Hearthpwn

Quote from MasterCopyPaster jump

Quote from Vinotan jump

why so complicated. wouldnt the simplest solution be:

draw 4 cards from a cardpool containing all cards.
draw 1 card from a cardpool containing only rare, epic and legendary cards.

(of course weightened by rarity)

usually the easiest solution is the way to go if you are not sure :P, plus its the easiest to calculate :P

I totally agree, this IS the easiest way to calculate. There are others, and all of them work the same for individual cards but not for packs. That was my point, that you can't try to calculate the expected number of rares/epics/legends on a pack if you don't know HOW packs are generated. And also that it doesen't matter: you want to know which road to take (in the long run, dozens of packs ahead), not where you will put your feet in the next step (chances for 1 pack only, and probably yield the same conclusion as the long run).

Is not a matter of the numbers being correct, is a matter of using math flawlessly. The difference between 71% of commons and 72% of commons only matter after thousands of packs, long after you finished your collection. But using correct reasoning can train you for the problems of tomorrow. That's why I don't like certain guesses.

Quote from Dinavergjump

Actually: 

Randomly generate a non-gold common
Give it a 1 in 5 chance of being turned instead into a non-gold rare
If now a rare, give it a 1 in 5 chance of being turned instead into a non-gold epic
If now an epic, give it a 1 in 5 chance of being turned instead into a non-gold legendary
Now determine if it should be turned into a gold version of the card, using this chart:
Odds of being promoted to golden:
Common: 1 in 50
Rare: 1 in 20
Epic: 1 in 15
Legendary: 1 in 10
Repeat steps 1-6 four more times to make 5 cards in a pack.
If, after doing this, all cards are common, turn a random card
into a rare and go to step 3) for it."

By the work of: https://www.reddit.com/r/hearthstone/comments/23mxqq/calculations_for_exact_pack_probabilities_and/

A pretty interesting read, and a clever method. I will run the numbers myself to check if it matches at individual card level. I can't do it at pack level, because why bother? I don't have real data to compare :(

 

I'm pretty sure there's a bunch of reddit threads that collect data, e.g. amount of common/rare/epic/legendary cards / pack.

At least that's where I got my averages from.

Quote from Vinotan jump

Quote from BHTrix jump

...

So sure, you could divide the number by 5, but when you do this, the number now specifies the chance a SINGLE CARD is a card you do not need, whereas the formula now takes into account ALL 5 CARDS - e.g. THE ENTIRE PACK.

...

So again this is a PER PACK total, whereas you're thinking PER CARD.

Thanks a lot for your long explanation and your patience with me :P

I guess what buggs me the most is the fact that there appear percentages above 100% :P but thats my personal problem I guess ^^

I think some confusion may result in the lack of destinction between "expectation value" and "chance to draw a new card".

Of course you should buy the pack which has a higher expectation value to get a new card.

But I think you will agree with me, that in general propabilitys can never be above 100%, whether I think per pack or per card.

If there is a 0.275%*0.275%*0.275%*0.275%*0.275% chance that I get 5xIcehowl, then by consequence, the chance to get a new card is 100% minus this number, right?

If I understand you right, then the number you are listing is the expectation value/expected number of new cards drawn per pack, right?
I agree that this number is propably right and perhaps more usefull than the propability to get at least 1 new card in the pack.

But: I think the value should not be in %, but listed/described as what it is: The expected number of new cards per pack is 4,9999.

 

---

First, for your, percentages can't be above 100% thing:

http://mathforum.org/library/drmath/view/58166.html

On the other hand, sometimes percentages are used like this: "The number of questions received was up 15.7%, from 5450 in February to 6305 in March." In other words, the increase from February to March was 6305-5450 = 855, and 855 is 15.7% of 5450. (These facts are true, by the way.) Now, what if the number of questions received went up to 14000 in April? (It didn't.) This would be an increase of 122% from March to April. There is nothing wrong with this - no law says that the number of questions can't do more than double from one month to the next.

