A Game You Can Always Win Part 1

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 spinit 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.

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