Facebook is usually a great place for me to get ideas for columns. Within any given week, the odds are someone has posted something absurd enough for me to use as a segue into a topic. This week, I had at least two of them. As they were loosely related, I'll use them as my lead in. One was about a study done about homeopathic medicines. Supposedly 68 different 'common' ones were studied and they did nothing significant to help the condition. The other was about the anti-vaccine movement that links vaccines to autism. This is not a political column, so I'm making no statement about either of these two issues (although I am willing to go on record as saying both of my kids had their vaccines). What I noticed in common for these topics was the number of people who simply dismissed the science behind the facts. Someone had a bad experience with a prescription but a good one with some homeopathic remedy so this becomes 'proof'.
As I read that, in that instant, I understood how people walk into a casino and play by hunches. I'm not an expert in chemistry, so I can only do my best to read some studies on medicines and vaccines and make the most informed decision I can. But I AM an expert at casino math. When I play, I don't play hunches. I play according to the science. With the exception of card room poker which involves bluffing, every other casino game is based on the science of math.
If I'm playing video poker and I'm dealt a 4-Card Straight and a Low Pair, I don't decide which way to play by what I think the draw cards will be. The casino doesn't decide to go on a streak of Straights! Each card is dealt randomly. When I hold a 4-Card Straight, I have 8 out of 47 chances to pull that Straight. PERIOD. It doesn't matter if in the moment I blinked I thought I saw a card that would complete the Straight. It doesn't matter if the last 8 hands were all Straights. It doesn't matter if the last 25 times I had this draw I didn't get a Straight, meaning it must be 'ready' to give me one. The probability of hitting the Straight is EXACTLY 8/47.
In similar fashion, the probability of winning if I go with the Low Pair is fixed as well. There are 16,215 possible draws. Each has the exact same probability of occurring. Of these draws, 45 will result in Four of a Kind, 165 will result in a Full House, 1854 will result in Trips and 2592 will give us Two Pair. The remaining 11559 will result in losing hands. It does not matter how we did during the last 100 Low Pairs we held. It does not matter that this time you are throwing away a 4-Card Straight. It doesn't matter what 3 cards you THINK will be drawn. All that matters is the math behind this hand. The math tells us that we'll win about 29% of the time. This compares to 17% of the time for the 4-Card Straight. But, most of the wins (all but 210 of them or about 2%) will be for LESS than if we win with the 4-Card Straight.
Winning percentage doesn't really matter either. Would you rather win 50% of your hands at even money (which means you would break even) or win 0.01% of your hands and hit a million dollar jackpot? The goal is to win money. For this, we turn to the science which tells us that if we hold the 4-Card Straight, we can expect to win back about 68% of every dollar we wager. If we hold the Low Pair, we can expect to win back about 82% of every dollar we wager.
If you face this situation once, it is completely impossible to get the expected value as a result. The only possibilities are that you lose, you win 2 (Two Pair), 3 (Three of a Kind, 4 (Straight), 6 (Full House) or 25 (Four of a Kind). But if you face either of these situations, you'll find that after only a couple thousand hands that you'll very quickly approach the theoretical expected value. Given that nearly 30% of your hands will be a Low Pair, this means that it should take only 10-20 hours of play before your Low Pair true payback begins to get very close to the 0.82 theoretical expected value. 4-Card Straights aren't quite as common, so it might take 100-200 hours of play. If you Play video poker for only a few hours a year, it might take a while. If you play regularly, it might take 6 months to a year.
In the short run, you might be able to 'guess' correctly and play hunches and come out ahead vs. using the strategy developed by the math. But, in the long run (which is not really all that long), you can only do yourself and your bankroll harm by playing these hunches. The games were designed by mathematicians. They were tested by mathematicians. They were approved by mathematicians. If you want to give yourself the best chance to win, you'll listen to that mathematician when he tells you how to play.