# 25 standard packs > 5 headliners. Here's why

SDS

After watching this Vsauce video on youtube about the Newton-Pepys problem regarding dice rolling probabilities, I got to thinking about pack odds with pulling diamonds. So if you're hellbent on sinking 37,500 stubs down the toilet, you're better off buying 25 standard packs instead of the total 5 headliner packs available to each person.

Scenario A is like rolling five 11-sided dice (5 headliner packs with 1:10 odds of a diamond)
Solution: 1-(10/11)^5= 37.9% chance of pulling a diamond

Scenario B is like rolling twenty five 51-sided dice (25 standard packs with 1:50 odds of a diamond)
Solution: 1-(50/51)^25= 39% chance of pulling a diamond plus a gold or better card in the 20 bundle

The math is better explained in this Wikipedia article, but there is essentially a 1.1% higher chance of pulling at least a single diamond from 25 standard packs over 5 headliner packs

SDS

True, but what if you want the headliner? The headliner obv has an increased chance (how much we don't know), so if you want that specific card, it's better to get headliners.

(Or you know buy it outright, but someones gotta buy packs so I can buy their card off the market)

SDS

@esmlb_rop said in 25 standard packs > 5 headliners. Here's why:

After watching this Vsauce video on youtube about the Newton-Pepys problem regarding dice rolling probabilities, I got to thinking about pack odds with pulling diamonds. So if you're hellbent on sinking 37,500 stubs down the toilet, you're better off buying 25 standard packs instead of the total 5 headliner packs available to each person.

Scenario A is like rolling five 11-sided dice (5 headliner packs with 1:10 odds of a diamond)
Solution: 1-(10/11)^5= 37.9% chance of pulling a diamond

Scenario B is like rolling twenty five 51-sided dice (25 standard packs with 1:50 odds of a diamond)
Solution: 1-(50/51)^25= 39% chance of pulling a diamond plus a gold or better card in the 20 bundle

The math is better explained in this Wikipedia article, but there is essentially a 1.1% higher chance of pulling at least a single diamond from 25 standard packs over 5 headliner packs

The only thing would be the value of the diamond. The headliner packs would be more likely to be a higher value right?

SDS

@eatyum said in 25 standard packs > 5 headliners. Here's why:

True, but what if you want the headliner? The headliner obv has an increased chance (how much we don't know), so if you want that specific card, it's better to get headliners.

(Or you know buy it outright, but someones gotta buy packs so I can buy their card off the market)

That's the thing, we don't know if specifically pulling a headliner is higher than 1:10 or if the 1:10 represents any diamond including the headliner itself

SDS

@baboonishace said in 25 standard packs > 5 headliners. Here's why:

@esmlb_rop said in 25 standard packs > 5 headliners. Here's why:

After watching this Vsauce video on youtube about the Newton-Pepys problem regarding dice rolling probabilities, I got to thinking about pack odds with pulling diamonds. So if you're hellbent on sinking 37,500 stubs down the toilet, you're better off buying 25 standard packs instead of the total 5 headliner packs available to each person.

Scenario A is like rolling five 11-sided dice (5 headliner packs with 1:10 odds of a diamond)
Solution: 1-(10/11)^5= 37.9% chance of pulling a diamond

Scenario B is like rolling twenty five 51-sided dice (25 standard packs with 1:50 odds of a diamond)
Solution: 1-(50/51)^25= 39% chance of pulling a diamond plus a gold or better card in the 20 bundle

The math is better explained in this Wikipedia article, but there is essentially a 1.1% higher chance of pulling at least a single diamond from 25 standard packs over 5 headliner packs

The only thing would be the value of the diamond. The headliner packs would be more likely to be a higher value right?

The stated odds don't really go into specifics, so I'm assuming those odds are for any diamond in general

SDS

@esmlb_rop said in 25 standard packs > 5 headliners. Here's why:

@baboonishace said in 25 standard packs > 5 headliners. Here's why:

@esmlb_rop said in 25 standard packs > 5 headliners. Here's why:

After watching this Vsauce video on youtube about the Newton-Pepys problem regarding dice rolling probabilities, I got to thinking about pack odds with pulling diamonds. So if you're hellbent on sinking 37,500 stubs down the toilet, you're better off buying 25 standard packs instead of the total 5 headliner packs available to each person.

