Perfection vs ‘good enough’ both sensible when gambling

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Recently, while my teenage son and I were debating something, he responded with “perfection is the enemy of good enough.” My initial response was to shoot back “good enough is the enemy of perfection.”

Since this highly philosophical discussion, I’ve given both of these phrases a lot of thought.

I’m very well aware that I am a perfectionist who was raised by a perfectionist. If you brought home a 99 on a test, my father wanted to know why you didn’t get a 100. If there is such a thing, however, as a realistic perfectionist, I think both my dad and I would qualify.

We strive for perfection, but also realize that it is often not realistic to truly attain it all the time. I think this is why I found the aforementioned quotes to be both interesting and a little befuddling.

My initial reaction that good enough is the enemy of perfection goes to my basic notion that we should always strive to be perfect. Over the years, I’ve been asked many times regarding the strategy for Three Card Poker and if it really matters if you go with Q-6-4 or just Q-High. The impact to payback is barely noticeable.

You might play for hours before getting a hand that plays under one strategy but not the other. Yet, the notion of settling for the easier Q-High frustrates me so. Clearly the strategy is “good enough.” But, is remembering Q-6-4 so hard that you one needs to go with Q-High? To me, this is a case where good enough became the enemy of perfection.

There were times my father’s work on video poker was criticized (mildly) by other analysts for being less than perfect. On one hand, my father was not prone to doing things less than perfectly – especially math work. On the other hand, he taught himself how to program a computer at age 60, so this was not totally his comfort zone.

In a nod to that realistic perfectionism I mentioned earlier, my father’s strategies for video poker were not designed to be 100% perfect. They were designed to be played by humans. And, not a bunch of rocket scientists, but the masses.

The process that my father used to analyze video poker was rather similar to the same one I use, which is most likely not all that different from the ones created by anyone else. We all have different degrees of shortcuts we use to speed up the process but the basic idea is the same.

We look at each of the 2,598,960 possible initial 5-card deals from a 52-card deck. We then analyze each of the 32 possible ways to discard and review each of the myriad ways to draw to each of these 32. Whichever of these 32 ways results in the highest expected value is the proper way to play the hand.

The calculation to do the above is absolute and assuming no error in the process will be 100% accurate. In other words, it will be perfect.

So, in a perfect world, a player could sit down at a video poker machine, press the deal button and then enter the five cards he was dealt into an app on his phone, which would run the process I just mentioned and tell him exactly which cards to discard.

Unfortunately, the casinos are not too keen on this idea. In fact, I was recently sitting at a blackjack table and pulled out my phone to check e-mails while the dealer was shuffling and got reprimanded. I knew you couldn’t use such devices at the table, but I assumed this meant while the game was in progress, not while waiting for the shuffle!

So, sitting at a video poker machine with your tablet in your hand will probably not be allowed. Because of this, the next best thing is that the results of analyzing all of these hands need to be summarized a bit. This is what we call a strategy table that lists the rankings of all the hands in order of their expected value.

Certain hands become essentially “exceptions to rules” when we try to summarize them. These exceptions could be listed as their own rows on the strategy table, but what would the impact be if the strategy table grew to be 50 or 60 rows instead of the usual 35 or so?

By ignoring these exceptions we cost ourselves maybe 0.01 or 0.02% of payback, but we greatly simplify the strategy table, thus reducing the probability of errors.

In this case, my son was right as perfection could be the enemy of good enough. My father could have put together a perfect strategy table, but if learning it became that much harder so that the likelihood of errors increased to the point where an average person would lose more in errors than he would gain in playing “perfectly” – would this still really be ‘perfect’?

At the end of the debate, it would appear that my father had already resolved the issue for us – and we were both right!

 

About the Author

Elliot Frome

Elliot Frome’s roots run deep into gaming theory and analysis. His father, Lenny, was a pioneer in developing video poker strategy in the 1980s and is credited with raising its popularity to dizzying heights. Elliot is a second generation gaming author and analyst with nearly 20 years of programming experience.

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