Marriage in the U.S. does not have a "positive expectation" because more than half end in divorce. Just as marriage is a gamble, the vast majority of games in Vegas, do not offer you a positive expectation of winning. But believe it or not, there are some exceptions.
If you flipped a coin and gave it away when it landed on heads and won another coin when it landed on tails, your expectation would be 0. Half the time you'd win, and half the time you would lose.
But if you lost 2 coins when it landed on heads, and only won 1 coin when it landed on tails, you'd have a negative expectation. You would win 1 coin 50% of the time and you'd lose 2 coins 50% of the time. The calculation of expectation works like this:
You multiply the probability of winning times the amount of each winning bet. Then you multiple the probability of losing times the amount of each losing bet. Then you subtract one from the other, and you have the expectation for the bet.
In the coin flipping example, you'd multiply 50% times 2 coin in the losing category, and you'd get a negative coin. Then 50% times 1 coin would be half a coin. So your overall expectation for each bet would be to lose half a coin.
On the other hand, if you WON 2 coins every time you landed on heads, and you only LOST 1 coin every time you landed on tails, then you'd have a positive expectation of half a coin per flip.
If you're smart you do it by calculating the expectation. If you have two pair, then you have a 100% chance of winning say 5 coins. But if you drop 2 cards to try to draw to a royal flush, you might only have a 5% chance of winning, but you're going to win say 4000 coins. That's an expectation of 5% times 4000 coins, or 200 coins vs 5 coins.
The percentage that I used in the above example just came off the top of my head, but it's an example of how you should be thinking about expectation, and it's an example of how you should be thinking about video poker strategy. What decision will give me more of a positive expectation?
Each winning and losing hand in video poker has a probability that you'll hit it. When you multiply all the winning possibilities times the amount you win when you hit them, then subtract what you lose when you don't hit a hand, you get the overall expectation for the game.
And some video poker games, if played perfectly, have a positive expectation. The main factor affecting this is not the probability of hitting a given hand, since that's relatively constant. It's the amount you get PAID for hitting the hand that makes the big difference.That's why a 9/6 jacks or better game is so much better than an 8/5 jacks or better game. And that's how a deuces wild with a full payback table has a positive expectation: the probability of hitting certain hands multiplied by the payout exceed the probabilities of losing times the amounts lost.
You're probably thinking that this sounds like a lot of complicated math, and it isn't worth learning. But look at it this way - how do you know whether to break two pair to draw to a better hand or not?
I'm not a mensa guy. But I am smart enough to take advantage of the positive expectation games, simply by following the map drawn by math/computer guys. Like riding a bicycle, it may seem difficult at first but with practice, it becomes automatic.
If you're interested, you can learn deuces wild video poker strategy here.
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