---

The chance you get 1 new card in a pack of 5 cards, being 499% (or in essence, 5 new cards), as per the way it's worded currently, seems perfectly fine to me. ;)

If it would be changed to 100% denominators - the wording would have to be: The chance you get 5 new cards in a pack = ......... which just seems really odd to me, especially when you reach percentages like 5%. At this point I don't want to know what the chance is I get 5 new cards in a pack - I want to know what the chance is I get 1 card, an epic card, or a legendary card. Which is why there's a small row with percentages above. I think common and rare cards, are just not that important.

If it would be changed to 4.99, to me that's really exactly the same as %, just divided by 100.

My real question is, if it bothers you so much, why not simply change your own spreadsheet and add a /100, and change the text?

Finally, as per your definition: The moment you reach a number below 100%, the spreadsheet is fine right? So it's only at the beginning of the expansion, the first 30 packs, where it's ''wrong''? :P

EDIT: here's what I'll do.

Find a PhD in mathematics, I'm sure there's plenty on the interwebs, trolling forums and the like.
Relay the ''problem'' to him, return with an educated solution, a way to do it better - I will change the spreadsheet.
Until then I do not think this discussion is of any value to the spreadsheet.
Be sure to mention that 1 card has a 100% chance to be of at least rare quality!

The solution has to take into account that there's 5 cards a pack, and therefor has to calculate the chances of each card being new, not just 1 card. And it has to calculate the chances of each card being new : individually.
The solution is preferably in %.
And it has to be simple, so 1 number, no more.

Quote from Rayman001 jump

You could change something in the Legend:

The first thing (light green) says: "Classic + Gnomes versus Goblins totals", but it's also TGT, you should add that there.

Thank you for the spreadsheet! It's awesome! :)

Thank you for helping making it better!
It's fixed, nice catch.

Quote from Vinotan jump

lets assume you have only 1 TGT card, Icehowl for example, because you crafted him. Then the spreadsheet says, you have a 499% chance to get a card you are missing. But there is a non-zero chance, that in the pack you buy, there are 5xicehowl in the pack :P

Extreme Example, I know, but it works with other, more realistic szenarios aswell :P

Theres got to be sth wrong ^^ obviously the chance can only be between 0 and 100% 

is just simply dividing by 5 the right solution? Propably not.

Other question: have you taken into account the fact that you are guaranteed at least 1 rare or higher card? 

because lets assume you have all common cards (crafted) but not a single rare or higher, then the chance for a missing card should be 100%. (or 500% if dividing the result by 5 would be right)

Yes the guaranteed card is in the formula.

You actually have 114% chance of getting a rare card. Since as calculated there's on average a 114 rare cards in 100 packs. So the number will indeed be about 143% since there's about 24 epic cards and 5.5 legendary cards per 100 packs.

I think dividing per 5 would still be accurate, the only difference is that 1 card will have 100% chance to be rare and thus have a 100% chance to be a card you do not need, whereas the other cards will probably be about 11.2% chance to be rare/epic or legendary. This would then be translated to 27-28% chance per card to be a card you do not need. I guess.

This is the reason my per pack approach - to me - makes a lot more sense.

Quote from Vinotan jump

but still: how can I have an above 100% chance to get a new card in the first place? :D

 since there is a nonzero (x%) chance that I get 5xIcehowl, the chance that I get a card I dont own should be 100 minus x% chance, right?

or am I missing sth here?

If you have 1 Icehowl, you will have a 499.7125% chance of getting 5 new cards in the pack, and a 0.275% chance you don't get 5 new cards in a pack. I think that's the bit you're missing here. (so that's a 0.275% chance you get 1 Icehowl, or 2, or 3, or 4, or 5.)

You could divide it by 5, since there's 5 cards in a pack.
The way you should look at it, is this; when you have gotten 5x icehowl in your first pack, and thus it's the only card you have - the chance that your first card will not be icehowl is 99.9425%, the chance your second card will not be icehowl is 99.9425%, the chance the third card will not be icehowl is 99.9425%, the chance the fourth card will not be icehowl is 99.9425% and the chance your last card will not be icehowl is also 99.9425%.

