Quick Ways To Calculate Odds
One of the things that probably keeps players from improving is the inability to calculate pot odds on the spot.
I mean, they've got all that math flying around in their heads, dividing x by some God-awful number like 47 or 46 and trying to come up with a fraction or a percent that can be compared to the amount that they're being asked to bet by some increasingly impatient opponents versus the pot, which is the same as it's been on the flop for the last eight hands because everybody keeps limping in, et cetera...
So this should make things easier. I tried to make things as simple as possible.
This is longer than it should be because I've got a lot of "why" stuff included. But there are really only three equations in here that should be memorized (and two of them are extremely simple integer multiplications).
Basically, the idea behind this is that working with percentages is easier than working with fractions because fractions involve division and division is hard, and a percentage method can therefore be done faster. So I minimized the division involved in figuring out pot odds.
Counting outs is easy. It involves simple addition and subtraction. So count your outs first.
Assuming that you only need to catch one of those outs to make your hand (Backdoor flushes and runner runner straights are both no-no's), the percentage likelihood of catching by the time the river rolls around is easy to find: multiply the number of outs you have by four, and then subtract one if you have eight or more outs (or don't; this isn't that big of a deal). That's the likelihood.
Nine outs equals 35 percent, five outs equals 20 percent.
Now, let's say that you want to calculate it just to the turn. The likelihood becomes outs times two, then add one more percent if you have six or more outs (or, once again, don't). Four outs equals 8 percent, nine equals 19 percent. If you're already on the turn and you want to figure it for the river, do the exact same thing as before.
There is a slight difference between dividing by 47 and 46, but it's pretty much negligible.
In fact, the odds that you'll hit on the river after not hitting on the turn are actually slightly (and I mean VERY slightly) better than hitting on the turn (and by VERY slightly, I mean not enough to justify chasing to the river more). The reason is simply that there is one fewer unknown card in the deck.
From there, it's just a matter of estimating the percentage of the pot that you're being asked to bet. Just trying to keep track of the amount of money already in the pot is the hardest part here, as you'll probably be too busy watching other players' reactions to what's going on to keep a super-accurate tally of cash in the pot.
Not that this matters, as an approximation is generally enough. Round up to the nearest ten dollar mark or whatever, if you want.
And don't worry about getting it super-accurate right away; if the percentage of the pot that you are being asked to bet is obviously higher than your chance of hitting your hand, you should probably fold. If it's obviously lower, you should probably stay in.
If it looks too close to decide on the spot, call time and crunch some numbers to figure out that last percentage.
Want another shortcut? Divide the pot by the bet amount to get x. Divide 100 by x to get your answer. And you remember remainders from before you learned to do long division? They are okay to use.
For example: you're being asked to bet $3 into a $36 pot. 36/3 = 12. 100/12 = 8 remainder 4, which comes out to 8 1/3 percent (divide the remainder by the original denominator to get that fraction).
The remainder part isn't even that important because it's only used to calculate a fraction of the percentage, and so should probably be rounded off anyway. Then take all of that mathematical info, add on the specifics of the situation you're in (for example, you're drawing to an open-ended straight against someone who is probably on a flush draw or vice versa), and make your decision.