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Introduction

In this article

• The bubble factor
  
• Why calling ranges vary
  
• How to adapt your play
  

This article will introduce you to the bubble factor and its impact in various SnG tournaments. You will learn how to adjust your game in the early phase, on the bubble and when you are in the money for each type of SnG.

We will focus on the following types of SnGs:

• Full-ring SNG with a 50%/30%/20% payout structure
• Short-handed SNG with a 65%/35% payout structure
• Double or Nothing SNG with a 20%/20%/20%/20%/20% payout structure

This article will require an understanding of the Independent Chip Model and the concept of odds and outs. Be sure you know what these are before you continue reading.

The bubble factor

We'll start with an example taken from the article on Expected Value in SnGs.

You and 8 other players all have a 1500 chip stack. You are last to act and one player has gone all-in in front of you. We will leave out the blinds to keep things simple.

You can use the ICM to find out how often you have to win for a call to be profitable regardless of your hand and your opponent's range. If you weren't playing for a structured payout, you would be getting 1:1 odds, meaning you would have to win more than 50% of the time in order to make a profit.

The ICM places a monetary value on your chip stack in different situations as follows:

• You fold: You still have 1500 chips, which are worth 11.1% of the prize money.
• You call and win: You have 3000 chips, which are worth 20.3% of the prize money according to the ICM. The other 1.8% belongs to the other players still in the tournament.

You can therefore calculate the odds needed to call (your hand's equity against your opponent's range) with the following formula:

P(Win) = EQ(Fold)/EQ(Win) = 11.1%/20.3%
P(Win) = 55%

You can see that you need 5% more equity against your opponent's range to call in the early phase of a full-ring SnG than in a cash game. The reason: When you win, your profit is less than your losses when you lose. Your 1:1 odds are, in fact, only around 0.8:1. Why? Because you need ~ 55% ( = 1/(0.8+1) ) equity, which corresponds to 0.8:1 odds.

The quotient derived from the costs of losing (in $) and gains (in $) is referred to as the bubble factor, and tells you how strongly the payout structure changes your pot odds in the situation at hand. This concept was introduced by Tysen Streib in his book Kill Everyone.

Important: The blinds don't play any role in the calculation of the bubble factor. The blinds affect your odds, but the bubble factor stays the same. This is one of the benefits of the bubble factor.

If you know your bubble factor, then it doesn't make a difference whether the blinds are currently at  100/200, 400/800 or 123/211. You calculate your pot odds as usual and divide them by your bubble factor. These are your odds according to the ICM. Also, EV(Fold), the expected value for the equity after a fold, refers to situations without blinds.

The bubble factor is always 1 in a cash game. You can easily incorporate the bubble factor into our example:

• When you lose, you lose 11.1% of the prize pool.
• When you win, you win 9.2% of the prize pool (= 20.3% - 11.1%).

This gives us a bubble factor of: 11.1/9.2 = 1.2.

You can then calculate your actual pot odds by dividing the left side of the chip pot odds by the bubble factor. For example, with chip pot odds of 1:1, your actual pot odds are 0.8:1, since 1/1.2:1 = 0.8. You can use the bubble factor to calculate your actual odds in complicated situations without using the equity formula a second time.

This is the first hand in a 9-handed full-ring SnG with a normal payout structure. The Big Blind is at 50 and all players have 1500 chip stacks.

UTG limps, UTG+1 raises to 100 and you raise to 300 from the BU. UTG goes all-in for 1500 and UTG+1 folds.

There are now 1975 chips in the pot and you must pay 1200 to call. Your are getting 1.65:1 pot odds, which means you need to win more than 37% of the time in order to break even.

Your actual odds, however, are only 1.375 : 1 (= 1.65/1.2 : 1), which means you need 42% equity to call.

In the early phase

Since the bubble factor is based on the payout structure of the tournament, the bubble factor varies from one type of SnG to the other. Start by calculating the amount of equity you need to win a coin flip in the early phase of the various SnGs.

Starting stacks are as follows:

Chip Distribution	9-max	DoN	6-max
UTG		1500
UTG+1	1500	1500
UTG+2	1500	1500
MP1	1500	1500
MP2	1500	1500	1500
MP3	1500	1500	1500
CO	1500	1500	1500
BU	1500	1500	1500
SB	1500	1500	1500
BB	1500	1500	1500

You can use the ICM to calculate your equity for folding and for winning/losing the hand. Once you have done so, you can define the bubble factor.

