Simplifying expert strategy to work for humans not computers
January 30, 2018 3:10 AM
by Elliot Frome
One of the complaints of utilizing a strategy that requires playing games properly is the notion it requires computer perfect strategy and humans are simply not that perfect. There is obviously some truth to this. Humans certainly are not perfect.
There are two aspects, though, to how this concern can be interpreted. The first is sometimes the strategy is so complex a human could not possibly play perfect strategy. The second is even where the strategy is easy enough for a human to learn, he will still make some form of mistake.
Let’s address the first variant. I believe I have fully acknowledged this in the past and that is why Expert Strategy is called Expert and not Computer Perfect. Sometimes, they are one and the same. Sometimes, there are very minor differences. And sometimes, we clearly need to simplify the strategy to have any hope a human can follow it. For example, in Three Card Poker the known strategy is play any hand Q-6-4 or higher. This is both Expert and Computer Perfect Strategy.
In blackjack, our strategy is nearly perfect. First of all, it doesn’t account for any counting of cards, but more importantly, we lump all the hands of a certain rank together. If you have a Hard 16 vs. a dealer 2, you should stick. But sometimes, if we were to break the strategy down further, we would find the player should do something different. So there is a subtle difference in the expected value of a 9-6, Hard 15, vs. an 8-7, vs. a 3-5-4-3 Hard 15.
The most common blackjack strategies are generally called Basic Strategy because it doesn’t take all these subtleties into account. While some players choose to take it to this level, it is generally felt the vast majority of players would struggle if they had to go down to this level of detail. We find the same concept in video poker with penalty cards.
Our strategy table doesn’t take into account which cards have been discarded. Sometimes, this can make a slight difference in the Expected Value and actually change how the hand should be played. But, remembering the 30-40 different lines on the strategy table can be challenging enough for most. Thus, Expert Strategy doesn’t bother throwing a bunch more lines at you.
In a game like Ultimate Texas Hold’em, I had to simplify the strategy greatly to get it to anything a human can play. Even then, I think what I deemed Expert Strategy is probably too complex for most and would need to be simplified for the average player. With this, we need to understand that simplifying inherently means mathematically inferior. It is not possible to create a strategy that has a higher payback than a computer perfect one or that strategy would be the computer perfect one.
When I’m writing about a game, I have to make a somewhat subjective decision about how much to simplify at what cost. In the case of blackjack or video poker, you might be giving up 0.01%-0.03% of payback. In Ultimate Texas Hold’em, a computer could probably play at a full 0.25% higher than a human playing Expert Strategy and probably 0.5% higher than one playing a more simplified strategy.
The tradeoff is the ability to adhere to the strategy. I don’t think remembering Q-6-4 should be beyond anyone’s ability. But, I’ve sat a table and heard people remark how playing Q High is good enough. True, there is not a huge difference in payback between the strategies. But is remembering the 6-4 part of it really that taxing on the human brain? I don’t think so.
In blackjack and video poker, is earning an additional 0.03% in payback worth adding complexity to the strategy? This is a decision you have to make on a personal level. Do you want to remember a half-dozen or dozen exceptions to the basic hands in a strategy table to earn this extra payback? You have to balance this out by the risk that by adding these rules you might be more likely to make a mistake than if you didn’t bother with them.
That brings us to the second type of human error. This is one where we know we have picked a strategy that might be less than computer perfect, but for a variety of reasons, we don’t adhere to it while actually playing. That half of this topic will have to wait until next week.