Are Two Heads Better Than One? Three heads are certainly more fun Dec 9, 2025
You’re playing a game with your lying friends Alice and Bob.
Bob flips a coin and shows it to Alice. Alice tells you what she saw - but she lies 20% of the time. Then you take your best guess on whether the coin is heads or tails.
Your best strategy is to trust whatever Alice says. You’re right 80% of the time.
Now Bob joins in. He makes up his mind independent of Alice, and he also lies 20% of the time 1.
1 Your friends are all liars!
You were right 80% of the time by trusting Alice.
How much better can you do with Bob’s help?
Here’s some empty space for you to think
I’m going to give you the answer below. So here’s some empty space for you to think in case you want to do the math yourself.
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