You need 55% equity to call a coin flip in a full-ring or short-handed SnG, but would need much more (67%) to call with 1:1 chip odds in a Double or Nothing tournament.

You should fold AKo in the early phase of a DoN, even if you know your opponent is on a random hand, since AKo only gives you 65% equity against his range. As you can see, you have to be very tight in a DoN.

On the bubble

Take a look at the bubble factor in various SnGs when you are on the bubble. We will assume all players have equal size stacks.

We get the following values:

ICM/Equity	Fold	Lose	Win	BF
9-max (4 players have 4000t)	25	0	38.5	1.9
DoN (6 players have 2250t)	16.7	0	20	5.1
6-max (3 players have 3000t)	33	0	55	1.7

You need 67% to make an all-in coin flip call on the bubble in a full-ring SnG, 63% in a short-handed SnG, and 83% in a DoN.

You can make somewhat looser calls when you are on the bubble in a SH-SnG than when in a FR-SnG.

If you have AKo and put your opponent on any two cards, you have 65% equity. You could make a close call in a short-handed tournament, but would have to make a tough fold in a full-ring SnG if you know your opponent will go all-in with any hand.

Things are even bleaker in a DoN-SnG. Aces have 85% equity against a 100%, which is enough to call, but kings only have 82%, which means you have to fold.

How does the bubble factor change when there is a chip leader?

Take a look at the following chip distribution for a FR-SnG:

CO 8000t
BU 4000t
SB 4000t
BB 4000t

Since the stack sizes play a role in defining the bubble factor, players will now have a different bubble factor depending on how the stack of the opponent in the hand compares to his own. There is a big difference between risking some of your chips by calling and putting your tournament life at risk.

You can calculate the bubble factor (BF) depending on your opponent:

Hero	Villain	Fold	Lose	Win	BF
CO	BU, SB, BB	33	22.33	41	1.3
BU, SB, BU	CO	22.4	0	33	2.1
BU, SB, BU	BU, SB, BB	22.4	0	35.7	1.7

The bubble factor tells how much better your odds must be in order to call against a certain opponent depending on your and his stack size.

Sample calculation of the bubble factor of the CO against the BB:

Situation after a fold:

CO  8000 33.0%
BU  4000 22.3%
SB  4000 22.3%
BB  4000 22.3%

Situation after call&lose:

CO  4000 22.3%
BU  4000 22.3%
SB  4000 22.3%
BB  8000 33.0%

Situation after call&win:

CO  12000 41.0%
SB   4000 29.5%
BB   4000 29.5%

The bubble factor is the quotient of the potential loss and the potential winnings.
Loss: 33.0% - 22.3% = 10.7%
Winnings:  41.0% - 33.0% = 8.0%

Therefore, we get a bubble factor of: BF(CO vs BB) = 10.7%/8.0% ~ 1.3

In the first row you see an example in which the chip leader is getting 2:1 odds after a short stack's push, but actually needs 1.67:1 in order to call.

You can easily create a bubble factor chart. Here's how this chart would look like for our example:

Bubble factor	CO	BU	SB	BB
CO	-	1.3	1.3	1.3
BU	2.1	-	1.7	1.7
SB	2.1	1.7	-	1.7
BB	2.1	1.7	1.7	-

The chip leader is the CO in this chart, but could obviously be in any position.

If the blinds are, for example, 400/800 and the chip leader is, say, in the Small Blind and both players fold in front of him before he goes all-in with 32o, the player in the Big Blind will be getting 1.5:1 odds. Since his bubble factor is 2.1, his actual odds are only 0.7:1, meaning he needs at least 59% equity against the chip leader's range to call.

Using the Equilator you get the following calling range for the Big Blind against a push with any two cards:

55+, A4s+,K9s+,QTs+, A8o+, KTo+ (17%).

If, however, the BB calls with a hand in this range, the SB's push with 32o has an EV of +1.3%. This means that the Small Blind wins $13 by pushing with the worst possible hand in a $100 SnG and that the Big Blind can't do anything about it if he wants to make a profitable decision.

This shows how much strength comes from having a large stack on the bubble.

If one of the other two small stacks were in the SB, the BB could call an any two push with any hand that has more than 53% equity against a random hand, since he would be getting 1.5:1 (0.9:1 after including the bubble factor).

