Guess my rule

2, 4, 6 fits my rule. What is it?

I have a rule for three numbers. 2, 4, 6 fits it. Pick a guess, then test any three numbers you like and I will tell you if they fit. When you are sure, name the rule.

2 · 4 · 6

First Second Third

500 players who test only triples their guess says will fit. Six tests each.

500 players who make every second test one their guess says will fail.

found out the guess was wrong
still sure, still wrong

Why your tests could not catch you

The rule is any three numbers that go up. Almost everyone starts with something narrower, like "up by two". Then they test 8, 10, 12 and 20, 22, 24. Every answer is yes, so every answer feels like proof. But a narrow guess and the wider rule say yes to exactly the same triples you tried. The only test that can catch a guess that is too narrow is one your guess says will fail, like 1, 2, 3.

Peter Wason first ran this game in 1960 with 29 people. In the studies since, only about one in five names the rule on the first try. Most of the others were not careless. They ran plenty of tests. They just ran the kind that could only say yes.

The same game in a trading room

A trader thinks "buy after three up days" works. He looks back and finds the times it did. Each one feels like a yes. The test that could catch him is the one he never runs: every time there were three up days, the losers too, next to the days with no signal at all. A rule that only ever met the cases picked to fit it has not been tested. It has been admired.

Before you trust a rule, ask: what result would have told me I was wrong, and did I look for it?

Sources

Wason, "On the failure to eliminate hypotheses in a conceptual task", Quarterly Journal of Experimental Psychology 12 (1960), 129–140.
Klayman and Ha, "Confirmation, disconfirmation, and information in hypothesis testing", Psychological Review 94 (1987), 211–228.
Gale and Ball, "Dual-goal facilitation in Wason's 2–4–6 task", Quarterly Journal of Experimental Psychology 59 (2006): about 20% name the rule on the first try.
The 1,000 players are simulated in your browser. Each holds one of the three narrow guesses and runs six tests. A player who also tests what should fail changes one number of a fitting triple until the guess says no.