Originally Posted by Anthony Garcia
I can play with approximate numbers?
I am going to shorten your whole question down to this simple question, because the answer to this question is yes. You can and usually will play with just the approximate numbers. If you have a flush draw, you can just go with the assumption that you'll hit it 36% or 33% by the river and not worry about the exact number (about 34.9676% -- although it varies depending on what the other player has). In reality, your decision is rarely that close that the approximate number and the actual number would give different answers.
This is even more apparent when you realize that you don't know an opponents exact cards for sure. You're making an educated guess about what he has and what you'll need to win. Sometimes you'll be wrong in one direction or the other. Sometimes, you might not have 9 outs. You might have fewer than you think. Sometimes, you might have more outs than you expect. You might even be ahead already.
You should have a general idea of how often you'll hit your hands. But, if you're worrying about hundredths of a percent, you're focusing on the wrong things.
Pot odds are important, but again, you do well by just getting close.
Pot is 475 then opponent bets 47? That's about 525-50 or 10.5 to 1. (There is 475 + 47 out in the middle, and you are risking 47 to claim it). Sure, the actual number is 11.1-1, but there's really very few situations where 10.5-1 is a fold and 11.1-1 is not. Actually, for 10.5-1, you can call with 4 or more outs. That's a pretty wide range.
After a hand is over, when you are doing hand reviews, you might want to nail down the exact numbers. Those post-play analysis sessions will help correct any errors you might have as well as fine-tune your instincts in future sessions. But, in the heat of the moment, just go with approximate values.