The Equilator gives us the following range:

44+, A2s+, K3s+, Q7s+, J8s+, T9s, A2o+, K6o+, Q9o+, JTo

Now compare this to a bubble scenario in a Double or Nothing. Each player has a 2250 chip stack.

We only have one value for the bubble factor, since each player has an equal number of chips in his stack.

ICM/Equity	Fold	Lose	Win	BF
MP2	16.7	0	20	5.4

How does a 5.4 bubble factor affect your strategy?

If one of your opponents goes all-in and you are getting 2:1 odds in the BB, you need 73% equity against your opponent's range to call. You need TT+ to call against a random hand.

Let's take a look at how this changes when there is a chip leader in a DoN. The chip stacks are as follows:

MP2 4500
MP3 2100
CO 2100
BU 2100
SB 2100
BB 2100

This gives us the following chart:

Bubble factor	MP2	MP3	CO	BU	SB	BB
MP2	-	3	3	3	3	3
MP3	5.4	-	4	4	4	4
CO	5.4	4	-	4	4	4
BU	5.4	4	4	-	4	4
SB	5.4	4	4	4	-	4
SB	5.4	4	4	4	4	-

When one of the short stacks pushes against the chip leader, he has a bubble factor of 3. This means that he needs 67% equity against the short stack's range to call with 1.5:1 odds, for example. If the short stack pushes with any hand, the chip leader should only call with 88+ even though he can only lose half his stack.

The chips he can win aren't that helpful, since he will probably survive the bubble anyway.

Let's flip things around: A short stack should only call the chip leader's push at 1.5:1 odds when he has more than 78% equity against the big stack's range.

He would need QQ+ to have at least that much equity against a random hand. If he were only getting 1:1 odds, AA would be the only hand the short stack could profitably call with.

Assume you are on the bubble in a SH-SnG with a 65%/35% payout structure. All players have equal size stacks.

You calculate your bubble factor as always and get:

ICM/Equity	Fold	Lose	Win	BF
BU	33	0	55	1.5

Let's look at the following example:

BU folds, SB pushes and you are getting 2:1 odds. You need 43% equity (instead of 33% according to the chip odds) against the SB's range with a 1.5 BF.

Let's look at how the situation is with a chip leader in a SG-SnG.

BU 4500
SB 2250
BB 2250

The BU's BF against one of the small stacks is:

ICM/Equity	Fold	Lose	Win	BF
BU	44	28	54	1.6

The chart is as follows:

Bubble factor	BU	SB	BB
BU	-	1.6	1.6
SB	1.8	-	1.3
BB	1.8	1.3	-

The chip leader needs 45% equity to call with 2:1 odds against one of the short stacks. The small stacks, however, need 47% equity to call a push from the chip leader, just 2% more.

As you can see, the calling ranges are not reduced as drastically when you are on the bubble in a SH-SnG. You can basically define your calling range by looking at the odds, regardless if it's the big stack or the other short stack pushing.

In the money

Once you're in the money, your play will vary greatly from one type of SnG to the other.

You're now heads up in a SH-SnG. Your bubble factor is 1, just like in a cash game and you can define your range by looking at the chip odds.

DoNs aren't played out once the players have reached the money, so there is no need to say more.

The bubble factor only comes into play in FH-SnGs when it comes to the 'in the money' phase. We will assume you are playing with a normal 50/30/20 payout structure.

Calculate the bubble factor when all players have 3000 chips.

ICM/Equity	Fold	Lose	Win	BF
Hero	33	20	43	1.3

Your bubble factor is 1.3, which means you need to play somewhat tighter, but are more willing to call with a wider range if your opponent is playing too loose.

Since the blinds tend to be pretty high by the time you are in the money, this phase is often much shorter than the bubble phase. You need a little more than 40% equity against your opponent's range to call with 2:1 odds, which is usually the case.

As you can see, there is truth to the saying, "When it comes to SnGs, you play for the money first, and for 1st place secondly."

We will conclude with a chart for ITM play when there is a small stack. Chip distribution is as follows:

BU 4000
SB 4000
BB 2000

Hero	Villain	Fold	Lose	Win	BF
BU	SB	36	20	46	1.6
BU	BB	36	29	42	1.2
SB	BB	29	20	36	1.3

Notice that your ITM play in a FR-SnG is very much like your bubble play in a SH-SnG and that the pushing and calling ranges do not differ greatly.

Using the bubble factor when you play

Calculating your actual odds is pretty complicated and most players have trouble doing so in the time allotted during live play.