Which totals at 499.7125%

So sure, you could divide the number by 5, but when you do this, the number now specifies the chance a SINGLE CARD is a card you do not need, whereas the formula now takes into account ALL 5 CARDS - e.g. THE ENTIRE PACK.

I personally do not know if a per card % is accurate with 1 card always having 100% chance to be rare or higher, but it might be.

The numbers I've taken, the percentages, come from a reddit post somewhere earlier in the topic, this reddit post had calculated how many common/rare/epic/lengedary cards where in a few thousand packs, making the numbers fairly accurate. And in these packs where on average 3.5711 uncommon cards, 1.149 rare cards, 0.2314 epic cards and 0.0555 legendary cards per pack.

So again this is a PER PACK total, whereas you're thinking PER CARD.

I'm not going to change the formulas to a per card percentage, I'm going to keep them on per pack, since per pack makes total sense to me. But you're free to make them per card, and add a /5 to the formula.

Quote from gummmbo jump

I can also report that the formulas on the new version don't work in Excel 2013 either.

Thanks, that's a big bummer :<

Quote from gummmbo jump

Quote from BHTrix jump

there's 5 cards in a pack.

499% simply means, 5 new cards from your first pack with a fresh collection, with a small chance of duplicates.

The issue is the way it's worded, the number you give makes sense when you describe it that way, but the spreadsheet says it's the chance that a pack has a card that you're missing. The actual chance that a pack has a card that you're missing has to be between 0% and 100%, obviously it's impossible for any probability to be over 100%.

What I think it's actually reporting is 100x the "expected number of new cards per pack". If you don't have anything other than basic cards, you'd expect to get 4.99 new cards in your next pack. I think that's a better way to describe it.

Also, while I'm at it, one small typo correction: Frothing Berserker is spelled "Beserker" in the spreadsheet.

 

Thanks! fixed the typo.

Quote from milk1 jump

I currently use your spreadsheet, or at least an old version of it and think it's brilliant, so firstly thank you very much.

 

Just wanted to ask, will you be making a new version, including the Grand Tournament cards?

 

If so, will I have to download a new spreadsheet and re-delete all collected cards, or not?

 

Either way I'm very grateful and thanks bhtrix.

Hey milk1, there is a new version up, and it is indeed already updated. I would advice downloading this new one and re-deleting your cards since a few things have changed that made it more accessible including a few bug fixes, name changes and the like (minor tweaks if you will)
You could try to copy and paste the TGT card set into your collection, but you might need to update the formulas - if you know how to, this is certainly a good solution.

The reason I made it more accessible. and moved the total cards to the top is mainly so that in the future it will be a lot easier to simply copy the new expansion into your existing sheet. (e.g. you simply copy everything at the bottom into the bottom of your existing sheet and you should be good to go.) I also updated all formula's so they get their values from the top section, this way I only have to update those numbers and it automatically updates the rest of the sheet - again making it easier to add new content without having people to re-download and stripe their cards off again.

If you use a version for openoffice I suggest you download v2 old, since the new formulas do not work in openoffice, unfortunately.
https://docs.google.com/spreadsheets/d/1GhqNiBv453OozFX3Fts6orc3wH5sfMmmkNPCjM7nfoE/edit?usp=sharing

For excell or others you might try v2 new, it has updated formula's for figuring out which pack is the best pack to buy. These formulas are somewhat more accurate. I haven't tested the new formulas in other programs, so I do not know if they work!
https://docs.google.com/spreadsheets/d/1rZobj5ALRs_7X4tH40Sx1g2h5QexptLifeeobAjorJw/edit?usp=sharing

If you plan on saving a copy on google docs itself, you should definitely get the regular v2.

I hope this helps!

Quote from Suskis jump

you wrote UNCOMMON instead on NEUTRAL in the classic section of neutral minions

Cool! thanks bro!

Missed that one! It's fixed now!

Quote from Nikos_the_great jump

There was another error that made the chance to find a new card wrong but now it's fixed.

