I had a request for a basics article on the fundamentals of pot odds and "how often does our opponent have to fold for my bluff to be successful" type math. Here it is. For the numbers-inclined, this will be review. It will eventually turn into an article that goes up on HUSNG.com.Calculating Pot Odds:Your pot odds are the the amount you have to call, divided by the size of the pot if you call. For example, if your opponent bets t100 into a pot of t200, the bet to call is t100, and the pot size if you call is t400. So, your pot odds are 25%. Another way of saying this is that you're getting 3-1, which represents 300 that is already in the pot against the 100 you have to call. Over time, if you win the t300 that was out there 1/4 of the time, and lose an extra $100 3/4 of the time, you'll break even. (.25)(+300) + (.75)(-100) = .75 - .75 = 0EV.Potsized bets are laying you 2-1, or 33% pot odds. A bet of t200 into t200 means that when you call, there will be t600 in the pot, and 200/600 simplifies to 1/3 or 33%.If your opponent bets a quarter of the pot, like t50 into t200, the pot will be t300 if you call, and 50/300 simplifies to 1/6, or 17%.Most of the time in game, you don't really have to do any math - just estimate based on the probabilities you already know - potsized bets are 33%, half pot bets are 25%, and quarter pot bets are 17%. Just pick where it seems to be in between, and you won't have to bring up a calculator when you're trying to figure out how often you need to be good.Don't get confused when you're facing a raise, and not just a bet. If you bet t100 into a pot of t200, and your opponent raises to t300, you just have to look two places: Down, at how much you have to call (t200 more), and then add that number to what's displayed as the pot size (It will say 600, which makes it 800 if you decide to call). 200/800 is 25%.Quick Check Problems:1. Your opponent bets t275 into a pot of t450 on the river. What percent of the time do you need to have the best hand for calling to have a better expectation than folding?2. On the river, you block bet t150 into a pot of t400, and your opponent jams for t650 more (800 total). How often do you need to be good for calling to have better expectation than folding?3. You're facing a bet of t263 into a pot of t448. Without using a calculator, estimate how often you need to be good for calling to have better expectation.Calculating how often your opponent needs to fold for a river bluff to be +EV:If you assume you have zero equity when you are called, and have no chance at winning the pot if you don't bet, this one is pretty to calculate. Just take your bet size, and divide it by how much will be in the middle once you make your bluff. For example, if the pot is t300, and you want to bet t200, you need a fold 200/500 of the time, or 40%. A potsized bluff needs to work 50% of the time, and a half pot bluff needs to work 33% of the time.If you're considering a bluff raise, it's the same equation - how much money you're putting into the pot instead of folding, divided by the quantity of that plus whatever was in the pot that you're trying to steal. So if the pot on the river was t300, your opponent bets t150, and you want to try a raise to t450, you need a fold 450/(450 + 450) of the time, or 50%.What complicates this is that in many situations, your expectation from deciding not to bluff, and instead check behind, isn't 0. Sometimes you decide not to bluff with queen high and end up having the best hand against a missed draw. When this is true, you need a higher percentage of folds for bluffing to be better than giving up.Quick Check Problems:4. On the river, you know you have no showdown value. The pot is t320. How often does a t180 bluff need to work for it to have better expectation than checking behind?5. Your opponent blockbets t100 into a t500 pot. You have t900 behind. How often does a jam have to work to be better than folding if you have no showdown value?6. In this article, I say that your opponent having missed draws in his range means that you need to get a bigger percentage of folds when you have marginal showdown value in order for a bluff to be good. However, bluffing and checking behind have exactly the same result against these hands - you win - so it doesn't matter what you do against those hands. So why does it matter if our opponent has them in his range when we're deciding whether to bluff? Isn't this a contradiction?