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 push… this one.
Hey.
Don’t touch that.
Or… anything.
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 blend… first, 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 the “Hunt and Target” method.
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 called “Parity,” 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 can “Hunt” on just one color, and then “Target” when we get a hit.
D6.
Hit… and 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?
Hit… and 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!