I know this has been discussed before but since Arena rewards were changed in the patch I'm curious, which is now more Gold efficient (you get more rewards for the Gold spent)? Even though Arena takes longer (obviously) I'd gladly spend all my gold on Arena if it gives me more cards/dust for my Gold than buying packs straight up.
Here are the Arena changes:
Arena rewards now give less dust and more cards.
More gold is guaranteed at 5 & 6 Arena wins.
At 9 Arena wins, you are now guaranteed an extra pack or a Golden card.
I'd gladly spend all my gold on Arena if it gives me more cards/dust for my Gold than buying packs straight up.
Without putting too much though into it, I would venture to say arena is more effective. My main reason: at 7+wins you get ALL the gold you spent back (and maybe some extra) so that in theory you could take the free arena run you get and never have to spend a dime to fill out your collection
Arena is potentially more efficient at 5 wins and up. If you are consistently getting 5+ wins, its more efficient on paper. That said, if packs are your concern you have to factor time into as well.
Bob wants a pack of cards so he can improve his constructed pool. He has 150g. He can invest 100g for a pack and have 5 new cards in about 10 seconds. He can also try out the arena and get one of the following:
1. A more expensive pack (150g for arena pass resulting in under 5 wins.)
2. An 'even' pack (5 or 6 wins *150g - ~50 for reward*)
3. Bonus pack (7+ wins, gold returned, plus pack)
Bob has to put about an hour into each of these options, and depending on his skill (and luck) he could end up paying more gold for that pack of cards (his primary reason for arena.)
There is a time investment into arena. So thats pretty much it. If you are good at arena, its more efficient, if you suck at arena, and packs are your primary concern (ie you aren't doing arena for fun) then you could just be hurting yourself.
So lets say I'm only average at Arena and only end up with 3-4 wins. Would the cards + dust value at that amount of wins be greater than the value of a single pack, break even, or be a loss? I'd assume it'd be closer to break even and 5-6 be profit (since that's what they buffed in the patch) but I just want to make sure.
I'm sure I could pull out good streaks often enough (6+ wins) but I've had some terrible runs too (~3 wins). So if I'm only breaking even on average I might as well save myself time and just buy packs.
So lets say I'm only average at Arena and only end up with 3-4 wins. Would the cards + dust value at that amount of wins be greater than the value of a single pack, break even, or be a loss? I'd assume it'd be closer to break even and 5-6 be profit (since that's what they buffed in the patch) but I just want to make sure.
I'm sure I could pull out good streaks often enough (6+ wins) but I've had some terrible runs too (~3 wins). So if I'm only breaking even on average I might as well save myself time and just buy packs.
Thanks for the insight. :)
Its still tough to gauge properly just because right now we have a bunch of data based on arenas before the changes. Once we have more numbers on how much dust is still being handed out for under 5 wins, and how much bonus gold people are actually getting on average for 5/6 wins then it will be easier to tell.
It's obvious, just grind out arenas. If you hit even 50 gold you break even if you include the pack, unless you're having a horrible win streak, Arena is always the option.
It does get a little tedious, and sometimes you just want to rip packs open, but I try to be moderate
The reward changes definitely favour Arena, unless you hardly ever achieve 4+ wins. Even winning only 4 times is hardly a deficite. 5+ always had 50G. Did 15 Arenaruns yesterday, worst session was 2-3 with a really bad deck, had one 8-3, rest was 5+. Due to bonusrewards (had a bonus golden rare once and a "normal" common) I netted way better than having just bought 15 Packs. Plus I was entertained for the whole day.
Add in the Funbonus and Arena is the winner :)
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I've done three arenas since the patch. First arena with 2 wins I got 40 gold (basically a pack and ~40 dust cost me 110), second I got 3 wins and 50 gold (broke even), third I got 4 wins and 60 gold. Arena is definitely the better way to go and way more fun too. I defintiely recommend it, even if you're new/mediocre
If you think about it for a second, you will realise that, on average, you win 3 games, because any player in Arena can only lose three times, so for each win above 3, another person has to win one time less, so the average will always stay 3 games. And now the question is: since you are granted a pack, are the 4 other rewards worth 50 gold? And of course, if you are an above average player, which cannot be assumed generally, you might get more, but on a general basis, I don't think arena is worth it. Even though it might be more fun.
