Hmm. As I realized in this post: http://lesswrong.com/r/discussion/lw/egk/circular_preferences_dont_lead_to_getting_money/7eg4 it really depends on which comparison you make. If you make a comparison between the X in the first bet, and the X in the second bet, etc, then you don't take the deal. If you make a comparison between the X in the first bet and the Y in the second bet, then you do. So I don't actually think it's well defined whether you would take the bet or not.
If you can self modify, yeah, but if you can't, you'll always make that bet.
Come to think of it, there's a much simpler way to get an undefined result: I offer you X, Y, or Z, no strings attached. Which do you pick?
Edit: for reasons given in the comments, I don't think the question of what circular preferences actually do is well defined, so this an answer to a wrong question.
If I like Y more than X, at an exchange rate of 0.9Y for 1X, and I like Z more than Y, at an exchange rate of 0.9Z for 1Y, and I like X more than Z, at an exchange rate of 0.9X for 1Z, you might think that given 1X and the ability to trade X for Y at an exchange rate of 0.95Y for 1X, and Y for Z at an exchange rate of 0.95Z for 1Y, and Z for X at an exchange rate of 0.95X for 1Z, I would trade in a circle until I had nothing left.
But actually, if I knew that I had circular preferences, and I knew that if I had 0.95Y I would trade it for (0.95^2)Z, which I would trade for (0.95^3)X, then actually I'd be trading 1X for (0.95^3)X, which I'm obviously not going to do.
Similarly, if the exchange rates are all 1:1, but each trade costs 1 penny, and I care about 1 penny much much less than any of 1X, 1Y, or 1Z, and I trade my X for Y, I know I'm actually going to end up with X - 3 cents, so I won't make the trade.
Unless I can set a Schelling fence, in which case I will end up trading once.
So if instead of being given X, I have a 1/3 chance of each of X, Y, and Z, I would hope I wouldn't set a Schelling fence, because then my 1/3 chance of each thing becomes a 1/3 chance of each thing minus the trading penalty. So maybe I'd want to be bad at precommitments, or would I precommit not to precommit?