Battleship by Milton Bradley is a game most of us would remember from our childhood.  (Pictured above is the Star Wars version.  I CAN HAZ!?)  You have a board and your opponent has a board and you place your ships on it and try to blow the other person out of the water.  Fun and games, right?

Well, the people at Book of Odds have done some math (some crazy in-depth ‘I don’t get laid’ math) and decided that there is only a 1 in 51,934,549,300 chance of playing a perfect game.  Meaning that every single time it is your turn, you hit a ship with no ‘misses’.  Here’s the quote:

For starters, these odds don’t take into account what happens when a ship is placed against the edges of the grid (either parallel to it or perpendicular) or in a corner. So at first, we did what any good scientist does in a pinch. We ignored that, and estimated.Setting aside pesky edge/corner conditions, and calculating based on the simple 1-in-4/1-in-2 strategy above, the odds of the shortest game of Battleship seem to be:

(17/100)*(1/4)*(1/2)^3*(12/95)*(1/4)*(1/2)^2*(8/91)*(1/4)*(1/2)*(5/88)*(1/4)*(1/2)*(2/85)*(1/4) =

(17*12*8*5*2)/(100*95*91*88*85*(2^17)) =

1 in 51,934,549,300

So there you have it. If you can stand to play over fifty billion games of it in your lifetime (or in a day), then you can play the perfect game of Battleship…once. Better start now.


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