Games of Chance

In this first quiz, we'll cover 5 quick "pro tips" for solving probability puzzles.

Whether you're a professional or a newbie, you'll have fun with these puzzles - and the scenarios get trickier as this quiz progresses.

Gaming Strategies


Pro Tip 1: Don't be overly tempted by large but unlikely payoffs.

Especially if you're playing a game many times, the best strategy often builds up gains slowly, rather than making a risky gamble for a large payoff.

You are about to play a game with a coin that is weighted so that there is a 90% chance that it lands heads and a 10% chance that it lands tails. If you want to maximize the expected amount of money you will win, would you rather...

A. win $10 if it lands heads,

B. win $50 if it lands tails, or

C. win $1,000,000 if it spontaneously combusts in the air. (You may assume that there is at most a 0.0000001% chance that the coin will spontaneously combust in the air.)

Choose wisely!

Gaming Strategies


Pro Tip 2: Look for a "simplifying perspective" when there are many possibilities.

In the problem below, you can map out all of the cases in a few minutes, but there's also a very clever, quick way to solve it using the right perspective!

Four mice are on the corners of a square. All at the same time, they each randomly and independently choose to walk along one edge of the square to a new corner. What is the probability that there is at least one collision before the mice reach their destinations?

Gaming Strategies


Pro Tip 3: Your intuition may mislead you.

For example, the "gambler's fallacy" is when a gambler believes that they're more likely to win than usual because they've been losing for so long that a win is "due."

You are going to flip 8 fair coins in total, and three of your first four flips have already landed tails. What's the most likely overall number of tails when you're finished flipping all 8 coins?

Gaming Strategies


Pro Tip 4: When you're studying a complex game, simplify it by breaking it into smaller games and/or scenarios that you've already worked with before.

For example, drawing a black card vs. a red card from a deck (and shuffling the card back in the deck when you're done) is just like flipping a coin if all you care about is the card's color, and 12\frac{1}{2} is a much easier fraction to mentally keep track of than 2652\frac{26}{52}.

Katherine and Zyan are playing a game using strange dice. Each die is a cube with six sides. Katherine's die has sides numbered 3, 3, 3, 3, 3, and 6. Zyan's die has sides numbered 2, 2, 2, 5, 5, and 5.

To play the game, Katherine and Zyan roll their dice at the same time and whoever rolls the higher value wins. If they play many times, who is likely to win more frequently: Katherine or Zyan?

Gaming Strategies


Pro Tip 5: "Most likely" does not necessarily mean "very likely."

When you're playing a game like poker where you can't know everything about the cards in play, don't play as if the most likely outcome is the only thing that could happen. Keep in mind that even if something is most likely it may still be very unlikely if there are lots of possibilities.

In Pokémon Go, eggs have a roughly 50% chance of being the 5-kilometer type.

Which is more likely?

A. Finding 2 eggs and getting exactly one 5-kilometer type.

B. Finding 2000 eggs and getting exactly 1000 5-kilometer types.

There's no need to calculate out these values exactly (one of these two probabilities is far larger than the other)—what's your intuition?

Gaming Strategies


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