I modified my Zilch strategy generation software to model the scoring rules for the Super Farkle game available at Facebook. I wasn’t previously a Facebook user so I created my account just to try out my strategy. Over several days, I played about 180 games of Farkle and was winning about 55% of the time. But I’m not sure if this means much for a few reasons.
First, almost everyone I played, played very well. I guess this makes sense since in Super Farkle you play for chips; and if you don’t play reasonably well, it will be very difficult to win enough chips to play at the higher stakes tables. The people I played against rarely made strategy errors that cost more than a few points. One notable exception was the common mistake of taking two-ones on an opening roll instead of just one-one. This play returns 57 fewer points for your expected score and it occurs with enough frequency to be significant in a typical game. But in general, I was impressed with how closely people played to the strategy that maximizes expected scores — especially at low turn score states. So if my strategy offered any advantage at all, it was probably very slight and I doubt 180 games was enough to make a clear differentiation.
Second, in Super Farkle whoever forms the table rolls first. The average score for a well-played Super Farkle turn is just under 550 points. One can argue the disadvantage to the player going second is half that or about 275 points. (Why don’t they just roll to see who goes first?) To make a fair test of the strategy, I should have played half my games by forming a new table, and played the other half by joining an existing table, but my competitive nature just wouldn’t allow me to concede 275 points to my opponent. So instead I spoiled my own test by always forming my own table. I suspect that the advantage of going first may have overshadowed any advantage my strategy was offering over the high quality play of my opponents.
Finally, and perhaps most importantly, there’s almost certainly something wrong with the Super Farkle dice. I detailed why I believe this to be so on the Farkle review page at Facebook. Here’s the text from that review:
This game is quite nice; but there is a serious problem. The probability of rolling a 6-die FARKLE is exactly 1 chance in 43.2. You can find this calculation all over the web. Here’s one professor at Michigan Ann Arbor that shows the calculation: http://notaboutapples.wordpress.com/2009/07/27/multinomial-coefficients-and-farkle/
Apparently I’ve played about 180 games of Farkle, but I’ve never once thrown a 6 die Farkle. If you assume a typical game has 15 turns, then that’s 15 x 180 = 2700 6-die rolls — and that’s not even considering hot-dice rolls. The probability of not throwing even one 6 die farkle in that many rolls is exactly:
(1-(1/43.2))^2700 = .000 000 000 000 000 000 000 000 000 344
If I’m counting my zeros right, that’s less than one chance in an octillion. Yes, octillion is a real number — a very very big number. So I suggest there is something wrong with the dice. Can I be sure there’s something wrong with the dice? Of course not, but I can say this. According to wikipedia, the visible universe is about 92 billion light years across. And 1 light year is about 6 trillion miles. And there are 5280 feet in a mile. If you lined people up one foot apart (you’d have to use skinny people) across our entire visible universe; and then sat them all down in front of their own laptop playing farkle; and had them all roll 6 dice over-and-over only stopping when they had their first 6-die farkle; then you’d expect about ONE of them (yes just one) to go as far as 2700 rolls without farkling. I suppose I could be that one person….uhmmm…yeah…right.
Maybe some manager made a marketing decision that 6-die farkles just annoyed people too much and the developers were simply asked to reroll the dice one time when a 6-die farkle showed up. Or maybe they are just using a really bad random number generator for their dice rolling engine. Or maybe there’s something more insidious going on. But something is surely amiss.
Interestingly, shortly after I posted this review, I was mysteriously logged out of Facebook and subsequent login attempts were denied. Coincidence? In any case, my foray into Super Farkle play is ended. I played enough games to at least see that the strategy was doing very well — and was highly consistent with the play of seasoned Farkle addicts veterans.