Don't try to figure out the exact BF for every single situation; the important thing is being able to roughly estimate your BF and to get a feeling for how you should adjust your range and how much equity you need to call in a certain situation (especially on the bubble!) depending on your opponent's chip count.

You can start my memorizing how much additional equity you need (BF!) in coin flip situations in various phases of SnGs.

For example, you need 55%+ equity against your opponent's range to make a coin flip fall in the early phase of a tournament, and 65% to call when you are on the bubble. This is because your bubble factor is 1.2 in the early phase and 1.8 in the late phase.

Nelson, Streib and Lee provide quite a few use bubble factor charts in their book Kill Everyone. They also go into explicit detail regarding the strategy that each player should then develop. They also take a look at the bubble factor in large MTTs like the WSOP or Sunday Millions. This book is a must for any serious SnG player.

We will conclude by giving you a simple chart that shows you how to adjust the odds according to the bubble factor. This should help you get a feeling for how strongly the amount of equity needed to call changes when the bubble factor changes.

Odds	To	Bubble factor	Equity in %
1.0	1.0	1.0	50
1.0	1.0	1.2	55
1.0	1.0	1.5	60
1.0	1.0	2	67
1.0	1.0	2.5	71
1.0	1.0	3	75
1.0	1.0	3.5	78
1.0	1.0	4	80
1.0	1.0	4.5	82
1.0	1.0	5	83
1.0	1.0	5.5	84
1.0	1.0	6	86
1.0	1.0	7	88
1.0	1.0	8	89
1.2	1.0	1.0	45
1.2	1.0	1.2	50
1.2	1.0	1.5	56
1.2	1.0	2	63
1.2	1.0	2.5	68
1.2	1.0	3	71
1.2	1.0	3.5	74
1,2	1,0	4	77
1.2	1.0	4.5	79
1.2	1.0	5	81
1.2	1.0	6	83
1.2	1.0	7	85
1.2	1.0	8	87
1.5	1.0	1.0	40
1.5	1.0	12	44
1.5	1.0	1.5	50
1.5	1.0	2	57
1.5	1.0	2.5	63
1.5	1.0	3	67
1.5	1.0	3.5	70
1.5	1.0	4	73
1,5	1.0	4.5	75
1.5	1.0	5	77
1.5	1.0	6	80
1.5	1.0	7	82
1.5	1.0	8	84
2.0	1.0	1.0	33
2.0	1.0	1.2	38
2.0	1.0	1.5	43
2.0	1.0	2	50
2.0	1.0	2.5	56
2.0	1.0	3	60
2.0	1.0	3.5	64
2.0	1.0	4	67
2.0	1.0	4.5	69
2,0	1.0	5	71
2.0	1.0	6	75
2.0	1.0	7	78
2.0	1.0	8	80
2.5	1.0	1.0	29
2.5	1.0	1.2	32
2.5	1.0	1.5	38
2.5	1.0	2	44
2.5	1.0	2.5	50
2.5	1.0	3	55
2.5	1,0	3.5	58
2.5	1,0	4	62
2.5	1.0	4.5	64
2.5	1.0	5	67
2.5	1.0	6	71
2.5	1.0	7	74
2.5	1.0	8	76
3.0	1.0	1.0	25
3.0	1.0	1.2	29
3.0	1.0	1.5	33
3.0	1,0	2	40
3.0	1.0	2.5	45
3.0	1.0	3	50
3.0	1.0	3.5	54
3.0	1.0	4	57
3.0	1.0	4.5	60
3.0	1.0	5	63
3.0	1.0	6	67
3.0	1.0	7	70
3.0	1.0	8	73

Conclusion

You can use the bubble factor to derive your actual odds in a SnG tournament.

You have also learned how strongly you must adjust your ranges in different phases of various types of SnGs and how to determine your BF against an individual opponent. 

The bubble factor gives you a feeling for when and how strongly you should adjust your ranges in certain situations in SnG tournaments.

LINKS
Related Articles: How High is Variance for SnG Players? [http://www.pokerstrategy.com/strategy/sng/1072/] The Independent Chip Model (ICM) [http://www.pokerstrategy.com/strategy/sng/175/] Odds in SnGs [http://www.pokerstrategy.com/strategy/sng/1478/] Discussion Forum: Discuss this article in the Forum [http://www.pokerstrategy.com/forum/board.php?boardid=1437]

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