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Generalizing the game The general principle is to re-evaluate probabilities as new information is added. He is purposefully not examining your door and trying to get rid of the goats there. For example: A Bayesian Filter improves as it gets more information about whether messages are spam or not. Click click click. Monty reveals the goat, and then has a seizure. The group that originally had 3. Just play the game a few dozen times to even it out and reduce the noise. The Monty Hall problem is a counter-intuitive statistics puzzle: There are 3 doors, behind which are two goats and a car. The odds are the champ is better than the new door, too. The more you test the old standard, the less likely the new choice beats it. Filtered is better. The game is really about re-evaluating your decisions as new information emerges. Monty gives you 6 doors: you pick 1, and he divides the 5 others into a group of 2 and 3. You pick a door call it door A. On and on it goes — and the remaining doors get a brighter green cloud. He closes the door and mixes all the prizes, including your door. Does it matter? About The Site BetterExplained helps k monthly readers with friendly, insightful math lessons more.{/INSERTKEYS}{/PARAGRAPH} A Bayesian Filter improves as it gets more information about whether messages are spam or not. Said another way, do you want 1 random chance or the best of 99 random chances? Happy math. This is what happens with the door game. Multiple Monty Monty gives you 6 doors: you pick 1, and he divides the 5 others into a group of 2 and 3. He then removes goats until each group has 1 door remaining. In general, more information means you re-evaluate your choices. Support the project on KickStarter. {PARAGRAPH}{INSERTKEYS}The Monty Hall problem is a counter-intuitive statistics puzzle:. Look at your percent win rate. Look at your win rate. He sees two doors and is told to pick one: he has a chance! Would this change your guess? Stay, Daughter: A Memoir by Yasmin Azad This heartfelt and humorous memoir describes life as it was for girls who were caught in the conflict between tradition and modernity. You might get 2 heads in a row and think it was rigged. If both doors have goats, he picks randomly. The best I can do with my original choice is 1 in 3. Does switching help? Monty goes wild Monty reveals the goat, and then has a seizure. Pick a door, Monty reveals a goat grey door , and you switch to the other. At the start, every door has an equal chance — I imagine a pale green cloud, evenly distributed among all the doors. BetterExplained helps k monthly readers with friendly, insightful math lessons more. As you gather additional evidence and run more trials you can increase your confidence interval that theory A or B is correct. My first guess is 1 in 3 — there are 3 random options, right? Read an excerpt Order on Amazon. Your uninformed friend would still call it a situation. Without any evidence, two theories are equally likely. These are general cases, but the message is clear: more information means you re-evaluate your choices. Yes, two choices are equally likely when you know nothing about either choice. Instead of the regular game, imagine this variant:. Understanding the Monty Hall Problem. You pick the name that sounds cooler, and is the best you can do. Monty started to filter but never completed it — you have 3 random choices, just like in the beginning. If you had a coin, how many flips would you need to convince yourself it was fair? You know nothing about the situation. What do you switch to? Information matters. Evaluating theories. Try this in the simulator game; use 10 doors instead of Your decision: Do you want a random door out of initial guess or the best door out of 99? Just pick door 1 or 2, or 3 and keep clicking. With the Japanese baseball players, you know more than your friend and have better chances.