5 Ways to Beat Old-School Games Using Math

5 Rock Paper Scissors: Opponents Are Biased Toward Rock, Against Scissors

If we told you that it's possible to cheat at a game as simple as Rock Paper Scissors, you'd probably think we were talking about the old "We didn't say it WASN'T the best out of three" technique, or the one where you try to convince the other person that there really is a secret fourth option.

But no, the cheats we're talking about are a little more sophisticated than that -- and not completely unlike a Jedi mind trick.

How to Win:

Professional Rock Paper Scissors players (yes, they exist) find that humans are fairly predictable when it comes to simple games like this. For example, it's well known that a rookie player is always more likely to start with rock, simply because rock looks more badass. Intermediate players can use this knowledge to counteract or rule out rock depending on how experienced their opponent looks.

Also, players in general are statistically less likely to throw scissors at any given time -- so all things being equal, you should go with paper.

Then, statistics show that players will often use the throw that would have won the last turn. After you throw down the paper, watch them come back with scissors.

Really advanced players, however, don't need to guess what you're gonna choose because they can decide that for you.

How? Well, one advanced technique consists of reminding the other player of the rules before the match starts, making sure to repeatedly flash them with the throw you want them to use -- for example, show them the scissors every time you say the word "scissors," but not the other ones, as you go over the rules. As long as you don't make it too obvious, their subconscious should take your suggestion and they will open with the move you commanded them to use.

Here's another cheat: Make it really obvious that you're going to throw paper next, and then throw paper. Subconsciously, your opponent will stay away from the move that beats paper (or whatever throw you were telegraphing) because they'll think that no one could be that obvious.

Yes, friends, with these techniques, you will always get to ride shotgun.

4 Monopoly: Buy the Orange Properties

There are so many "special" editions of Monopoly based on ridiculous things (Simpsons Monopoly, Batman Monopoly, Canadian Monopoly) that it's getting increasingly hard to remember what the original version even looked like. However, at its core, the game is the same: It still involves collecting fake money, and it's still about making sure you hate every member of your family by the time you reach the end of the game.

The most common strategy for winning Monopoly seems to be buying as many properties as you can and then sort of hoping other people fall on them so that you can overcharge them into bankruptcy. While the game does require some skill (knowing when to build, or trade, or tip over the board and tell everyone to suck it), everyone knows that it's mostly about dumb luck. It's all about the roll of the dice, right?

How to Win:

Well, everyone's wrong. There is a simple, winning strategy based on how often everybody winds up in jail. Here, let's examine a regular Monopoly board for a second:

To the untrained eye, it would appear you have an equally likely chance of landing on any square -- until you consider the Jail square, which you can be transported to by landing on "Go to Jail," by rolling doubles three times or by drawing certain cards from the Community Chest and Chance piles (not to mention just normally arriving there to visit your uncle Greg).

Someone on the Internet went ahead and compiled the exact probabilities of landing on any given square (because that's what the Internet is for) and found out that Jail is the place you're most likely to end up. By far.

Considering this, then, the most visited squares that aren't Jail are the ones immediately after it on the board: purple, red and orange.

Another citizen of the Internet with too much time on his hands calculated the cost of each property versus the potential returns and the probabilities of players landing there, and concluded that the orange squares give you a far better return for your money than any other place on the board (except the railroads, if you can get all four). If you focus on securing those properties early on, you'll be wiping your ass on fake money in no time.

This tactic won't guarantee that you win every single game, because there's still an element of chance and you're always one unlucky dice roll away from getting screwed on Park Place. Still, remember to thank math and Cracked when you're winning that game of Strip Monopoly you're already thinking of suggesting.

3 Coin Toss: Results Are Biased Based on the Starting Position

People have been tossing coins to settle arguments for as long as coins have existed (or arguments, whichever came later). The Greeks did it, the Romans did it -- hell, the British still flip a coin to decide an election when there's a draw.

Coin tossing is used in numerous contexts (from sport matches to deciding who gets to pick the pizza toppings) because it's a simple, reliable way to choose between two options where each side has the exact same chance of winning. It's like asking God himself to make the decision for you when you can't be bothered to do it yourself.

How to Win:

Well, apparently God isn't as unbiased as we like to think. It turns out that a coin is always more likely to land on the side that's facing up when you flip it (and you should bet accordingly). Why? Because physics, that's why.

A group of researchers at Stanford University calculated the exact odds of a flipped coin landing on either side, and it turns out that there's a 2 percent discrepancy between the two: 51 percent for the side that's facing up versus 49 percent for the side facing down. They achieved this by building a coin-tossing machine, filming it in slow motion with special cameras and carefully analyzing the results.

