I have never seen a Fundamental Theorem of Casino Tournaments spelled out concisely. David Sklansky's Fundamental Theorem of Poker has got me thinking that we need a general one for all casino tournaments. A good Fundamental Theorem of Casino Tournaments could serve as a template for deriving a fundamental theorem of blackjack tournaments, etc. It could also be a reference that casinos could use for determine what players want so they can more intelligently design their tournaments. Here's what I propose. I look forward to your comments and suggestions for improvement. The Fundamental Theorem of Casino Tournaments 1. Luck is defined as the mathematical variance of a game favoring or disfavoring a player. Skill is defined as the ability to employ strategies and make decisions that maximize the utility of favorable luck and minimize the cost of unfavorable luck. 2. The differences between players’ short-term outcomes is mostly influenced by luck. The differences between players’ long-term outcomes is mostly influenced by skill. Skilled players need less favorable luck than lesser skilled opponents to win a tournament. 3. Skilled players should select games that maximize the influence of skill and minimize the influence of luck on the players’ short-term outcomes. They should select games that reward sound strategy and that maximize the number and complexity of decisions. 4. Skilled players select games with lesser skilled opponents to increase the opportunity for profit. Skilled players select games with equally or more skilled opponents only for the purpose of increasing their own skills.

I came up with another rule as I've been pondering this. A mistake is defined as a decision that fails to maximize the utility of favorable luck and fails to minimize the cost of unfavorable luck. Skilled players employ strategies and decisions that induce opponents' mistakes and maximize their effect on outcomes.

The Fundamental Theorem of Casino Tournaments 1. Luck is defined as the mathematical variance of a game favoring or disfavoring a player. Skill is defined as the ability to employ strategies and make decisions that maximize the utility of favorable luck and minimize the cost of unfavorable luck. 2. A mistake is defined as a decision that fails to maximize the utility of favorable luck and fails to minimize the cost of unfavorable luck. Skilled players employ strategies and decisions that induce opponents' mistakes and maximize the mistakes' effects on outcomes. 3. The differences between players’ short-term outcomes is mostly influenced by luck. The differences between players’ long-term outcomes is mostly influenced by skill. Skilled players need less favorable luck than lesser skilled opponents to win a tournament. 4. Skilled players should select games that maximize the influence of skill and minimize the influence of luck on the players’ short-term outcomes. They should select games that reward sound strategy and that maximize the number and complexity of decisions. 5. Skilled players select games with lesser skilled opponents to increase the opportunity for profit. Skilled players select games with equally or more skilled opponents only for the purpose of increasing their own skills.

As to number 5. That has more implications to your new endeavor than BJ tourneys. The dearth of BJ tourneys results in the likelihood of more experienced, more skilled players in competition for an ever shrinking prize pool. As a result you don't get to pick an event that necessarily gives you an advantage. Not all bad as you test and refine your skills against the best. Trolling Poker ring games aptly fits #5, for high stakes poker tournaments bring out the more skilled and more experienced and just plain larger number of participants, increasing variance.

See the article by Greg Raymer on page 33. He gives an article that describes luck and skill as not being zero sum as if on a scale from 1 to 100, but as an intersection of two points on a graph. Very interesting. https://twitter.com/CardPlayerMedia/status/1405958942899937284?s=09