I recently had a conversation with a friend who was visiting Las Vegas. She likes to play video poker and had read the books I had given her. But, she said, most of what was in the book just went over her head.
So, we spent some time chatting about how video poker strategy is developed and why you play certain hands the way you do. I’m not sure if even after we were done, she fully understood everything, but part of my point to her was that she doesn’t have to.
There is no requirement that you understand how an expected value is calculated nor do you need to memorize specific expected values. What needs to be learned to learn the strategy is the order of the strategy table.
There’s an old joke that goes something like this – If you tell people that an all-powerful being created the universe, most will believe you. If you tell them not to touch something because it has been recently painted, most will touch the object because they don’t believe you.
This sort of explains the need to explain how expert strategy was created. You’re welcome to simply believe it, but I’m guessing the majority of the people reading this column are going to still want further proof than to simply take my word for it. In the case of my friend, she might be willing to go with the trust me method, but I’ve known her for nearly two decades.
Ironically, it is frequently easier to explain something with the use of pen and paper as opposed to a conversation around a dinner table. Unless someone is very quick with numbers, they’d rather see the details spelled out in black and white.
One of the quick examples that I gave to her was the case of the four-card flush and the low pair and the four-card straight and the low pair. Her first reaction was to keep the low pair in both situations. I explained how the situations are radically different.
In the case of the four-card flush, there are nine ways to make the flush which pays six, for a total of 54. In the case of the four-card straight, there are only eight ways to make the straight and they pay only four each for a total of 32. This 22 unit difference amounts to nearly 0.5 unit difference in expected value, which is a rather large gap.
Of course, you’re never really comparing a four-card straight to a four-card flush. Rather, you’re comparing each to a low pair. The low pair sits between the two, albeit much closer to the straight than the flush.
This large gap was the segue into the second part of our conversation. Not all mistakes are created equal. If you routinely play a low pair over a four-card flush, you’ll be costing yourself about 40 cents for every dollar wagered. This is not small. This is not even medium. This is disastrous! You turn a net winner into a net loser.
When you consider that about 25% of all four-card flushes are also a pair and that about 2/3 of these will be a low pair, we are talking about a very common hand. More than 3% of our hands are four-card flushes. All in all, we are talking about roughly 0.5% of our total hands. This may sound insignificant, but it simply isn’t.
You’ll get three or four of these an hour, and if you play them wrong, you’ll cost yourself $1.50-$2 per hour if you are a max-coin quarter player. Over time, this will add up to significant dollars.
On the other side of things, if you were to routinely play a four-card straight over a low pair, the gap there is only about 0.1 or one quarter of that of the flush/low pair situation. You still don’t want to be making this mistake often, but it will cost you only 35 -50 cents per hour.
The point I was making to my friend was that if even clearing up this one mistake in your strategy can greatly increase your payback. Yes, expert strategy payback is calculated based on perfect play, but we are all human and prone to errors. If you make an occasional mistake because you misread a hand, it will cost you, but an error rate of 1 in 1,000 will be unlikely to cost you much.
If you are making a repetitive mistake because you didn’t learn the entire strategy table, it will depend on which parts you didn’t learn. I, obviously, suggest you learn the entire table.
If dealt an off-suit JKA and choose to keep all three instead of just the JK, the cost to your bankroll will be far less than misplaying four-card flushes. The hand is rarer and the difference in expected values is simply not as large. The impact is a function of both of these.
Elliot Frome is a second generation gaming analyst and author. His math credits include Ultimate Texas Hold’em, Mississippi Stud, House Money and many other games. His website is www.gambatria.com. Contact Elliot at [email protected].