A Game You Can Always Win

A Game You Can Always Win


Vsauce — Kevin here, with a game you can
always win. Grab a friend and take turns counting using
numbers from 1 to 10. The first person to get to 100 wins. Which can always be you. To demonstrate, let’s have a friendly game
between me and uhhh… I guess.. I’ll just play with myself. Hey me! It’s good to see me. Am I ready to play? Yes. Yes I am. Okay, add numbers between 1 and 10 and the
person who gets to 100 first wins. I’ll write the sum in between mes so you
can follow along. I’ll start the game. 1 7 4 9 2 10 1 You’re just picking numbers randomly like
me, right? Uhh… yeahhh… Okay cool, 3 8 8 3 5 6 Seriously, though. We both have 50/50 odds of getting to 100. Um. Sure! Alright. 4 7 9 2 Uh. Wait. 89? If I play 1, that’s 90 and you can play
10 and win and… if I play 10 that’s 99 and you can play 1 and win. Oh, weird. I, uh, must’ve gotten lucky. Yeah, right. 5. [94] 6! 100, I WIN! Every. Time. Here’s how. Uhh..you can go now, me. Uh, fine. Well, I want a rematch later. I guess I’ll just uhhh…see ya in the mirror? Yeahhhhh. Okay, now let’s play a match between me
and you and I’ll explain along the way how it works. The easiest way for me to know I’m going
to win every time is for me to go first and start with the number 1. No matter what number you add next, 5, 3,
8, whatever it is, I just subtract your number from 11 to get my next play. So if I start with 1 and if you say 4, then
our sum is 5. To get my next number, I do 11 minus 4, which
equals 7, so 7 is my next play: 7 plus 5 gives our game a new total of 12. Then you say… 8. Cool. 8 plus 12 gives our game a new total of 20. I do 11 minus your 8, which is 3. So, I play 3 and our new total is 23. As long as I stick to this strategy I’m
guaranteed to be the first to 100. This is why it works. Regardless of your number, mine will always
result in a sum that’s part of an arithmetic series separated by elevens: 1, 12, 23, 34,
45, 56, 67, 78, 89, and… then finally 100. Since the highest number you can play in the
game is 10 — if I separate your moves by eleven… I rule the world! Or at least… this simple number game. Gotta start somewhere. When you play this with your friend can they
ever win? Yes. If you mess up the series. While going first, playing 1, and subtracting
every opponent’s number by 11 is the easiest way to stick with the series, after a few
rounds you might want to switch things up to prevent them from figuring out your strategy. You could do that by starting with a number
other than 1 and choosing wrong numbers until later in the game when you land on a number
in the arithmetic series like 67 or 78. So if you’re playing with a friend and you
pick random numbers until the sum is 65, then you could play 2 to bring your total to 67
and then you’re right on track. From there just subtract your friend’s numbers
every single time by 11 and you will be the first to 100. To players who don’t realize that the optimal
strategy depends on that series, this game seems like a game of chance — but once you
know the series, you have the secret number knowledge. But if adding up to 100 isn’t your cup of
tea you could try a similar game with matchsticks. These are Inq’s Durable Match-Like Puzzle
Sticks that come in the new Curiosity Box that is out right now. It’s packed with a booklet that features
22 different puzzles that you can try to solve yourself when you get these matchsticks. But for right now we’ll use the matchsticks
to visualize another game you can always win. Alright. You have eleven matchsticks spread out on
a table. You and a friend take turns removing either
1, 2 or 3 matchsticks and the player who picks up the last match loses. If you go first, you can always win this game. Since you don’t want to pick up that last
match, let’s work backwards to uncover the secret. We’ll play a game between Mr. T and Skeletor
because… why not?. Alright, let’s skip to the end of the game
to workout the winning strategy. If it’s Skeletor’s turn and Mr T. leaves
Skeletor with 2, 3, or 4 matches, Skeletor can leave T. with the final losing match. So, T. will want to make sure he leaves Skeletor
with 5, to guarantee that Mr. T keeps his jewelry. Here’s why. If there are 2 matches left, then Skeletor
just takes 1 and leaves Mr. T. with the final losing match. If there are 3 matches left, then Skeletor
takes 2, Mr. T. loses. And if there are 4, then Skeletor takes 3,
then Mr. T loses again. But if T leaves 5, no matter what Skeletor
plays next — 3, 2, or 1 — T can make a winning move and pity the fool accordingly. The arithmetic series that will rig the game
for T is separated by 4’s… 1, then 5, and then… 9. Mr. T. will want to leave Skeletor with 9
matches to make sure that ALL his plays match up with the series. If Skeletor and T start with 11 matches and
T goes first, that means his initial play will be to remove 2. Since each player can only remove a maximum
of 3 matches per turn, you can dominate the game every time by going first and making
moves that stick to this series. … which is why the game works with 20 matches,
too. To guarantee a win with 20 matches on the
table, your first play should be to remove 3 to land you at 17. So let’s say T. starts and removes 3 to
get to 17. No matter what Skeletor does, T just needs
to get to 13 to stay on course to win. So, if Skeletor removes 2 to get to 15, then
Mr. T. just needs to remove 2 to get to 13. Now T. needs to get down to 9. So, if Skeletor removes 3 to get to 10, then
Mr. T. just has to remove 1 match to get to 9. The next milestone is 5, so if Skeletor removes
1 to get to 8, then Mr. T can remove 3 to get to 5. And now it’s officially over. Skeleton can’t do anything — 1, 2, 3, it
doesn’t matter. Mr. T. is leaving Skeletor with the final
losing match. Let’s see if it’ll fit in his hand. What about this one? Good enough. Both the counting game and this matchstick
one are referred to as “Nim-like,” because they’re conceptually similar to a game from
ancient times that evolved into what mathematicians now call Nim. Players take turns removing objects from heaps
or stacks, and the player to remove the last object loses… but it gets a lot more complex
than sticking to a basic arithmetic series. We like complex. Humans have been inventing brain-teasing games
to pass the time, sharpen their minds, and extend collective knowledge for as long as
recorded history shows. One of the oldest games we know about is Senet,
with board pieces from Ancient Egypt dating back over 5,000 years. About the same time humans were inventing
the precursors to our modern written language systems, we were developing number games to
occupy ourselves and tease out a better understanding of the quantifiable world. Creating artificial challenges — and then
out-thinking them — is a way we exercise our minds. By discovering the hidden patterns that govern
reality, whether we’re just practicing with a matchstick game or unwinding the great scientific
challenges of our times, we’re engaging in an integral part of what makes us — us. Even those of us who use Skeletor to explain
math games. And as always – thanks for watching. Hey, the brand new Curiosity Box which includes
the matchstick game and a bunch of other awesome hand-picked, designed and developed science
toys is available right now. Michael, Jake and I created this subscription
box to bring physical Vsauce to your doorstep. So, check out the link below, it’s CuriosityBox.com,
to secure yours right now. I’m going to stay here and, uh, try and figure
out some of these puzzles. Alright. Move one match to make a square. Uhh. Um. SQUARE.