Your math is faulty, your statistics are meaningless and not based on anything other than pure speculation. The average win rate could be 4 or 5 or 6.
Your math is faulty, your statistics are meaningless and not based on anything other than pure speculation. The average win rate could be 4 or 5 or 6.
Max of 3 losses Max of 9 wins
For someone to win, another person has to lose For the average win rate to be 5, for example, then then you would expect there to be another 5 losses from another person, which is impossible because the loss caps at 3 and the losses carry over to a second player, therefore, you can never expect a balance of winners:losers
This is twofold: - One, there are more losers than winners. Losers are those who fail to be reimbursed, winners are those who win back the entrance fee. This leads to $1.99 or making use of other resources for gold. Blizzard likes $. This equation will always favor the $1.99 while allowing for room to grow and push for returns, satisfying both sides of the party. - Following, you cannot expect to always gain net value investing gold in arena because there are more losers than winners. Higher chance of entrance fee being reimbursed are still at 7 wins, with gains on net gold slightly above at 5~6 wins, raising the overall re-entries in arena and balancing out the curve ever so slightly. The rewards are still RNG below the 7 mark and you can't expect to get 50 gold to break even on net gold while including the pack.
Now, to bring Enchanting Dust into the equation, the issue is that it has no real conversion rate, but I think a somewhat generous baseline would be 260 Dust = 100 Gold or a 2.6:1 ratio. The price of one pack put against the minimum amount to craft a pack with 4 commons and 1 rare, which we all know to be the minimum you can pull. With that said, it will take you *Edit: Accidentally a decimal
All things considered, I still prefer Arena as a means of getting the most out of my gold because I can trust my skill enough to do so.
Umm, no. The math is not faulty and completely correct, it is you that seem to have a faulty understanding of rudimentary mathematical ideas. The amount of wins cannot exceed the amount of losses in a closed system, fairly basic. Every win is also a loss for someone else, therefore the average win rate can never ever be 4, 5 or 6. Think about it...
Of course, any given player in the system may well have an average winrate of say 6, but as for the entire system its impossible that the average winrate would ever be that, because that would mean that there would be more wins than losses overall.
That would be true if you had to play 6 matches no more, no less as well as a small and finite player base. With Hearthstone you have neither. The format is 9 wins OR 3 losses, whichever comes first.
Your math is faulty, your statistics are meaningless and not based on anything other than pure speculation. The average win rate could be 4 or 5 or 6.
If you think about it, for every win there is a corresponding loss. Therefore, for every 4-3 run there is a 2-3, for each 5-3 there is a 1-3, etc. So the average arena run across all the board will be 3-3. Now individual players can and will exceed that win rate for their personal average, but for each of them there will be others who win 1-2 games in an average arena run.
3-3 is not the automatic default average win:loss ratio.
9-3 is not part of the dataset, the arena would end at either the 9th win or 3rd loss. That aside, each outcome in the dataset is not equally likely to occur. As many others have pointed out, there are an equal number of wins and losses as a whole within the Arena, for every game there is 1 winner and 1 loser (therefore a 1:1 win:loss ratio). This ratio makes it so that the number of 0 to 3 win runs will occur much more frequently than 4+. As pointed out, it makes it impossible for the average win ratio in arena to be higher than 3
No, you still do not understand the underlying math. And I just said that 3-3 is not the default average win-loss ratio, sometimes its actually less. Like the scenario when one player goes 9-0 and three others go 0-3. The average wins (and losses) in that system is actually 2,25. 3-3 is the upper limit of a win:loss ratio.
But the average number of wins in the system can NEVER go above 3, do you not see that? Show me a scenario when it happens if you want to prove me (and math) wrong.
