Placeholder Image

Subtitles section Play video

  • Vsauce!

  • Kevin here, in the control room of the USS Pasadena -- a Los Angeles Class nuclear-powered

  • fast attack submarine.

  • The Pasadena is over 100 meters long, has a crew of nearly 130, and is propelled by

  • a thermal-neutron reactor that generates 35,000 shaft horsepower.

  • And it has a lot of buttons, so I'm gonna pushthis one.

  • Hey.

  • Don't touch that.

  • Oranything.

  • Right.

  • I'm here with Petty Officer John Davis, Machinist Mate Nuclear First Class and trained

  • rescue diver with the United States Navy.

  • I'm 100 meters deep in the Pacific Ocean with an expert in thermodynamics, nuclear

  • reactor technology, fluid dynamics, mathematics and more.

  • And we're gonna tap that knowledge to get to the bottom of a game that's been a staple

  • of kitchen tables for a century: Battleship.

  • Battleship evolved from a pencil and paper French game called L'Attaque, which eventually

  • became Stratego.

  • By the 1960s Milton Bradley developed the classic 10 x 10 grid in which each player

  • places 5 ships: a carrier that occupies 5 spaces, a battleship on 4, and a cruiser and

  • submarine that are each on 3, and a destroyer on 2.

  • Ships can't overlap, but they can touch.

  • The actual gameplay is really simple: the first player guesses a location on the grid

  • -- say, C4 -- and the second player says whether that shot hit one of their ships or missed

  • entirely.

  • If it's a miss, then we both mark our grids with a white peg.

  • If it's a hit, then we'll mark it with a red one.

  • The object is to hit each location on all 5 ships and sink them.

  • And it seems like there's really no perfect way to start.

  • We've got 100 possibilities, and all of them equally valid.

  • With 17 possible hits, our first random shot is going to hit about 1 in 5 times.

  • So

  • I'll start.

  • F7.

  • Miss.

  • Random guesses in Battleship are just a massive exercise in probability, and a simulation

  • by Nick Berry of DataGenetics showed that using this random system means over 99% of

  • games will require at least 78 shots.

  • Uhh.

  • E7.

  • Miss.

  • Playing totally randomly would be really, really inefficient, and unless both players

  • are choosing all shots randomly, you'd lose almost every time.

  • And real randomness is actually pretty, pretty hard.

  • Research as early as the 1930s showed that humans aren't capable of generating a random

  • number sequence, and modern research in economics shows that decision-making is incredibly difficult

  • when we have to try to make sense of randomness.

  • A3.

  • Miss.

  • Computers are a lot better at handling randomness.

  • But pure randomness just isn't optimal here.

  • The way most people play Battleship is a blendfirst, they shoot randomly until they get

  • a hit, and then they go up, down, left and right around that hit to find the next part

  • of the ship.

  • D5.

  • Ugh.

  • Hit!

  • That's what Berry calls theHunt and Targetmethod.

  • You start by randomly firing shots, and then work around your hits to sink ships.

  • By repeating that strategy, the average game will take about 65 shots.

  • That's better than random, but it's not great.

  • H8.

  • Miss.

  • The next level strategy is what's calledParity,” where you recognize that the

  • board of 100 spaces is actually no more than 50.

  • Because the smallest ship has to occupy at least 2 spaces, we can think of the Battleship

  • board like a checkerboard of alternating colors.

  • We canHunton just one color, and thenTargetwhen we get a hit.

  • D6.

  • Hitand sunk.

  • Battleship's smallest unit is 2, so once the Destroyer has been sunk -- like you just

  • did -- then that expands to 3, then 4 and 5.

  • Hunt and Target with Parity improves our average number of moves nearer to 60, so it's a

  • little better.

  • But still not optimal.

  • Uhh.

  • B2.

  • Miss.

  • We can employ a rough algorithm in our minds that takes into account both the board and

  • whether ships of a certain length are likely to be in a certain position on that board.

  • G9.

  • Uhh.

  • Miss!

  • A computer can do this perfectly judging the probability of a given ship's length being

  • placed in the leftover spaces on the board.

  • This will change with every single move and will create a sort of heat map that suggests

  • where we should guess next.

  • I'm gonna guess.

  • next...

  • D4.

  • Hit!

  • You'll start the game with no information at all, so the best option is to shoot near

  • the center and adjust from there.

  • Guess, recalibrate, repeat, each time refining your probability based on the layout of spaces

  • left and the length of the ships you haven't sunk.

  • A9.

  • Hit!

  • We can't do this as fast or as perfectly as a computer, but we can generate a pretty

  • good approximation in our minds.

  • As we play each game of Battleship, we're employing a probability density function and

  • refining an algorithm in our brains with every move.

  • Statistically, there's a massive payoff to this approach: It drops the number of shots

  • required into the 30s or 40s, with Berry finding that all 100 million games he simulated were

  • completed by about 65 moves.

  • C4.

  • Hit.

  • That's how so much of practical math, science and engineering works.

  • We make an approximation, and then hone in on the details the best we can considering

  • all the variables, unknowns, and randomness -- and then put it together with constant

  • adjustments to make something complex function flawlessly.

  • B9.

  • Ugh.

  • Hit.

  • It's a constant process.

  • But whether you're optimizing the probability behind a 50-year-old board game or navigating

  • one of the most advanced naval vessels ever created... today we have an opportunity to

  • learn, refine, and evolve faster than ever before.

  • Wait.

  • Did you say, B4?

  • Uhhh.. yeah?

  • Hitand you sunk my submarine.

  • W..wait.

  • Not...

  • Not this submarine?

  • ... No.

  • Okay.

  • Good.

  • And as always -- thanks for watching!

  • To check out more videos like this go to sailorvs.com.

  • Did I say it right?

  • I said it right, right?

  • Okay cool.

  • Phew!

  • And it's got a lot of buttons.

  • So I'm gonna touch this one.

  • Please don't touch that!

  • Uh.

  • Right.

  • Or anything.

  • Sorry.

  • Nuclear.

  • I'm such an idiot.

  • Okay yeah!

  • If you like it -- I like it!

Vsauce!

Subtitles and vocabulary

Operation of videos Adjust the video here to display the subtitles

B1 battleship randomness probability submarine sunk board

The Battleship Algorithm

  • 2 0
    林宜悉 posted on 2019/06/19
Video vocabulary