As a follow on to the last post, I probably should have explained what I meant by bubble factor. Bubble factor is the mathematical recognition of the fact that in most tournament situations, chips lost are more valuable than chips won. For example, it may be that if you have a 10K stack, your tournament equity is $100. If it increases to 11K, your equity goes up to $105, but if it decreases to 9K, your equity shrinks to $90. That means that if you risk 1000 chips on a 50/50, while it seems a fair bet in terms of cEv, in $Ev it's a losing proposition, because half the time you win but only gain $5 in $Ev, compared to a loss of $10 if you lose. So the bubble factor here is 2. For this to be a good bet, you'd have to be getting 2 to 1 (in chips) rather than evens.

This is all based on ICM, which if you don't understand I suggest you Google and read up on until you do. For example, play around with this calculator. Start by putting in a starting stack of 1500 for 10 players and you get the (obvious) result that everyone's equity is 10% at the start of an STT. Now check out what happens if one player stacks another first hand by changing one guy to 3000 and another to 0. The guy who doubles up increases his equity to 18.44%, the guy who loses obviously goes down to 0, and everyone else increases to 10.19%. This shows two things:

(1) Why it's correct to play tight early on and avoid confrontations, particularly if there are loose players willing to play each other. Simply put, you can gain equity with zero risk simply by folding and letting them knock each other out

(2) If you get into an all in here, you will gain less (8.44%) if you win than if you lose (10%). This means calling an allin when you think you're 50/50 is incorrect. The "bubble factor" here is about 1.2 (you lose 1.2 times more equity if you lose an all in than you win if you win one), so to call an allin, you need odds of 1.2 to 1 rather than evens for a 50/50.

Now look at the situation on the bubble. If everyone has an even stack (3750), everyone's $Ev is obviously 25% of the prize pool. If two guys stack off, the winner's equity increases by 13.33%, and the loser loses 25%. So on the bubble in this situation, bubble factor is almost 2, meaning you'd need to think you were a 2 to 1 favourite to call an all in, or be getting 2 to 1 pot odds on a 50/50.

Bubble factors also depend on relative stack sizes. I suggest you play around with the calculator to get a good feel for different situations. This will tell you the correct way to play the bubble. For example, if one guy has a huge stack, say 12K, and the other three only have 1K, then the big stack's bubble factor is negligible, but the other 3 guy's is huge. If they call an allin from the big stack and lose, they lose three times what they gain if they win, so they can only correctly call with a hand that's a 3 to 1 favourite. This means in essence the big stack should be pushing every hand. Even if the others realise what he's doing, they can only call with a big pair (tens or better), since these are the only hand that are a 3 to 1 favourite gainst a random hand. Even AKs is only about 9 to 4 against a random hand.

Obviously as the table gets shorthanded the blinds force you to play more, and you can't just sit there folding because ICM tells you too. The correct strategy is therefore to take advantage of the fact that others have bubble factors too and can't call willy nilly. Again, I suggest you play around with the calculator to get a feel for what you should do in different stack situations. As a general rule:

(1) If you're short on the bubble, push a lot until you're even stacked with at least one other. For example, you should be pushing every hand from the SB when it's folded to you unless the BB is a giant stack who you think will call light

(2) If the stacks are even, you must play tight (your bubble factor is 3!). You should only be calling allins with jacks or better and possibly AK. I say possibly AK because while it's not 3 to 1 against a random hand, people won't be pushing random hands in this situation but will be pushing a lot of weaker aces that you are pretty much a 3 to 1 fvourite aganst.

(3) If you're the big stack with at least twice as much chips as anyone else, you can open push any two cards from the SB and button (exploiting their high bubble factor compared to yours), but you can only call allins with premium hands.

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