# We Should Communicate Probabilities With Flips

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tags: #probability

## Flipping Coins

If someone walks up to you and offers $100,000 if they flip a coin and it lands heads, youâ€™re correct in believing that you have no means of predicting the outcome. If that same person offers you the same bet on a weighted coin with a 60% chance of heads, all of a sudden youâ€™re daydreaming about what cool new car youâ€™re going to buy. If the coin has a 90% chance of heads, youâ€™re mentally putting the deposit down on the new car long before the coin enters the air. This is bad thinking, this is a base 10 problem, and this can be solved.

## Flipping Multiple Coins

Our someone changes the bet: you win unless she flips 3 tails in a row. This feelsâ€¦ different. Is that deposit refundable? The first thing we learn about probability is the multiplication rule: your odds of losing in this new game are 12.5%, giving you pretty close to the 90% chance of buying your new Audi. But suddenly, this feels bad. You can *envision* losing.

The problem with communicating probabilities with decimals is that 60% feels monumentally bigger than 50%, and 90% feels so close to 100% that itâ€™s not even worth thinking about. Multiplying these numbers by 10 doesnâ€™t help -- even if 9 in 10 dentists recommend a toothbrush (an entire dentist doesnâ€™t like the toothbrush!), itâ€™s still a sure thing since 9 feels really close to 10.

## The â€śFlipâ€ť as a Unit

We can solve our base 10 problem with a new unit: the flip. Two conversion tables are below, and are relative to the concept of the â€świnning outcomeâ€ť or the â€ślosing outcomeâ€ť. The colors in the tables reflect reckless optimism on the top and loss aversion on the bottom. Choose the top if youâ€™re watching basketball, and a more extreme version of the bottom if youâ€™re running a nuclear power plant.

What we notice here is that with flips, 60% hardly feels better than 50% in our one shot betting situation. That doesnâ€™t mean 60% isnâ€™t *better* than 50%, but we need to be careful using these probabilities to change our planning and decision making. When the weather forecaster says thereâ€™s a 70% chance of rain or Nate Silver says [insert candidate here] has a 71.4% chance of winning a presidential election, they are still delivering information, but not quite as much as our base 10 communication system would lead you to believe.