Scenario A is like rolling five 11-sided dice (5 headliner packs with 1:10 odds of a diamond)
Solution: 1-(10/11)^5= 37.9% chance of pulling a diamond

Scenario B is like rolling twenty five 51-sided dice (25 standard packs with 1:50 odds of a diamond)
Solution: 1-(50/51)^25= 39% chance of pulling a diamond plus a gold or better card in the 20 bundle

The math is better explained in this Wikipedia article, but there is essentially a 1.1% higher chance of pulling at least a single diamond from 25 standard packs over 5 headliner packs

The only thing would be the value of the diamond. The headliner packs would be more likely to be a higher value right?

The stated odds don't really go into specifics, so I'm assuming those odds are for any diamond in general

Might be a dumb question, but can you get a headliner out of standard pack? As you can tell, I don't buy them much lol. I've found for me it's better to just buy the card I want because I never pull anybody good out of a pack

SDS

@esmlb_rop said in 25 standard packs > 5 headliners. Here's why:

@eatyum said in 25 standard packs > 5 headliners. Here's why:

True, but what if you want the headliner? The headliner obv has an increased chance (how much we don't know), so if you want that specific card, it's better to get headliners.

(Or you know buy it outright, but someones gotta buy packs so I can buy their card off the market)

That's the thing, we don't know if specifically pulling a headliner is higher than 1:10 or if the 1:10 represents any diamond including the headliner itself

No, I'm not saying it's higher than 1 in 10, but it says "increased chance to find featured headliner player". So if you do pull a diamond, it's a bigger chance it's that headliner card, so you have more of a chance of pulling that specific diamond from a headliner then a standard.

SDS

@esmlb_rop said in 25 standard packs > 5 headliners. Here's why:

After watching this Vsauce video on youtube about the Newton-Pepys problem regarding dice rolling probabilities, I got to thinking about pack odds with pulling diamonds. So if you're hellbent on sinking 37,500 stubs down the toilet, you're better off buying 25 standard packs instead of the total 5 headliner packs available to each person.

Scenario A is like rolling five 11-sided dice (5 headliner packs with 1:10 odds of a diamond)
Solution: 1-(10/11)^5= 37.9% chance of pulling a diamond

Scenario B is like rolling twenty five 51-sided dice (25 standard packs with 1:50 odds of a diamond)
Solution: 1-(50/51)^25= 39% chance of pulling a diamond plus a gold or better card in the 20 bundle

The math is better explained in this Wikipedia article, but there is essentially a 1.1% higher chance of pulling at least a single diamond from 25 standard packs over 5 headliner packs

what a wonderful thread and post - we need more guys like you in the forum - thank you for explaining the math out too that is awesome

have a great weekend to all

SDS

@eatyum said in 25 standard packs > 5 headliners. Here's why:

@esmlb_rop said in 25 standard packs > 5 headliners. Here's why:

@eatyum said in 25 standard packs > 5 headliners. Here's why:

True, but what if you want the headliner? The headliner obv has an increased chance (how much we don't know), so if you want that specific card, it's better to get headliners.

(Or you know buy it outright, but someones gotta buy packs so I can buy their card off the market)

That's the thing, we don't know if specifically pulling a headliner is higher than 1:10 or if the 1:10 represents any diamond including the headliner itself

No, I'm not saying it's higher than 1 in 10, but it says "increased chance to find featured headliner player". So if you do pull a diamond, it's a bigger chance it's that headliner card, so you have more of a chance of pulling that specific diamond from a headliner then a standard.

Yeah I see what you mean now. SDS hasn't explicitly stated if any random diamond pulled has a higher chance of actually being a headliner, but I'm thinking that it is since there's a ton flooding the market

SDS

@baboonishace said in 25 standard packs > 5 headliners. Here's why:

@esmlb_rop said in 25 standard packs > 5 headliners. Here's why:

@baboonishace said in 25 standard packs > 5 headliners. Here's why:

@esmlb_rop said in 25 standard packs > 5 headliners. Here's why:

After watching this Vsauce video on youtube about the Newton-Pepys problem regarding dice rolling probabilities, I got to thinking about pack odds with pulling diamonds. So if you're hellbent on sinking 37,500 stubs down the toilet, you're better off buying 25 standard packs instead of the total 5 headliner packs available to each person.

