I'm discussing with Paul Harris (radio personality and avid poker player) a point about the probability of hitting the high hand promotion at a low stakes table compared to a high stakes table.

In a recent blog post by Paul ( http://www.harrisonline.com/poker-st...n-new-england/ ), he stated:

"...Twin River doesn’t offer high-hand jackpots every half-hour, but that means they also don’t take a rake for it, which is fine with me, since those jackpots tend to go to people playing at the lowest limits, where there are more tables, and thus the chances of hitting a big hand are more likely."

I made a comment that "his statement about the high hand promo going to lower limit players reminded me of when people say you should drive to Chicago (I'm from central Illinois) to buy your quick pick lottery ticket because "all the winners" are from Chicagoland. The chances of him hitting a high hand promo at a higher limit table and me at a low stakes table on a given day, would be the same mathematically, no?"

He replied "No, because there are so many more low-stakes tables in most poker rooms. In St. Louis, there might be only one 2-5NL or 5-10NL game running, while there are a half-dozen 3-6L and 1-3NL games going. That's why the players voted years ago not to have the extra dollar raked from the 2-5/5-10NL games for the bad beat (and are thus ineligible for the jackpot and high hand bonuses)".

My response was "I guess we'll agree to disagree. Say there are 9 low stakes tables with 10 players each and 1 higher stakes table with 10 players. A total of 100 players. I agree that the high hand is more likely to occur at a low stakes table but my odds at a low stakes table would be the same as your odds at a higher stakes table, one in a hundred.

Granted, that one player in a hundred is more likely to be sitting at a low stakes table, but the individual odds for each player would be the same. In an infinite numbers of trials, each seat in the room would be dealt the high hand the same number of times. Nine times out of ten it will be at a low stakes table but the likelihood of a particular seat hitting are all the same".


While there are valid reasons for players to vote to decline participation in high hand promos, I guess my point is:

Declining to participate because you think you have less of a chance of being dealt the high hand at a high stakes table in a room with a disproportionate amount of low stakes tables, is not a valid reason.

Am I right?

It's not going to be literally identical because of hands/hr, looseness leading to nonsense straight flushes with 52s, etc, but his argument is stupid and yours is basically fine. The vast majority of the reason it's won more often by low-limit players is that low-limit players in aggregate are dealt more hands to try to win it with.

If 9 of the tables have blue felt, and one table has green felt, 90% of the HH winners will be from the blue tables, but I doubt most people would suggest that playing on a blue table increases the odds of hitting the HH.

Don't be ridiculous! But I suggest that the green table doesn't participate in the high hand jackpot, of course.

Exactly.

Though if play is slower at the higher stakes table (because people are thinking more and more carefully weighing up their decisions because of the money involved) than at the lower stakes tables then the probability skews to playing at the lower stakes table....because your chance is not relative to how many other players there are but to how many hands you play relative to the total number of hands played by all.

Also there may be more hands that go to showdown on lower stakes tables (more calling stations). Hands that don't get to see all 7 cards are less likely to be the biggest hand....but then again: if lower stakes go to showdown more often that means their hands may even take longer than those at high stakes (even though these play more carefully)...


...it's an enigma wrapped in a conundrum wrapped in a mystery....I'm sure I can come up with another few things that would skew the distribution this or that way. (LAGs get more chances than TAGs and whatnot...)