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In modern history, followed by the black side’s response. The graphic is based on an extensive data set of chess games going back to 1850.The first moves are usually pawn moves, and the destination squares for the pawns are labeled on the chart. In the Indian Defense, Black’s first move is with the knight, labeled with an “N.” (Click here for a complete guide to notation for chess.)Programmer and chess player Oliver Brennan designed a program to calculate the probabilities of survival for each piece using data from 2.2 million master-level tournament games. Kings have the highest survival rate, of course, because they can’t be taken. Rooks also tend to be hardy because they spend a lot of time at the back of the board and are generally more active in endgames. The knights and central pawns have the lowest survival rates. Many popular openings involve d and e pawns undertaking suicide missions, which are sometimes counter-attacked with c pawns. The wing pawns have a higher survival rate, prompting one forum user to comment, in what generally seems like a great rule for warfare, “If you can’t be the king, be the little guy hiding in the corner.

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”An extensive study by Persi Diaconis, Susan Holmes and Richard Montgomery of Stanford found that if a coin is tossed and caught, it has about a 51 percent chance of landing on the same face it was launched. If a coin is spun rather than tossed, it has a more than 50 percent chance of landing on the heavier side (which is heads on a U. S. quarter).

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In the video above by Numerberphile, Diaconis explains some of the math behind the idea. If this is true, how should you “win” a coin toss? First, always be the chooser and/or the tosser when you can. Don’t allow the same person to both toss and choose — unless that person is you. If the coin is being tossed and you’re the chooser, choose the side that is face down. The coin is more likely to land with the same side up, but most people will invert the flipped coin onto their other hand before they reveal it. Did you know there is a way to win at Connect Four literally 100 percent of the time? Connect Four is what mathematicians call a “solved game,” meaning you can play it perfectly every time, no matter what your opponent does. You will need to get the first move, but as long as you do so, you can always win within 41 moves. Here’s a mathy explanation, or you can watch the YouTube video above. This map by Seth Kadish shows adjacency in the game of Diplomacy. Adjacency can be both a good and a bad thing, Kadish says, allowing for more options to support your units but also more ways to be attacked.

If you’re a more conservative player, you would want to play one of the more defensible positions: Turkey or France, rather than Germany or Austria. Your probability of getting on “Jeopardy!

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” is in itself pretty slim, but if you do make it on, look to statistics to help you find the Daily Double. Nathan Yau of Flowing Data created this cool graphic showing the probability that Jeopardy’s Daily Double was found in a given location for seasons 1 through 31.As Yau writes, Jeopardy fans criticized contestant Arthur Chu for jumping around the board, rather than choosing clues top to bottom in the traditional way. But his strategy was a good one: Historical probability suggests the Daily Double is much more likely to be found toward the bottom of the board than the top. Monopoly players are sent to jail for all kinds of reasons.

And that means that the properties about one roll of the dice outside of jail are visited most often. As Walter Hickey, formerly of Business Insider and now at FiveThirtyEight, writes, jail serves as a “sink” — people are sucked from places on the rest of the board and emerge from jail. That gives the orange and red properties a critical significance, as this video of 500 simulated rapid-fire Monopoly games shows. The jail insight means the orange and red properties are generally the best investments, but they aren’t the only ones. The graphic above, by Walter Hickey for Business Insider, shows the probability of landing on each space on the board. Notice the higher probability for spaces between jail and the “go to jail” space, as well as the railroads, and the lower probability of Chance spaces. There’s one more thing you need to understand to play Monopoly strategically: how many houses to buy and where to put them. Tim Darling, who blogs at the site Amnesta.

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net, calculated the “breakeven time” — the number of opponent rolls that you need to make back the money that you invest in different numbers of houses on different properties. The properties are listed vertically at the left. The longest breakeven times are marked in blue, while the shortest are marked in red. Right away, you can see that buying a single house on Mediterranean or Baltic Avenue is one of the worst uses of your money. Generally, you get the best return on your investment when you buy three houses on a property, or all four of the railroads.

Owning one or two railroads is not as good — though it does prevent your opponents from owning all four. Ever wonder what the speediest game of Monopoly would look like? Profdjm computed the shortest theoretically possible game of Monopoly, which they demonstrate above. With the right sequence of rolls, Chance and Community cards, the four-turn, nine-roll game can be completed in just 21 seconds. This graphic by Seth Kadish of Vizual Statistix shows you where to hang out and not to hang out while moonlighting as Pac-Man. The darker areas are more dangerous, since they are farther from an intersection.

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The lower half of the board is also more difficult to clear, says Kadish, especially the bottom row where you can get trapped by ghosts on either side. There are a few special spots on the board: In the squares outlined in blue, ghosts cannot turn upward to follow you when they are in scatter and chase modes – only when they are frightened. And in the infamous hiding spot outlined in green you can sit indefinitely, assuming the ghosts didn’t see you move there, Kadish says. If you ever get to play on “The Price is Right,” would you rather go home empty handed — or with a new car? To go home with all the prizes, you don’t need to know the price of a karaoke machine, an oven range or Reese’s Peanut Butter Cups — all you need is to understand some strategy, explains Ben Blatt at Slate. Blatt argues that people can use game theory — a school of thought in economics that looks at how people make decisions — to win lots of things on “The Price is Right.” For example, in the show’s first segment, Contestants’ Row, four people are chosen from the audience to guess the price of an item. The contestant whose guess is closest to the actual price without overbidding wins the prize and continues on to more lucrative games. If you are the last contestant, game theory says that you should bid one dollar more than the highest bidder, Blatt says. Blatt looked at 1,500 Contestants’ Row games and found that if final contestants had used this strategy, they would have won 54 percent of the time. Instead, they won only 35 percent of the time. The graphic above shows his solution for another “Price is Right” game, called Now or Then, in which contestants have to guess whether each of six small prices is labeled with its current price, or a price from an earlier date. Four items are always Now and two are always Then. Blatt says that most contestants try to figure out which prices are earlier and which are later, but instead they should just follow the decision-tree above. Like Connect-Four, Now and Then is a solved game, meaning that if you use the right strategy you can win 100 percent of the time. If you were playing the familiar game of rock-paper-scissors against a computer, probability dictates that you would do equally well by picking any one of the three options.

Whether you pick paper, scissors or rock, your chance of winning would always be one in three. But because people are far less random than computers, you can devise a strategy that will give you a greater chance of winning when playing rock-paper-scissors against a human. This video by Numberphile breaks down the best strategy for winning at rock-paper-scissors, drawn from an awesome study of a massive tournament at China’s Zhejiang University (The Post’s Caitlin Dewey explained that study here). Basically, when people win they tend to stick with the same choice of rock, paper or scissors, while when they lose they are much more likely to switch to another option. Okay, this isn’t quite a data visualization, but it will help your Scrabble game. Memorize these two-letter words from WinEveryGame.

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com and you’ll have a lot more options for making words in tight spaces and using all your tiles at the end of the game. Chris Beaumont, a software engineer at Counsyl, created some cool visualizations showing the strength of different hands in Texas hold ’em. The graphs are based on Beaumont’s enumeration of all roughly 1.3 trillion hands of heads-up Texas hold ’em, plus data on several million online poker hands. The graphic requires a little explanation: The one on the top left shows the strength of a hand averaged over all opponent hands, with blue indicating hands that win more often than lose, and pink squares hands that lose more often than win. This graphic doesn’t take into account that opponents can fold weaker hands, meaning your hand won’t perform as well as this

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