Originally Posted by DiamondDog
I'm guessing the section on effective odds in Theory of Poker was written with particular reference to limit games (where it's considerably easier to calculate that kind of thing)?
Yeah probably. In a limit game you can never be forced to put in more than an easily calculated amount. With NL you'll have to guess, and make use of upper and lower bounds. It's a bit of an art.
There are shortcuts though. The worst case for effective odds is if your entire stack goes in. If this is better than your pot odds then you can call, period. For the best case you might assume, say, 1/2 of the pot of each street? Most players that you have any reason to fear are not making bets a lot smaller than this.
This is why you don't auto-call in the big blind. Say the button min-raises, the pot is now 3.5bb and you have to call 1bb, so you're getting 3.5:1. You're not really a 3.5:1 dog against his range so this seems like an auto call.
But if effective stacks are 100bb, the worst case is that you are calling 99bb to win 101.5bb - this is so close to 1:1 that you might as well conclude that it's 50%. In the worst case scenario you'd practically need 50% equity to call.
If half-pot is the best case and you think he'll fire every street:
after you call preflop it's 4.5bb
on flop he bets 2bb, you call 2bb, pot is now 9.5bb
on turn he bets 5bb, you call 5bb, pot is now 19.5bb (let's just say 20)
on river he bets 10bb, you call 10bb.
So overall you're calling 1+2+5+10 to win 3.5+2+5+10
which is (17+3.5)
17+1) or 20.5:18 or 1.13:1, requiring an equity of about 47%
If future bets dwarf current bets then in general effective odds are way more important than immediate odds. That means that if your call is at ALL close in terms of immediate odds it's an automatic fold in effective odds.
All the above assumes a lot of mechanical decisions on both players part which is of course not how poker works. But if you are considering a call explicitly on the merits of your hands equity, this is how you do it. To get a better idea of when to call you have to also consider bluffing, or that he won't bet every street, etc, etc. In particular if he doesn't bet the turn very often then the above effective odds might be more like (7+3.5) : (7+1) or even better. But even if he's only going to bet a total of 5bb for the rest of hte hand your effective odds are 8.5:6 which is WAY worse than the immediate odds of 3.5:1