Poker Math In Sit n Go Bubble Strategy, How Many More Chips Is That Big Stack Really Worth?
This article looks at whether making a negative expectation call (according to ICM) at the bubble of a Sit n Go can be balanced by the extra chips that you gain from having a big stack. Here we assume an understanding of The Independent Chip Model (ICM for SNGs). If you are unclear on this subject then an introduction to ICM is a great background article. We will also build on the ‘Outside The Box’ thinking introduced by Albatross77.
Making a negative expectation (-$ev) call near the bubble of a Sit N Go costs money… not some mathematical ‘virtual money’ but real hard cash. The best way of looking at this is that if your call is – 1% and the prize pool is $100 you have cost yourself a dollar! The same goes for declining a positive expectation (+$ev) call.
Of course there are factors which change this, usually the presence of a micro-stack. The fold or call still costs you money – but (for example) if the micro-stack is all-in next hand you might decline the opportunity in order to ‘lock up’ 3rd place. That is to say you loose a couple of dollars in equity today as you have a better bet tomorrow (a great chance to increase your $ equity by simply folding).
Having a big stack at the bubble is a profitable situation. The reason behind this is that nobody wants to go out in 4th place. If your opponents are trying to get into the money you can steal their blinds with impunity. If they understand ICM they will not call without a monster hand – and the chances of having one are low. Your big stack should grow considerably while the bubble is still alive.
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Building A Big Stack Before The Bubble - An Example
So, we will look at an example of a pre-bubble situation and ask whether taking a gamble could be worthwhile – that is taking a -$ev situation on the basis that winning the hand will give you more prize pool equity than what you are risking.
Prize Pool = $100
Blinds: 200 / 400
5 Players All Have Stacks of 2000 chips ($20 in Equity Before Posting Blinds)
You are in the Big Blind and everyone folds to the Small Blind who pushes all in. You know that this player understands ICM and will thus push a wide range here, any pair, ace, king and Q-2 suited or better + most suited connectors. You have K-8 suited. Here are the ICM numbers:
$ev Fold = $16.83c
$ev Call = $16.10c
This is a fold according to the raw numbers. The difference of 73 cents comes out of your long term profit each time you make the call.
Building A Big Stack Before The Bubble - Quantifying Your Later Advantage
However, if you call and win you have 4000 chips at the bubble while your 3 opponents each have only 2000. In order to work out our real expectation for the call we have to make an estimate as to how many more chips you might win by virtue of having a big stack. This is dependant to a large extent on your opponents understanding of bubble play. If this is good then a ‘walk’ in your next Big Blind and one more set of blinds is probably conservative.
This is 1200 more chips for you, let us look again at the ICM numbers with 400 taken from each opponent.
After the ‘gamble’ you have 4000 chips (equity = $33) and each opponent 2000 chips (equity = $22.33c). After 1 round and 1200 more chips you have 5200 (equity = $37.71) and each opponent an average of 1600 chips (equity = $20.76).
This clearly shows that taking a negative expectation situation today (at minus 73c equity) has actually lead to an increase in equity of $4.71 those times that you win. Of course you will not win every time – the final step in this example is to factor in your winning chances. For K-8 suited against the small blinds range this = 48.8%. So you risk 73c to win ($4.71/40.8%) = $2.30c – that is more than the edge ICM suggests taking.