Managing human error in casino strategy

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One of the criticisms of almost any gambling strategy is that it requires you to play “perfectly,” and this is not realistic of a human.

There is some truth to this.

For sure, the theoretical payback can only be achieved if you play the strategy perfectly. Sometimes, the strategies are not perfect. They have already been altered to give a human a reasonable chance to play the strategy presented perfectly.

For example, in the game of Ultimate Texas Hold’em, the strategy for the 2x Wager consists of about 10 or 12 rules. This can already prove challenging for a human. If a complete computer-perfect strategy were presented, it would likely have hundreds of rules. No human, short of Rain Man, would be able to play this even close to perfect.

In the case of UTH, it is very difficult to put a precise impact to the payback based on this difference. A complete computer simulation of every hand would take weeks or months to run. From what I have read, there are some analysts who have attempted this and the impact seems to be about 0.25% to the payback.

I commend these analysts for undertaking the work, but to date, I have not seen any strategy based on this work. So, we don’t know with certainty just how insanely complex it would be, not only to play, but to even figure out what it would be.

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In a similar fashion, the impact to a game like video poker is far less. The strategies I present for video poker can be slightly simplified. They do not take into account what are called Penalty Cards. These are cards that would have value if you kept them, but not enough to be worth keeping most of the time.

There are limited cases where these cards might change the strategy you want to follow. Generally speaking, the overall impact to the payback of video poker is about 0.01 to 0.03% of payback if you follow the more complex strategy. But, as the strategy gets more complex, the likelihood of human error goes up.

This brings me to the second half of the equation. How much might human error impact our payback? There is no one-size-fits-all number for this. We need to break this down into two categories.

The first is errors of strategy knowledge. This is where you make a repetitive mistake because you don’t know the strategy. If you repeatedly keep a 4-Card Straight over a Low Pair, the impact will add up. Given a particular error of this type, an approximate impact can be calculated using the frequency of the hand in question and the difference in expected value between the right way to play the hand and the way the Player actually plays it.

Sometimes, the expected value difference is only 0.01 or 0.02 and the hand in question is relatively rare. In this case the impact would be minimal). In the case I mentioned a moment ago, the hand in question is not nearly as rare and the expected value difference is about 0.14.

So, it is not going to make a 2% difference in payback, but it might make a 0.05 or 0.10 difference. If you make several errors of this type, it will add up. If you throw Low Pairs to keep 2-Card Royals, you might cost yourself a lot more.

Not knowing the strategy creates roughly the same impact as simply ignoring the strategy you know. In Ultimate Texas Hold’em, observation tells us many Players are timid about making the 4x wager.

Some of these Players may be aware of when to do it, but simply are nervous about putting $20 out on their base $5 wager on hands they see as marginal. This impact can be significant, increasing the house advantage four-fold and more depending on just how timid the Player is.

The second category of error is the simple case of not recognizing a hand. If this is a repetitive issue, then the impact becomes more similar to not knowing the strategy. If you don’t recognize a 5-6-7 suited as a 3-Card Straight Flush, this amounts to the same as not knowing how to play a 3-Card Straight Flush.

If, however, this is a case of you’ve been playing for 2 or 3 hours and you simply miss a hand in which you had a Pair of 7’s and instead play the one High Card you had, this does not throw the balance of the universe into question.

On a theoretical level, you’ve likely not even lowered the payback by 0.01% if you’ve made one or two mistakes over a 3 hour period. If you are making mistakes more frequently than this, it is probably a sign to stretch your legs.

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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].

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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