Scenario A is like rolling five 11-sided dice (5 headliner packs with 1:10 odds of a diamond)
Solution: 1-(10/11)^5= 37.9% chance of pulling a diamond

Scenario B is like rolling twenty five 51-sided dice (25 standard packs with 1:50 odds of a diamond)
Solution: 1-(50/51)^25= 39% chance of pulling a diamond plus a gold or better card in the 20 bundle

The math is better explained in this Wikipedia article, but there is essentially a 1.1% higher chance of pulling at least a single diamond from 25 standard packs over 5 headliner packs

The only thing would be the value of the diamond. The headliner packs would be more likely to be a higher value right?

The stated odds don't really go into specifics, so I'm assuming those odds are for any diamond in general

Might be a dumb question, but can you get a headliner out of standard pack? As you can tell, I don't buy them much lol. I've found for me it's better to just buy the card I want because I never pull anybody good out of a pack

Yes, you can. I have pulled Ozzie Smith and Vida Blue from Standard packs within the last 3 weeks

SDS

@baboonishace said in 25 standard packs > 5 headliners. Here's why:

@esmlb_rop said in 25 standard packs > 5 headliners. Here's why:

@baboonishace said in 25 standard packs > 5 headliners. Here's why:

@esmlb_rop said in 25 standard packs > 5 headliners. Here's why:

After watching this Vsauce video on youtube about the Newton-Pepys problem regarding dice rolling probabilities, I got to thinking about pack odds with pulling diamonds. So if you're hellbent on sinking 37,500 stubs down the toilet, you're better off buying 25 standard packs instead of the total 5 headliner packs available to each person.

Scenario A is like rolling five 11-sided dice (5 headliner packs with 1:10 odds of a diamond)
Solution: 1-(10/11)^5= 37.9% chance of pulling a diamond

Scenario B is like rolling twenty five 51-sided dice (25 standard packs with 1:50 odds of a diamond)
Solution: 1-(50/51)^25= 39% chance of pulling a diamond plus a gold or better card in the 20 bundle

The math is better explained in this Wikipedia article, but there is essentially a 1.1% higher chance of pulling at least a single diamond from 25 standard packs over 5 headliner packs

The only thing would be the value of the diamond. The headliner packs would be more likely to be a higher value right?

The stated odds don't really go into specifics, so I'm assuming those odds are for any diamond in general

Might be a dumb question, but can you get a headliner out of standard pack? As you can tell, I don't buy them much lol. I've found for me it's better to just buy the card I want because I never pull anybody good out of a pack

Yes, you can. I have pulled Ozzie Smith and Vida Blue from Standard packs within the last 3 weeks

Thank you!

SDS

@baboonishace said in 25 standard packs > 5 headliners. Here's why:

@esmlb_rop said in 25 standard packs > 5 headliners. Here's why:

@baboonishace said in 25 standard packs > 5 headliners. Here's why:

@esmlb_rop said in 25 standard packs > 5 headliners. Here's why:

After watching this Vsauce video on youtube about the Newton-Pepys problem regarding dice rolling probabilities, I got to thinking about pack odds with pulling diamonds. So if you're hellbent on sinking 37,500 stubs down the toilet, you're better off buying 25 standard packs instead of the total 5 headliner packs available to each person.

Scenario A is like rolling five 11-sided dice (5 headliner packs with 1:10 odds of a diamond)
Solution: 1-(10/11)^5= 37.9% chance of pulling a diamond

Scenario B is like rolling twenty five 51-sided dice (25 standard packs with 1:50 odds of a diamond)
Solution: 1-(50/51)^25= 39% chance of pulling a diamond plus a gold or better card in the 20 bundle

The math is better explained in this Wikipedia article, but there is essentially a 1.1% higher chance of pulling at least a single diamond from 25 standard packs over 5 headliner packs

The only thing would be the value of the diamond. The headliner packs would be more likely to be a higher value right?

The stated odds don't really go into specifics, so I'm assuming those odds are for any diamond in general

Might be a dumb question, but can you get a headliner out of standard pack? As you can tell, I don't buy them much lol. I've found for me it's better to just buy the card I want because I never pull anybody good out of a pack

Yes, you can. I have pulled Ozzie Smith and Vida Blue from Standard packs within the last 3 weeks

Meanwhile us living in the bottom shelf of the pack-luck algorithm get no such love from SDS lol. I've had abysmal pulls since 15

SDS

Me, with not enough stubs for either: UGHHH...
Question: Are you guaranteed at least one diamond for 50 standard packs? Or is that just maybe? I would think you would get 2 or more diamonds if you buy 50 packs.

