assumed) range. Take a look at how your calling range would look against various ranges:

• 100% - 98.2%: every hand except 42o, 32o
• 90% - 96.4%: every hand except 72o, 52o, 42o, 32o
• 80% - 91%: every hand except 83o-, 73o-, 63o-, 53o, 43o-, 32o
• 70% - 87,3%: every hand except 94o-, 84o-, 73o-, 63o-, 52o-, 43o-, 32o
• 60% - 82,5%: every hand except 72s, T4o-, 94o-, 84o-, 74o-, 63o-, 53o-, 43o, 32o
• 50% - 78%: every hand except 72s, J4o-, T5o-, 95o-, 84o-, 74o-, 63o-, 53o-, 32o-
• 40% - 71%: every hand except 72s, 32s, Q4o-, J6o-, T5o-, 95o-, 85o-, 74o-, 640-, 53o-, 43o-, 32o-
• 30% - 63.5%: every hand except 92s, 83s, 72s, 62s, 42s, 32s, K4o-, Q7o-, J6o-, T6o-, 95o-, 85o-, 74o-, 64o-, 53o-, 43o-, 32o
• 20% - 52.4%: 22+, A2s+, K2s+, Q2s+, J3s+, T4s+, 95s+, 85s+, 74s+, 64s+, 53s+, A2o+, K9o+, Q8o+, J8o+, T7o+, 97o+, 86o+, 76o
• 10% - 22.5%: 22+, A8s+, K6s+, Q8s+, J8s+, T8s+, 97s+, 87s, ATo+, KTo+, QTo+, JTo

Particularities in a SNG

Collin Moshman wrote in his book Sit'n Go Strategy, "If you are getting better than 2 to 1 on a pre-flop all-in call, and your call closes the action, calling is nearly always correct". Shortly thereafter he goes on to say that you should, in fact, fold if losing the hand would cripple your stack.

This statement is too general in nature and rarely proves to be true. Take a look at the next two situations:

You are on the bubble in a SnG.
(In this article, SnG refers to 10max SnGs with a 50/30/20 pay out structure.)

Hero has 43o in the BB.
Blinds 150/300

CO 2830
BU 5065
SB 825
Hero 6280

2 folds, SB bets 825, Hero ?

Hero must pay 525 chips to play for 1125 chips. He is therefore getting 2.15:1 pot odds and must win app. 32% of the time to break even.

The question now is, what are your actual odds? In order to answer this question, you need to use the ICM to calculate your equity if you fold, call and win, and call and lose.

• Equity(Hero wins) = 37.75%
• Equity(Hero folds) = 33.97%
• Equity(Hero loses) = 32.11%

The following must be true for a call to be $EV = 0:

 

Equity(Hero| Hero calls) = Equity(Hero| Hero folds)
I * (EQ(Hero wins)) + (1 - I) * EQ(Hero loses) = EQ(Hero folds)
I = EQ(Hero folds) - EQ(Hero loses)/(EQ(Hero wins) - EQ(Hero loses))
I = 0.3397 - 0.3211/ 0.3775 - 0.3211
I = 0.0186/ 0.0564
I ~ 33%

The variable I represents the needed equity. You can now use I to calculate your actual odds. If your chance of winning is X/Y, your actual odds are Y-X : X, or (Y-X)/X : 1.

In our example you would have (3-1)/1:1, or 2:1 odds.

As we continue, cOdds will refer to your odds based on chips, and $Odds to your odds based on your odds according to the ICM. In our example, the cOdds were 2.15:1, but the $Odds only 2:1.

According to the ICM, you need 1% more equity to call than you need to call when calculating your odds based on chips alone. You should call with 43o, since you have 35% equity against his random hand range. The difference between the cOdds and $Odds is rather marginal in this example.

You are 5 handed in a SnG.

Hero has J7o in the BB.
Blinds are 200/400

UTG 1365
CO 2620
BU 4125
SB 3240
Hero 3650

UTG bets 1365.3 folds, Hero ?

Hero's cOdds are app. 2:1, meaning he needs 33% equity to call. Using the same formula from the last example, you can calculate that you need 37% equity to call, which corresponds to 1.7:1 $Odds.

