How to Judge a Casino Tournament

Probability theory governs whether or not tournaments are good deals. Happily, you don't have to be a Nikolai Ivanovich Lobachevski to do the math. No entry fee? Good! An up-front charge but all or most of the tariff returned in prizes? Almost as good! And, it's easy to figure since participation and award details are stated in advance. Or you can ask.

Say a casino charges $350 and limits entry to 200 players; the kitty is $70,000. If the entry fee includes a hotel room and some goodies, allow for what these items are worth to you. For instance, imagine the event is packaged with a room for two nights, a cocktail party, and a banquet. You might deduct $125 from the $350 to get $225 and multiply by 200 to get an effective $45,000 pot. Next, add up all the prizes. Finally, compare the outflow to the inflow. The less the casino keeps, the better the deal.

A tournament may be a good bet but still one you should shun. Or, pundits may pan the percentages but a competition may make sense for you anyway. These decisions are in the domain of utility, not probability, theory. The primary criteria are how trifling you view what you must risk to take part and how grand you fantasize the prize. A secondary element involves the odds you have to fight to be a winner. And third are intangibles like camaraderie, opportunities to form new friendships, and illusions of grandeur.

Some tournaments have no entry fees and don't require players to buy-in at the tables; it's all funny money. But winners collect bona fide bucks. Casinos use these "invitationals" to thank high rollers for loyalty, encourage future patronage, and get current business through side action. There are reasons solid citizens might decline to enter such tournaments, like having to wear clown costumes and honk horns while playing the Jamboree Jester slots, but - even there - refusals would be few.

More often, entrants gamble with their own money. So, while the meet may be a sensational deal - the entry fee is zero or the prizes exceed the gate - add up the mandatory bankrolls for each round. You can sometimes lose most of your buy-in and still progress to the next level. Can you justify spending this much? If not, steer clear of the affair.

What about entering tournaments in which the house skims an exorbitant profit off the top? Assume you're comfortable with what you might have to spend. Then consider the potential haul, the field you must beat to win it, and factors like your proclivities for schmooze and pandering. Your personal priorities may well warrant what it costs to participate.

Here's what I mean. Picture a tiddly-winks tournament with the following parameters.
entry fee: $750
number of participants: 101
grand prize: $38,500
four consolation prizes (each): $3,500
total buy-ins for three rounds: $2,750

Statistically, this is a scenario for suckers. The casino is garnering $75,750 and giving back $52,500. But you can afford the $3,500 it may cost, often play tiddly-winks with this high a stake, covet the $38,500 payout, and know you'll never make as much in a normal game. Under these conditions, utility may dominate probability in an arguably rational decision to enter.

Interestingly, a tournament of this type might be less alluring if the casino improved it technically, paying out all the entry fees and awarding lots of prizes, but none over $7,500. Conversely, it might be more appealing if the casino made it theoretically worse, doubling the number of participants and lowering the total return but raising the big score to something like $100,000. In fact, everyone might say you were stupid to enter a tournament under such conditions. Unless, of course, you won. As Sumner A Ingmark, the poet of providence, postulated:

The paths that lead to fortune and glory,
Are only clear a posteriori.