The ultimate "truth" of poker is the answer to the question, does your strategy defeat their strategy? (Or in other words: if you played forever, who would come out ahead?) The challenge is to work towards this truth using the hands you play as evidence. Steps in that direction:
Let's take a hand as an example. You're playing 1/2 Hold'em with 50 big blind stacks. It's folded to you in the cutoff and you open KK to $6. Button and small blind fold and big blind raises to $18. You go all-in for $100 and he calls with JJ. He hits a Jack and wins the $201 pot (the $1 is from the small blind). You lose $100. Raw cash results aren't meaningless -- given enough hands, they will begin to approach your expected value in the games you play -- but "enough hands" here means many thousands. In the short term results can be, of course, very misleading.
2. Expected value-adjusted results
This is a simple way to account for one kind of luck. Whenever all the money goes in you calculate your expected value and consider that the result of the hand. In our example hand, all the money went in pre-flop. KK beats JJ 81.5% of the time, so our expected value is .815 * 201 = 163.8. Subtract the $100 we invested, and that means we made $63.80 on this hand. We've stripped away the luck element that kicks in after the money goes in the middle, but there's still a lot of luck in how the cards are dealt out to begin with. We were lucky to get dealt KK, the second-strongest starting hand, and even more lucky that our opponent held JJ, the fourth-strongest. If he had AA we would have gotten all the money in way behind; if he had 72 he would have folded and would have just won the blinds.
3. Our hand v. their range
The concept of a range is probably the most important idea in poker strategy. A range is all possible hands you can hold given your actions. In the example hand, the big blind had JJ, but let's say his range for raising and calling a shove there is pocket pairs tens and better, ace-king, and ace-queen. Our equity against that range is 67.6% -- still ahead, but not by as much. His range still includes JJ, as well as QQ and TT, all of which have only 18% against KK. But he can also have AQs (32%) or even AA (82%). (You can download a free tool for calculating these numbers at pokerstove.com). According to these numbers, our profit for the hand is .676 * 201 -100 = 35.88. Not surprising, given that we had such a good hand.
4. Our range v. their hand
Same concept, but flipped around. Now we'll calculate the equity of our range against his actual hand. Let's say our range for opening the cutoff then shoving over a raise is all pocket pairs, AJ+, and all suited aces. I won't get into the reasoning behind that range, or whether it represents a good strategy right now; but if you're wondering why our range includes so many more hands than the big blind's, it's because we pushed all-in, so our range includes bluffs, but he called an all-in bet, so he doesn't have any bluffs. Anyway, that range has 35.9% equity against JJ. According to this measure, our expected value from the hand is .359 * 201 - 100. So we lost 27.84 on the hand. This makes intuitive sense: in actuality we held KK, the second-strongest starting hand in Hold'em, but our range is comprised mostly of weaker hands. It also suggests something that will be no surprise to experienced players: his strategy of getting it in with jacks 50 big blinds deep is a winning play, even though it didn't appear to work out well in the actual hand.
5. Our range v. their range
Using the ranges described above, the equity of our range against his range is 39.3%. So when all the money goes in, we lose an average of .393 * 201 - 100 = -21. This still isn't the whole story though, because both sides had several opportunities to fold (or just call) along the way. In particular, he had to call our all-in bet to get to showdown. So while we are generally behind when all the money goes in, we should be making money on the hands that don't go to showdown because sometimes our bluffs will work and we'll take down the pot. Whether or not that compensates for the money we lose at showdown depends on just how often he's folding. If he's never folding, we should shrink our range to just the strongest hands. If he's folding a lot, we should expand our range to include more bluffs.
6. Reciprocality: a useful shortcut
This concept doesn't fit neatly into the hand range framework described above, but it can be useful for getting an idea of whether or not you're making money. (Reciprocality isn't a real word, but while reciprocity is, it doesn't mean the right thing, so there you go.) The basic idea is to ask what would happen if you and your opponent switched places. In the example hand, as long as we're both reasonable players, we're probably getting all-in here. Any time you would do the exact same thing with places reversed, no theoretical money changed hands, despite appearances. It's only when your strategy differs from your opponent's that you can make money.