For those who already copied it, the fix is really easy: just go to the yellow brackets above "CHANCE THAT A CLASSIC PACK HAS A CARD YOU'RE MISSING", and:

in the yellow bracket under "common", when you click it its value at the top must read

=COUNTUNIQUE(E46:E59,E63:E75,E79:E91,E95:E107,E111:E123,E127:E139,E143:E155,E159:E171,E175:E187,E191:E271)/95*357.11

which has two mistakes: E46 should be E47 and the divided number near the end, 95 should be 94.

In the yellow bracket under "rare", change D46 to D47 and 82 to 81.

and in the yellow bracket under "epic", change C46 to C47 and 38 to 37.

 

This error was only in the classic pack set, everything else is correct.

 

Thanks!

Quote from Nikos_the_great jump

On the top of the spreadsheet you added a quicklook, where you list every class and below them "Uncommon". Shouldn't that be "Neutral"?

Yes! Thanks! fixed it.

Well, my chances changed from:

23.52% to 42.1%
and
17.78% to 21.54%

So which ever's lower, still remains the lowest, there can be either a big or a small variation though.

I should maybe add that for GvG the lowest percentage, I miss 1 rare card, which I think is where your chances drop dramatically, whereas for Classic I still need 1 common and 14 rares. (Unleash because I dissed it when they nerfed it :D)

Quote from Nikos_the_great jump

Quote from BHTrix jump

Also, if you really want to break your brain - here's a fun one for you.

What's the chance that after getting 98 epic out of 100 epic cards, you are left missing 2x the same card, instead of 2 different cards?

 

 

Actually the chance to have 2 same cards in the end is high, if you take into account the nature of the game. I miss 5 rares from the classic set, and 4 of them are Flare and Gadgetzan Auctioneer, because I disenchanted them when they got nerfed and never found them since, haha. That's how I came across the issue. The spreadsheet tells me I have the same chance to find a new card in the classic set and gvg, which isn't true (rares especially influence the percentage a lot).

Dinaverg's right though, without weird situations like mine the data shouldn't favor one or the other set. But still, it's nice to see the actual chance to find a new card in the set. It was very inaccurate before, because consider this:

By some miracle you found exactly 1 copy of each of 100 rares, the chance to find a new one would appear to be half while in fact it would be the exact starting one. Of course there's no chance of that happening, but still, if in the end you're missing 5 different cards, which isn't unlikely, the chance shown would still be very wrong. So it's not a discrepancy of 1%.

Now it's fixed though, so thanks! I'll have to write off all the cards again, copying the missing parts seems like more work...

Ye I had to write them off again also - which isn't so bad because I get to see the discrepancy now for myself, still having the old version.

But you're right, if there's 100 different rares, and you need 2 copies of each, if you happen to find 1 copy of each, when you get 100 rares, you still have a 100% chance to find a new rare in a pack. I'll post the difference in % for fun when I'm done updating my collection -again- :P

Quote from Seeteufel2 jump

I haven't downloaded yours to check the formulas, but these 499% just don't make sense, so something must be inaccurate.

Below is a screen of my own Excel Sheet, below right is the TGT odd calculation. It shows 100%, and I didn't include any "trick" to reduce it. The 100,01 is a rounding error by Excel in the binomial calculation, and the # boxes are related to the binomial calculation aswell, they disappear as soon as I put in at least 1 card in my collection (top left).Looks like this when I put in that I have 2 rare and 10 commons, for example:

(Left: Only considering cards you don't have at all, Right: Considering cards that you don't have at all AND non-legendary cards you have only 1)

(The Avg Dust/Pack calculates the crafting value for cards you still need for a full collection with 2 of each non-legendary and the disenchant value for cards you already have 2 copies or 1 in case of legendaries)

I keep saying this,

there's 5 cards in a pack.

499% simply means, 5 new cards from your first pack with a fresh collection, with a small chance of duplicates.

However I wouldn't mind the code for all that, especially the dust/pack seems very interesting.

Quote from BoltBase jump

Not sure if i should be worried or not that i have a 472.7386031% chance of finding a classic card i need in a pack. Is this intended or is it a bug? Should the percentage really be that high? 

You get 5 cards a pack - so if your collection is really fresh, ye.

The first pack you open will have 499% of containing new cards - that's 5 new cards. Small chance of duplicates in first batch though.