I'll offer my thoughts on some of these to get the conversation started.
I'm not sure I understand your exponential comment, so I'll just explain what seems to work best for me.
Early in a typical SNG or MTT, assuming my and most stacks are > 30 BB, and there are no antes, I would typically raise to 3.0x the BB. This is still less than 10% of my stack, which keeps the stack to pot ratio nice and allows for plenty of post-flop play.
With one limper, I would normally raise to 3.5x BB, which costs less than 4.0x and accomplishes the same things.
If it folds to me in the small blind, I would normally raise to 3.0, 3.5 or even 4.0x, in an attempt to end the hand pre-flop, rather than be forced to play a hand out of position.
Once typical stack at my table fall < 30 BB, I normally decrease my default raise size to 2.5x BB. I keep dropping my raise size as the tournament progresses, trying to always invest > 10% of a typical stack pre-flop. Eventually, I will just barely be over a minimum raise (i.e. raising to 888 with 200/400 blinds).
It depends. Do you have position? Who was the raiser? Is there a flush draw? What do you know about your opponent? What does he think of you? Etc.
It depends. Do you have position? Who was the raiser? Is there a flush draw? What do you know about your opponent? What does he think of you? Etc.
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