Hi all,

I was just in the midst of some musings about casino economics and thought I'd stop by and ask for some thoughts.

I once heard (possibly on these boards) that casinos have a tendency to be very risk-averse, and that some analysts would argue they ought to be less so. I'm thinking in particular about casino-wide betting limits. At my local casino, which is quite large, and attracts a lot of international play, I believe the maximum bet is $300,000. I'm not 100% on these details, but that's what I remember hearing, and also that it was reduced from $1 million a few years ago. I think this applies to Baccarat, with Blackjack having a lower maximum. To put this into perspective, this is at a store where yearly profits are of the order of $300 million.

Now, one purpose of such maximums is to limit the casino's potential exposure to cheating or advantage play, at least in theory. In practice, I imagine if an AP had the same bankroll as a casino, the correct advantage play would be to open a casino, rather than playing at one, so the AP's max bet is likely to be the limiting factor, not the casino's. Still, I'm no expert, and I'd love to hear some other thoughts on this.

The other (probably more significant) purpose of an absolute max bet is to limit the casino's exposure to variance. Obviously no casino wants to wipe out their yearly profits by accepting a single enormous wager and losing. So I want to ask all of you, what is the correct size for a casino-wide betting maximum? What factors affect it, and how would a casino correctly calculate it? And is it true what I heard? Do casinos tend to incorrectly set this value too low?

Here's what my intuition suggests so far: a big casino like the one I described accepts thousands of bets every day, and from them it makes a very consistent profit. It also accepts very large bets, and if a few go the wrong way, the profits for the day or week could be eliminated. This may be viewed as an unacceptable outcome by management, or investors, but probably isn't that bad in reality. Is it possible that the replenishability of the casino's bankroll is being overlooked? After all, the low- and medium-stakes bets are so numerous that they must show a very consistent profit on a daily or weekly basis. As long as enough money is kept in reserve to always be able to accept these bets (and fund new capital works, and self-insure against natural disaster, and whatever else casinos need money for), isn't the rest of the casino's bankroll more or less a suitable playground for extremely high-action risk-taking, safe in the knowledge that there will be more money to play with next week, month or year, and that the casino is sure to win in the five- or ten-year long term? If so, how much higher could the maximums safely be set? Obviously there are lots of unknown variables, but I'd love to hear even very qualitative responses.

Thoughts? Other examples?

Lastly, if anyone has a good grasp of the theory of table maximums, I'd be curious to hear more about those, too. I recently tried to google an explanation of the reasoning behind table maximums (other than the obvious relevance to card counting in blackjack) and all I could find was the repeated assertion that table maximums are not put in place to prevent progression betting systems. Apparently lots of people think that they are. Huh.