100 thoughts on “A Game You Can Always Win

  1. collection of number games and math puzzles:

    Android: https://play.google.com/store/apps/details?id=air.Ganaysa.NumbersPlanet

    iPhone + iPad: https://itunes.apple.com/app/id1451594331

    Amazon Kindle: https://www.amazon.com/dp/B07M6D2CB7/

  2. How about two of them use the same strategy then what happen?
    Both of them win?
    Or one of them lose?
    If one of them lose then this game doesn't exist

  3. Oh yeah this game I remember finding the trick myself when I was a kid… I won all my next battles and I thought I was smart. Also when I encountered someone who knew the trick the beginning was always awkward like "who starts" you no me

  4. I remember when I was like 7, in french class we played a game where we had to add either 1,2 or 3 to a number and if you get to 11 you have to sit down. It was all in french of course but same idea

  5. Also there’s a game called 21 whoever says 21 first loses (you can only say 1 2 or 3 numbers) so basically what you do is to make sure you can have a higher chance at winning let them start then the numbers you have to say are 4 8 12 16 when you say 16 you automatically win the game
    The main number here is 16 if you say 16 you win

  6. Now I want to make a program to automate this process with any minimum and maximum take per turn, and with a max goal in mind.

  7. Lol I did this to 2 of my friends, it was 89 and my friend realized he was going to lose, so he said 6 and my other friend thought that the sum was 96 and he said 4 but the total was 99 and my friend won

  8. This is meh
    Him : game
    Meh: UwU
    After the game aka the explanation
    Me:It’s math!!
    2 mins later
    Me brain is flat

  9. Guy1:Did you do it?!!
    Guy2:do what?
    Guy1:you know what!!!!
    Guy2:no I don’t
    Guy1:how dare you lie!!!
    Guy1:how do you know!!!!
    Guy2:I watched it
    Guy1:why!!!!
    Guy2:because of the algorithm
    Guy2:we are always watching

  10. If u follow the strategy if they say 10 first than it would be 1 and then it would be 11 so the strategy would be lost….

    Edit: oh…. u start it off with one! Got it!

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