Vsauce! Kevin here, with the ultimate representation of good and evil, an epic battle of morality
that has raged on game boards across the globe for over 2,000 years.
Snakes and Ladders.
Wait. Snakes and Ladders? That's nothing but a really simple kid’s game, right?
WRONG. While the rules are simple, the math, psychology and hidden spiritual lessons are
surprisingly complex. So to highlight that unique combination in a visual way, I commissioned
an intricate version of the game that harnesses electricity to demonstrate the unpredictable
gameplay. The circuit that's made as we play will not only show the path to victory, but
will also REVEAL THE MEANING OF LIFE. Sort of.
This custom game board was created by engineering YouTube wizard Allen Pan. The winner of this
game of Snakes and Ladders will trigger this mystery box to do... something. I seriously,
100% do not know what’s inside this box or what will happen when the first player
reaches the final square: but we’re about to find out together.
I do know that it’s powered by 16 AA batteries, Allen put it together in an afternoon, and
he promised me. He promised. That it will not burn down my house. So that’s good.
Here’s how it works.
Allen 3D-printed yellow and red game pieces that contain about 50 feet of stainless steel
conductive thread. He’s put a nail juncture at every snake’s head and tail, on every
ladder’s top and bottom, and at the end of each row on the board. I’ll start by
hooking up both game pieces to this bolt and tightening this nut down on it. I'll be red
and you'll be yellow. And as we play, I’ll wrap the steel thread around these junctures,
which will weave a path up ladders and down snakes to show a trail of each player’s
movement on the game board.
Here's the important part! When the winning player’s piece touches a node on the final
square, that will complete a circuit to the battery-powered mystery box. And whatever
this thing does -- it will do.
Now let's climb some ladders and slide down some snakes. Or chutes.
You probably know this game as Chutes and Ladders, since that’s the name Milton Bradley
gave it in 1943 when it was imported to the US and sold for 50 cents. I guess they thought
snakes were scary and weird -- WHICH THEY ARE. But the game actually goes back much,
much further than your Grandpa Joe.
It actually originated in India in about the 2nd century BC, and was meant to teach children
the importance of karma and kama -- existance’s push and pull between one’s destiny and
the actions that disrupt the path to that destiny. The gameplay is obviously very simple:
the two players started at Square One -- which may actually be where we get the phrase “starting
at square one” -- and then roll a die. The then player moves that number of spaces. If
there’s a ladder, they ‘climb’ that ladder to a new space. If there’s a snake,
they slide down that snake to move backwards down to the snake's tail. And if there’s
nothing on a space, it’s the other player’s turn. The first player to get to the final
100th space wins.
That’s it. That’s the game.
In the official rules you need an exact roll to reach the 100th space, so like if you’re
two spaces away you need to roll a 2 to win, but that can get pretty tedious. Most people
just call it a win when you roll at least high enough to get to the final space, and
I’ll do the same.
Boards historically labeled ladders that advance your piece with good, virtuous actions, like
generosity or learning. Conversely, snakes were depicted along with vices like greed
or gluttony. Navigate the snakes and ladders successfully and the winner escapes saṃsāra,
life’s cycle of death and rebirth, to reach moksha, or salvation.
Who knew a game literally recommended for 3 year olds was this profound?!
Just from looking at this board I can see that snakes are a lot worse than the ladders
are beneficial. But how much worse? We can figure out the breakdown of this board’s
10 ladders and 11 snakes:
(4, 16) +12 (12, 33) +21
(49, 51) +2 Not much of a help there.
And (88, 92) +4
Alright, SNAKES: (21, 3) -18
(50, 11) -39 (93, 25) -68
That's like falling down a well. And (99, 58) -41
Alright so the advantage of ladders we're looking at.
118 / 10 = +11.8 per ladder
And for snakes we're looking at. 388 / 11 = -35.27 per snake
It’s almost exactly THREE TIMES worse to land on a snake than it is beneficial to land
on a ladder… and there’s an additional snake in there just to make it tougher. Because
why not?And this whole thing is probably just random? NO IT'S NOT.
An integral message of this game is that it’s harder to follow a path of good than it is
to follow a path of bad. It’s just easier to slide down into bad into choices and bad
habits than it is to lift yourself up with virtuous deeds.
And as subtle as the game’s hidden moral lessons hidden may be, get a load of the unseen
mathematical operation.
This absolutely ancient board game is actually a 101-state absorbing Markov chain -- a series
of events that depends on the state of the prior event, which we first explored in Parrondo’s
Paradox -- that could theoretically go on forever, especially when you’ve got so many
punishing snakes.
And if you want to make absolutely sure the next time you’re playing this with your
5-year-old sister Sally that it doesn’t last 9 hours. Well, you can’t! I mean, it’s
not likely that a game will last the rest of your lives, but with just the right combination
of rolls and snakes, it actually could.
Because Snakes and Ladders isn’t a game of skill. There’s nothing you can do to
speed up a win, and there’s no mistake that you can make to lose. All you can do is roll
and see what happens.
Okay this is taking a while. What if I really, REALLY, want to know when this game will end?
I can use board states and random rolls to run a Monte Carlo simulation that gives us
the most common length of our Snakes and Ladders game, and the odds of any given length.
Four! Four. Four. Yes. We are close! One, two, three. Four for you! One, two, three
four.
Okay, look, uh. Until this moment I have left this battery out for a reason. I was worried
that, I don't know, I would've messed something up. And then this thing would've done something.
And then I wouldn't have been able to put whatever happens back in here. The fact is
we're at 98 and it's my turn. And as long as I don't roll a one it is the actual moment
of truth.
I’ve reached the end of the board, I’ve successfully ascended ladders and overcome
the pitfalls of the evil snakes. So I'm gonna put this battery in now. It is fully charged.
As they say it is lit. Okay I'm gonna move everything so that you get the best possible
look at whatever is about to happen next.
Don't roll a one. Don't roll a one. Don't roll a one. Don't roll a one. Okay, four.
Alright. Why am I so nervous about this? Here we go!
Ahh! Ahh! Ahh! Ahh!
It was actual, oh my gosh. It was actual snakes! Well, not actual snakes but spring-loaded
snakes. The...the gearing up of it was actually almost as scary as the exploding snakes themselves.
Sigh.
Snakes and Ladders is a remarkable combination of mathematics and human psychology that was
invented centuries before the stochastic techniques needed to analyze it were known, let alone
to board game designers. Think about it: a game intended for children needs to average
just the right length. Too short and it’s not interesting enough; too long and it gets
boring. Snakes and Ladders nailed this so perfectly that thousands of years later, kids
are still growing up playing the game -- and that isn’t an accident.
Billions of people across 100 generations have played Snakes and Ladders without even
considering the deep story of numbers, morality, and the essence of human existence buried
below its childish facade.
In describing the Hindu board game Leela, which is a 72-space version of Snakes and
Ladders, Harish Johari said, “There is really only one Game, the Game in which each of us
is a player acting out his role.”
And while sometimes in life we land on ladders that launch us ahead and other times we step
on snakes that slide us back, you gotta just pick up the die and give it another roll.
Because the game goes on until eventually you reach your goal... whether that’s reaching
nirvana or triggering a mystery box of springy snakes.
And as always -- thanks for watching.