A poker player tries a different game, and wins (non-grumpy content)

I hadn't done anything with my UltimateBet account in a long time, so decided to see what was happening there. Sometime earlier this year, as it turns out, they added Roshambo (Rock Paper Scissors) to the games you can play. I had to try it out.

I went for the $0.50/match table (match is best of 3 throws). I knew that I would outthink myself and second-guess, third-guess, and fourth-guess myself into utter insanity if I actually tried to analyze what an opponent would throw and then take counter-measures. So instead I opened Excel, did a one-cell spreadsheet of =RANDBETWEEN(1,3), then hit F9 before every throw. This would generate a randomly selected integer between 1 and 3, and I would go with that, no matter what I thought my opponent would do. (After I got tired of switching back and forth between applications, I had Excel print out a list of 1000 of these random digits. It's easier to just run my finger down the page, but the effect is the same.)

24 hours later, I've done surprisingly well. I've made $11 in maybe 3 hours of playing online. Not exactly a huge rate of return, but it's the win rate that has me intrigued more than the dollar income. I've taken on 9 opponents and defeated 8 of them, all in sets of at least 3 matches, to a max of 19 matches.

Unless this is just the good side of variance, I don't get it. Using a truly random strategy, I shouldn't be able to win or lose. In fact, in the long run, I should lose exactly $0.02/match, which is the UB rake on the game. I'm obviously not outplaying my opponents in any meaningful sense, since I'm not even trying to strategize. But it seems to me that it shouldn't matter how "well" or "badly" opponents play, either--they could go for "rock" every single damn time and be able to tie me over the long haul. And, of course, they could have been using the same random strategy, for all I know (although I was quite sure I could pick up patterns against some of them).

What's more is that I'm confident I could have done better by occasionally departing from my random-number list, because there were times when I felt extremely confident what an opponent was about to do, and I was nearly always right in those spots. There was some definite bleed-over from poker habits involved here, because I could figure out what my opponent must be thinking that I was doing, based on what would appear to him/her to be a pattern I was engaged in.

So am I right that this initial success is just an unusually lucky run, or am I missing something? That is, is there some way that an opponent can systematically make his outcome against a random strategy worse than average? If so, I don't see how, but it's not something I've thought about in enough depth to have clear thoughts on yet.

The only things I've read about Roshambo strategy are Rafe Furst's chapter in the Full Tilt Poker Strategy Guide, but that's just about getting inside an opponent's head, which I haven't even been trying very hard to do. I also found a couple of pretty superficial online strategy guides, but haven't looked around enough to see if there are in-depth discussions, though I assume there must be.

For now, I'm pleased to be winning, even if it's only small amounts, and even if it is just dumb luck, because it's fun and a nice diversion from poker.


Addendum, November 11, 2007

Immediately after writing the above, the pendulum of statistical variance turned against me. Since then, I have engaged in 23 contests, ranging from 1 to 31 matches (each match being best of 3 throws), winning 5, tieing 5, and losing 13. Ignoring contests/sessions against particular opponents, and lumping together all of the results since my last post, there were 137 matches, including 62 wins and 75 losses. This is easily within the expected range given by the binomial distribution; a handy online calculator for such things (http://faculty.vassar.edu/lowry/binomialX.html) tells me that a coin flipped 137 times will have an outcome at least this skewed from an exactly even split about 31% of the time. That would have to be at around 5% or less to make me think that there was something other than pure chance operating.

The experiment has sufficiently convinced me of what I suspected before: that playing a random strategy basically yields random results. My initial success was a statistical blip, which has been reversed with the subsequent games. What's more, I've concluded that playing a random strategy is pretty boring, and playing with a non-random strategy is probably only a little less so. I may revisit the game from time to time for a bit of diversion, but I feel like I've pretty much exhausted my interest in it for the foreseeable future.