Assuming you are up against a random hand, you should call with every hand except 32o. When you take the $Odds into account, you see that you should fold 82o, 73o-, 63o-, 53o-, and 43o- as well. The difference: You have a 99% calling range based on the cOdds, but only a 91% calling range based on the $Odds.

You should fold more often against tighter ranges (for example, a range of 50%). Reduce your calling range from 83% (cEV) to 56% ($EV). You should therefore fold 1 in 3 hands found in your cEV = break even range. You should call against a 100% range with J7o, but fold to a range of 50%.

As you can see, putting your opponent on a range is critical when making an odds call.

How do you know how much equity you need to make an odds call?

In order to answer this question precisely, it is important to ask yourself the following questions:

• 1. What will your position (in chip count) be if you fold?
• 2. How will your position change if you play?
• 2.1 Would your position change if you lose? If yes, how many places?
• 2.2. Would your position change if you win? If yes, how many places?
• 3. What position would your opponent be in if you play?
• 3.1 Would his position change if he wins the hand? If yes, how many places?
• 3.2 What position would your opponent be in if you fold?

Answer these questions in the next two examples and compare the results.

Example 1:

• 1. You will still be chip leader.
• 2.1 No, you would still be the chip leader.
• 2.2 Not really, although having more chips wouldn't hurt.
• 3.1 He will still be the small stack.
• 3.2 His stack will still be smaller.

This can also be mapped out on a graph:

Example 2:

• 1. You will still be in 2nd, but the chip leader's lead will shrink.
• 2.1. Yes, you only have ~2200 chips left and are a small stack. Still, you can generate fold equity against the CO, SB and UTG.
• 2.2 Yes, you will be the chip leader with a 3 BB lead and will be on the bubble (which could be a good reason to make a -EV call, but that's a completely different topic).
• 3.1 Right now, he is one of four small stacks fighting for 2nd or 3rd place.
• 3.2 He will still be a small stack, but won't be far behind the CO.

Looking at the graph you see:

Once you've answered these questions you can begin asking yourself how your hand can play out against your opponent's range.

One thing becomes very clear when looking at these examples: You should usually fold the weakest hands, even if you think you can make an odds call, especially when you aren't sure what kind of range your opponent is on.

When you are not looking to put your tournament life at risk, you can generally play things on the safe side by only calling with hands that have 2-3% more equity against your opponent's range than would be needed to make a cOdds call.

The next example will show you how much equity you need when a call would cripple/bust you.

You are 6 handed in a SnG.

Hero has Q2o in the BB.
Blinds are 200/400

UTG 2590
UTG+1 2175
CO 1085
BU 3420
SB 4360
Hero 1370

4 folds, SB bets 1370, Hero?

Your cOdds are 1770:970, or 1.8:1. You need to win at least 35% of the time in order to break even. Your $Odds are 1.4:1, which means you need another 6% in equity to call against your opponent's range.

Assuming the SB will go all-in with a 60% range, you can call with 22+, A2s+, K2s+, Q2s+, J7s+, T8s+, 98s, A2o+, K2o+, Q6o+, J8o+, and T9o. You should fold Q2o, since it only has 38% equity according to the ICM. This is not a cut and dry fold, however, since you could argue that you will lose equity when you have to post the SB in the next hand, and that the ICM often overestimates the equity of a very short stack.

You should have 5-6% more equity than needed for a cOdds call when you are in danger of losing your stack or being crippled.

Of course, the ICM is not perfect. Sometimes you should even make calls that appear to be -$EV.

When would a -$EV call make sense? For example: You have a 5-6 BB stack and are in the BB; a loose opponent pushes from a steal position. If the blinds will increase after you fold and you will lose a lot of your fold equity, this may be the right time to give it a shot.

Conclusion

The odds you are offered in a SnG are usually your actual odds. But don't forget, you are playing against ranges, not against specific hands.

Once you are getting 3:1 or better, you can usually call without worrying too much about your opponent's range.

The blinds can lead to situations, in which you must stray from the ICM's recommendations. However, your basic strategy should follow the ICM.

LINKS
Related Articles: How High is Variance in SnGs? The Independent Chip Model (ICM) Discussion Forum: Discuss this article in the Forum

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