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Expected Value and the Anti-Peter Principle

26 June 1999

All professional gamblers rate games according to the "expected value." This concept, in fact, is so important to gamblers that, as with Yahweh of old, you rarely hear the word spoken — just the initials: E.V.

No professional would ever place a bet on any game if he or she didn't know the E.V. was positive. Professional gamblers don't gamble; they only bet on sure things. There are often arguments among pros about how to figure out the E.V. Pros want to know what the precise E.V. is of a game, whether the risk outweighs the E.V., or whether the E.V. of one available game is higher than that of another game. These arguments arise from the fact that the factors that determine the E.V. of a game are based on assumptions that are less than perfectly accurate.

These days, a blackjack player can easily run off a computer simulation of a few million, or a few hundred million, hands to test his system under very precise game conditions, thus arriving at the E.V. of that game. But real world conditions never match computer simulation conditions. If I tell my computer to deal 75 percent of the cards between shuffles, that's precisely where the electronic "cut card" will be placed to signal a shuffle. Human dealers don't cut with this precision, and as most knowledgeable players know, a five percent change in the actual level of penetration will have a drastic effect on the E.V.

Likewise, my computer is going to play my counting system perfectly. It won't ever make a dumb mistake, lose the running count, miscalculate the true count, forget a strategy index number, purposely misplay a hand because the pit-boss is watching, not catch a mispayment on a bet, or do any of dozens of other things that happen in real world casinos, but never in computers.

For gamblers in games other than blackjack, figuring the E.V. is even more difficult. Tournament players, poker players, sports and horse bettors, must always factor in the skill level of the competition — something blackjack players don't have to consider.

Many years ago, at one of the University of Nevada Gambling conferences, noted author Stanford Wong presented a paper in which he "proved" that a blackjack player using the Kelly Criterion would win at only half the rate of his expected value. If this sounds like a contradiction of what the term "expected value" means, it struck author Peter Griffin as illogical also. Griffin published a rebuttal to Wong's paper at the same conference, which essentially stated that the expected value of the expected value is the expected value.

I know many pro gamblers who would refute this Gertrude Steinism on empirical evidence. Keith Taft, notorious computer/electronic whiz whose ingenious devices plagued the casino industry for many years until the anti-device laws were first passed in Nevada and New Jersey in the mid-80s, told me that based on his teams' results with their shuffle tracking computers, "Your expected value is usually about half of what you estimate it to be."

"Why is this, Keith?"

"I don't know, Arnold. I just know that the experience of our computer teams over the long haul — and I'm talking about many teams over years of play — was to win about half of what we predicted based on our computer simulations."

I believe that what is at work in the world of professional gamblers is a principle that has been known in the business world for decades as the "Peter Principle." This principle states that each person in a corporation will rise to his own level of incompetence, thus ensuring that the corporation will always under-perform its expectations. As Lawrence J. Peters postulated in 1969 in his book of the same title, people who succeed in the corporate world are continually promoted to positions of greater authority until they reach the level where they no longer excel — and that's where they stay. Every position is thus ultimately filled by a person who under-performs.

Professional gamblers, despite their hard-nosed image, are in fact the world's most die-hard optimists. These are people who are willing to bet everything they have on themselves. Blackjack players continually try to learn more complex systems so that they can beat tougher games, until their mental and psychological talents "peter out" in games that are beyond their capacity. And that's where they stay. There are a lot of big money blackjack players who make less money with black chip play than card counters with less talent make with green chip play. The black chippers resign themselves to smaller spreads, more camouflage, and shallower deck penetration in order to prove to themselves that they can succeed at that level.

Poker players, likewise, continue to go up the ladder until they find themselves pitted against players they can't easily beat, and that's where they stay. Poker players who could make a comfortable living in $20-$40 games, struggle to survive in $100-$200 games.

So, here's a suggestion for all professional gamblers that could earn you more money this year than any other strategic play you might try: take one step down! I call this the "Anti-Peter Principle."

If you're playing blackjack, spreading from $100-$600, move down to green ($25 chip) play and see what happens to your actual win rate. Do you find you can spread more aggressively? Use less camouflage? Play with less emotional involvement?

And simplify your system! If you're fighting with a multi-level count, attempting to side-count aces, using a hundred strategy indices — give yourself a break. Go back to the simple hi-lo count. Forget the ace side-count. Toss out most of those rarely used index numbers. Play fast with confidence and aggression. Do you find that you make more money even at lower stakes?

If you're a poker player, go down a level to the games where you know you're the best player at the table, where you know your opponents are all struggling at their own level of incompetence. Don't you find you make more money even though the pots are smaller? Are you playing this game for the "image" of being seen as a contender with the big players? Or, are you in it for the money?

A number of gamblers have recently told me that they were really hoping to move up a level to bigger games. I think most might be wiser to either stay put, or move down a level into bigger profits.

Copyright © 1999 by Arnold "The Bishop" Snyder

Arnold Snyder
Arnold "The Bishop" Snyder is the author of "Blackbelt in Blackjack" and the editor and publisher of the Blackjack Forum.

Arnold Snyder Websites:

Books by Arnold Snyder:

Blackbelt in Blackjack
Arnold Snyder
Arnold "The Bishop" Snyder is the author of "Blackbelt in Blackjack" and the editor and publisher of the Blackjack Forum.

Arnold Snyder Websites:

Books by Arnold Snyder:

Blackbelt in Blackjack