Sure, the complex can stump people easily, making even geniuses seem feeble-minded. But true capital-S Stupid is immune to simplicity. Capital-S Stupid is so powerful that a coin flip can be read as less than a 50/50 chance. Number 3 has my vote, Kevin.
It looks to me (having read only the article, not the paper) that the subjects weren’t asked, “On average, how many times will a fair coin toss come up heads?” but rather, “How many times out of these ten tosses will this coin come up heads?” You’d be right in thinking that, given enough coin tosses, the ratio of heads to tails would tend toward 50%. But for any particular set of ten coin tosses, you might get all heads, all tails, or any combination in between. Since order isn’t considered (a heads followed by nine tails is taken as equivalent to nine tails followed by a heads), you’re slightly more likely to get five heads than four or six, and quite a bit less likely to get all heads or all tails. But in any particular set of ten tosses, you’re more likely to get some combination of heads and tails that isn’t a 50/50 ratio than you are to get exactly five heads and five tails. So guessing a number other than five isn’t really that insane after all.
..and, come to think of it, the graph isn’t too far off. If you list every possible combination of heads and tails for ten tosses (1024 in all), and count the number of heads in each one, here’s what you find:
0: 1
1: 10
2: 45
3: 120
4: 210
5: 252
6: 210
7: 120
8: 45
9: 10
10: 1
If you graphed these, it’d look a lot like the graph of people’s responses to the question.
My issue isn’t that they didn’t assume it’d be 5 x Heads & 5 x Tails, it’s that there’s seemingly no rationale for the guesses they did make. From the assumption that the coin is not somehow rigged, the premise guides people towards responses that have no logical grounding — “I usually lose stuff like this, so the coin’ll be mostly tails” or “I’m a lucky person, it’ll be mostly heads”.
Odds are 50/50. Sure, someone can think that it won’t fall that way, and there’s chance it won’t, but there’s no controllable influence nudging it one way or the other. Hence, my agreement with Kevin Drum’s 3rd option: the study is built on something that by definition is logically invalid. It’d be like asking people based on their luck how likely they are to be struck by lightning if they stand outside in a storm holding a 9 iron. Remove the luck part and you have a real question — but nothing worth writing about.