SDS

@jz2016cubs said in 25 standard packs > 5 headliners. Here's why:

Me, with not enough stubs for either: UGHHH...
Question: Are you guaranteed at least one diamond for 50 standard packs? Or is that just maybe? I would think you would get 2 or more diamonds if you buy 50 packs.

What part of 1 in 50 odds do you not understand?

State of our school system must be horrible

Look up definition of odds

SDS

@CalisGW said in 25 standard packs > 5 headliners. Here's why:

@jz2016cubs said in 25 standard packs > 5 headliners. Here's why:

Me, with not enough stubs for either: UGHHH...
Question: Are you guaranteed at least one diamond for 50 standard packs? Or is that just maybe? I would think you would get 2 or more diamonds if you buy 50 packs.

What part of 1 in 50 odds do you not understand?

State of our school system must be horrible

Look up definition of odds

1. That was a dumb question, but wasn't sure.
2. Yes, the school system is awful, I agree.
SDS

@jz2016cubs said in 25 standard packs > 5 headliners. Here's why:

Me, with not enough stubs for either: UGHHH...
Question: Are you guaranteed at least one diamond for 50 standard packs? Or is that just maybe? I would think you would get 2 or more diamonds if you buy 50 packs.

The odds are based on the entire user base, so you are not guaranteed a diamond in 50 packs.

Think of it like this, if I pull 2 diamonds in 50 packs, and you pull no diamonds in 50 packs, the overall odds are still 1:50 because it's based on everybody, not per user.

SDS

@eatyum said in 25 standard packs > 5 headliners. Here's why:

@jz2016cubs said in 25 standard packs > 5 headliners. Here's why:

Me, with not enough stubs for either: UGHHH...
Question: Are you guaranteed at least one diamond for 50 standard packs? Or is that just maybe? I would think you would get 2 or more diamonds if you buy 50 packs.

The odds are based on the entire user base, so you are not guaranteed a diamond in 50 packs.

Think of it like this, if I pull 2 diamonds in 50 packs, and you pull no diamonds in 50 packs, the overall odds are still 1:50 because it's based on everybody, not per user.

OHHH. That makes a lot of since. Thanks!

SDS

@eatyum said in 25 standard packs > 5 headliners. Here's why:

@jz2016cubs said in 25 standard packs > 5 headliners. Here's why:

Me, with not enough stubs for either: UGHHH...
Question: Are you guaranteed at least one diamond for 50 standard packs? Or is that just maybe? I would think you would get 2 or more diamonds if you buy 50 packs.

The odds are based on the entire user base, so you are not guaranteed a diamond in 50 packs.

Think of it like this, if I pull 2 diamonds in 50 packs, and you pull no diamonds in 50 packs, the overall odds are still 1:50 because it's based on everybody, not per user.

Fun fact: there is a higher chance of pulling a diamond in 51 packs than pulling 2 diamonds in 102 packs. That's another takeaway from that Newton problem

SDS

@CalisGW said in 25 standard packs > 5 headliners. Here's why:

@jz2016cubs said in 25 standard packs > 5 headliners. Here's why:

Me, with not enough stubs for either: UGHHH...
Question: Are you guaranteed at least one diamond for 50 standard packs? Or is that just maybe? I would think you would get 2 or more diamonds if you buy 50 packs.

What part of 1 in 50 odds do you not understand?

State of our school system must be horrible

Look up definition of odds
You could have just said no, 1:50 odds doesnt guarantee a 50 bundle to return 1 diamond chief

SDS

@esmlb_rop said in 25 standard packs > 5 headliners. Here's why:

@eatyum said in 25 standard packs > 5 headliners. Here's why:

@jz2016cubs said in 25 standard packs > 5 headliners. Here's why:

Me, with not enough stubs for either: UGHHH...
Question: Are you guaranteed at least one diamond for 50 standard packs? Or is that just maybe? I would think you would get 2 or more diamonds if you buy 50 packs.

The odds are based on the entire user base, so you are not guaranteed a diamond in 50 packs.

Think of it like this, if I pull 2 diamonds in 50 packs, and you pull no diamonds in 50 packs, the overall odds are still 1:50 because it's based on everybody, not per user.

Fun fact: there is a higher chance of pulling a diamond in 51 packs than pulling 2 diamonds in 102 packs. That's another takeaway from that Newton problem

Pfft, math