The reason for the discrepancy is actually pretty simple. Let's say you flip a coin with heads facing up. As it turns in the air, heads will be facing up as many or more times as tails, but never less. Tails, on the other hand, will be facing up as many or fewer times as heads, but never more (since it didn't start out that way). This accounts for the 2 percent difference, which may not seem like a lot to you right now, but try not to drive yourself crazy thinking about it when you're trying to decide something by tossing a coin. By picking the side with more probabilities, you're practically making a decision already.

So maybe you'll end up spinning a coin on its edge ... which is even more biased to one side, it turns out. According to the same study, when you spin a coin, most of the time it will land with the heavier side down. Since heads usually has more shit on it than tails, some coins can land on tails 80 percent of the time.

2 Pac-Man: There's a Hiding Spot in the Maze

Pac-Man may seem like an easy kiddie game to you, but what's the highest level you've ever reached? Five? Six? Come on, fire up your smartphone or iPad or whatever (there's probably a downloadable version for your toaster even) and let's see how well you do. In fact, this game is so hard that it wasn't until almost two decades after its release that someone actually completed all 256 levels.

And the reason why this game is so hard is that those relentless ghosts never stop going after Pac-Man (possibly because he was their murderer) -- the whole game becomes a frantic dance to avoid getting cornered between ghosts. So to even have a shot at reaching the double digits, you'd have to be incredibly skilled at dodging them and getting the timing just perfect ...

How to Win:

... or just know how to hide from them. Yep, there's a "blind spot" on the maze where the ghosts can't reach you. Here's a demonstration of it:

As long as a ghost isn't practically biting your ass already, the moment you reach that spot, they'll start cluelessly circling around without ever touching you. This happens because the ghosts aren't actually programmed to chase you -- if they were, the game would be impossible. Instead, each one has different patterns: Only the red ghost (Blinky) is programmed to go after you. The pink and blue ones (Pinky and Inky) only want to position themselves at a specific place relative to you, and the orange one (Clyde) just moves around randomly.

The fact that the ghosts move entirely based on your position means that you can trick them into going around in circles without touching you, which allows for bathroom breaks or making out with all the groupies that will naturally form around you from being so good at Pac-Man. What's more, advanced players have used this information to create a series of patterns for Pac-Man that you can use to breeze through each maze without ever touching a ghost, like this one for level 1:

Since every maze after level 20 is exactly the same (because at that point the developers said, "Eh, no one's gonna get that far anyway"), when you reach that point, it's just a matter of repeating the same pattern over and over ... for only six hours.

1 Battleship: Aim for the Center

The whole point of Battleship is you can't see your opponent's board, or where their little plastic ships are positioned. So the game essentially consists of calling out random numbers until you luck out and get a "hit." If it wasn't for the fact that a clever game designer made it about ships blowing the hell out of each other, we're pretty sure it never would have caught on.

Since each player is free to place the pieces anywhere they want on the Battleship board, that means it's just about lobbing pegs at the board until you accidentally hit one, right?

How to Win:

Actually, it's not as random as it seems. Statistically, you're far more likely to score a hit closer to the center of the board. How do we know this? Because someone went through the trouble of simulating billions of possible Battleship boards and used that information to create this:

That is a map representing which squares are more likely to have a ship in them, with the brighter ones toward the center being the luckier ones. The reason for this is that there are only so many ways to place the ships so that they'll fall on a specific square. Look at the carrier, which takes a whopping five squares: There are 10 ways to place it so that it touches a square on the center, but only two ways to position it so that it touches one in the corner.

You can see it here -- taking only the carrier into account, the probability anus clenches down even more:

Whereas if you're looking for that elusive patrol boat (which only takes two squares), it loosens up considerably:

Patrol boats, you see, are more likely to hang out near the corners simply because in most cases the center will already be taken up by all the larger boats, leaving them little place to hide.

But if using probability maps isn't dishonest enough for you, the same guy who created them also came up with this interactive board where you can plot your shots in real time and see the stats for each square adjust accordingly. Tested against a computer opponent, it won nine out of 10 games.

It's almost like having a powerful radar, which should come in pretty handy when you get to the part of the game where aliens come down and only that guy from Friday Night Lights can save the world. (Hollywood wouldn't lie to us.)

Karl loves him some games, and you can check out his Facebook, Twitter or blog by clicking the shit out those links. Or you can enjoy his review of his favorite game.

For more dilemmas that aren't, check out 5 Things That Are Way Easier Than They Look in Movies and 6 Places That Are Shockingly Easy to Break Into.

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