[CaptainNurple]

(mods: if you think this fits better in the poker theory forum, please move it there)

Perhaps this has been discussed before, if so feel free to post links, but this seems like a fun problem to me:

1) Given a 10-handed Hold 'Em table (or whatever constraints you want), how large is the complete set of every possible scenario?
2) Based on this number, estimate the likelyhood that "everything" has happened in Hold 'Em in the history of the game. Or, alternately, estimate the average length of time required for "everthing" to happen, stating your assumptions (e.g. average hands per hour, one table versus all the tables in the world-how many?, etc)

Another way of thinking about this problem is to pick any possible scenario, (e.g. pocket 2's versus pocket 7's, flop of A27, turn is a 2, river is a 7--including all suits and their distribution) then wonder if it's ever occurred. Then extend that to include every possible scenario.

What's interesting to me about this is that you can easily calculate the probability of any one weird/unlikely event, and for isolated events the chances seem pretty good it has occurred at some point in the past. But since each event in isolation seems likely to have occurred in the past, that would seem to imply that everything has occurred. But that seems less likely, and complicates matters severely, in ways I haven't entirely thought through, and I'd be curious to hear what people think.

For example, the "human" factor hugely complicates things, because for "everything" to have occurred, many people would have had to do irrational things. This, more than anything, makes me think that "everything" has probably not yet occurred.

Nevertheless, even if "everything" hasn't occurred, there should be a way to estimate how long, on average, it should take to occur (using something like "table hours" as a base unit, with one table hour representing a predetermined number of hands).

And yes, this is useless to our poker skill.

But sometimes useless is fun [img]/images/graemlins/grin.gif[/img]