Entropic strategy in Two Truths and a Lie

The classic social game "two truths and a lie" asks each player, at their turn, to say three self-facts as the title says, which other players, listening, then seek to tease apart. It gets boring if listeners can easily and reliably tell which "fact" is false. To make it more exciting, the natural strategy would be to pick two absurd true facts and one dull fake fact.

• I picked my diet by poring over a spreadsheet
• I've been to Mexico twice
• I butter my bread on both sides

With this strategy used at a moderate level, listeners mostly guess the more absurd true fact as the probable lie. At an extreme, listeners correctly recognise the lie as the most plausible-sounding one. We can do better.

Some people (me), by confusing people, derive fun; some witnesses (my friends), by watching, derive collateral fun. Disagreement begets excitement, which, except when violent, likewise adds to fun. Information-theoretic entropy roughly measures confusion and disagreement. The optimal "two truths and a lie" strategy is the most fun strategy is the one making the greatest entropy from the listeners' guesses is that which makes each "fact" seem equally probable as the lie.

• I can bench-press my body mass
• I eschew my phone for a full day per week
• I got personally featured on a minor news show

This balance becomes numerically apparent if listeners declare their guesses. Even if the game focuses wholly on the speakers, the entropy will become cognitively apparent as listeners notice a similar truth-propensity between all three statements.