# Let's learn the ins and outs of how odds work on Quidd.

### First, let's define some terms.

Set Odds
Set odds are the chances that the pack you open will have one of the cards from that set.

Item Odds
Item odds are the chances that the pack you open will have that specific card.

Another way to look at this is by thinking of the odds of getting something as being "1 in ___." So if the odds for a card in the pack are 5%, it’s like saying “1 in 20 packs” will contain the card. This does not mean that if you open 20 packs you will get this card. Odds only work with large numbers, so all we can really say is that if 20,000 packs are sold, approximately 1,000 of that card will be pulled overall. Even so, since there is randomness, it’s possible that 1,200 are pulled. Or 800!

It's just like this: Imagine you have a huge jar with 1,000 pieces of candy in it and 50 of them are Skittles. That's 5% or a 1 in 20 chance of pulling out Skittles. It doesn't mean that if you pull out 20 pieces of candy, 1 of them will always be Skittles. That's how odds work!

Any questions? No? Great!

Just kidding. Here's the number one question we get about odds:

### "Why don’t the percentages add up to 100%?"

As the great Professor Farnsworth once said, “I’m afraid we need to use… Math!”

Let’s start outside of Quidd with a coin flip example. With one flip, the odds of getting heads are 50% and the odds of getting tails are 50%. The odds of getting one or the other add up to 100%. Nice.

Now flip the coin twice. What are the odds of getting at least one heads? The answer might surprise you:

# 75%

The chance of getting at least one tails is also 75%. The odds add up to 150%. Whaaaaaaa?

Think of the possible outcomes from two coin flips. You could get both heads, both tails, first heads then tails, or first tails then heads. Those are the only four possible outcomes.

Notice that 50% of the outcomes have one of each. These outcomes overlap, which causes the percent chance of getting one of each to be counted twice in the odds. Three of those four outcomes contain at least one heads and three contain at least one tails. That’s ¾, or 75% chance of each.

### How does this translate to pack odds?

When a pack has 5 cards in it, we say that it has “5 draws.” Each draw is like a flip. So as long as there is more than one draw in a pack, the odds will not add up to 100%, just like the odds of getting heads plus the odds of getting tails in two flips don’t add up to 100%.
With me so far? Great!

Another question we get a lot is:

### “The odds say 10% but I bought 10 packs and didn’t get one.”

So how many packs would you have to open to get a card that has 10% odds?
Well, it’s a bit of a trick question. With odds, there are no guarantees, only probabilities. All we can say is that opening a certain number of packs gives you a certain percentage chance to get the card.

### Here is the universal formula that applies to odds.

You can use this to figure out your chances of getting the card you want!

where

So what if the pack says 10% odds for the card? If you open 10 packs, how likely are you to get the card?

That's right. If you open 10 packs at 10% odds, you have about a 65% chance of getting the card.

This diagram shows 60 circles, where 10% of them are purple. You can pull 10 circles and not necessarily get one that's purple.

### Want more? Of course you do.

How many packs would you have to open for a 90% chance at getting a card with 10% odds?

How do we get that? Solve for n.

So this means you would need to open about 22 packs for a 90% chance at getting a card with 10% odds. How fun is that?

### Hopefully this helps explain how odds work.

Let us know if you have any questions! Have fun collecting and check out the odds as you open new packs.