And no, it has nothing to do with playing exactly 6 matches or not. I know that the chances of someone actually admitting that they were mistaken on an internet forum is close to zero. But I ask that you trust me in this, I do have 4+ years of math on an university level and currently work as a math/physics teacher. All the 9 win stop rule does is to actually LOWER the average amount of losses per run in the system, and by that, also lower the average amount of wins per run.
I have no problems admitting I'm wrong when I'm wrong. Math is not my forte unless it's discrete. But something just seems really off about that 3 win average when you're playing out of a possible 11 matches. I asked Theck if he can math it out for me, hopefully I get a reply. Not arguing for arguments sake.
if you hate arena go there only if you can get at least 6 wins if not better buy packs you get good enough gold in constructed now, 4 and lower wins rarely give more than 10 gold now in arena.
No, theory is made so you can accurately model things. Whether or not you have to go the whole 9 yards depends on how well you want to model something.
In any case, this is a closed system with an analytical solution that's easily arrived at via combinatorics. I've written up the results in a pdf here:
That also contains a link to an m-file that you can run in MATLAB (or FreeMAT or Octave, most likely, it doesn't use any fancy functions) that will calculate the average number of game you'll play and the average number of wins you'll rack up per deck for a user-definable probability of winning (first line, p=0.5, change the 0.5 to anything from 0-1).
If you have a 50% chance of victory per game, then you'll play an average of 5.9 games per deck and win 2.95 of those games. If your chance of winning is higher than 50% (i.e. a very good player), then of course those numbers go up.
No, theory is made so you can accurately model things. Whether or not you have to go the whole 9 yards depends on how well you want to model something.
No cutting corners in most cases, but where you can, referencing them replaces most of the dirty work because it's already substantiated by most of the community in question. Sure, shoddy work in the strictest sense, but as for how accurate, there's a nice number 3 that I can use in the scope of this situation without exiting my realm of comforting laymanliness to traverse into the world of combinatorics nor being technically incorrect as far as I understand.
I know this has been discussed before but since Arena rewards were changed in the patch I'm curious, which is now more Gold efficient (you get more rewards for the Gold spent)? Even though Arena takes longer (obviously) I'd gladly spend all my gold on Arena if it gives me more cards/dust for my Gold than buying packs straight up.
Here are the Arena changes:
Without putting too much though into it, I would venture to say arena is more effective. My main reason: at 7+wins you get ALL the gold you spent back (and maybe some extra) so that in theory you could take the free arena run you get and never have to spend a dime to fill out your collection
Arena is potentially more efficient at 5 wins and up. If you are consistently getting 5+ wins, its more efficient on paper. That said, if packs are your concern you have to factor time into as well.
Bob wants a pack of cards so he can improve his constructed pool. He has 150g. He can invest 100g for a pack and have 5 new cards in about 10 seconds. He can also try out the arena and get one of the following:
1. A more expensive pack (150g for arena pass resulting in under 5 wins.)
2. An 'even' pack (5 or 6 wins *150g - ~50 for reward*)
3. Bonus pack (7+ wins, gold returned, plus pack)
Bob has to put about an hour into each of these options, and depending on his skill (and luck) he could end up paying more gold for that pack of cards (his primary reason for arena.)
There is a time investment into arena. So thats pretty much it. If you are good at arena, its more efficient, if you suck at arena, and packs are your primary concern (ie you aren't doing arena for fun) then you could just be hurting yourself.
So lets say I'm only average at Arena and only end up with 3-4 wins. Would the cards + dust value at that amount of wins be greater than the value of a single pack, break even, or be a loss? I'd assume it'd be closer to break even and 5-6 be profit (since that's what they buffed in the patch) but I just want to make sure.
I'm sure I could pull out good streaks often enough (6+ wins) but I've had some terrible runs too (~3 wins). So if I'm only breaking even on average I might as well save myself time and just buy packs.
Thanks for the insight. :)
Its still tough to gauge properly just because right now we have a bunch of data based on arenas before the changes. Once we have more numbers on how much dust is still being handed out for under 5 wins, and how much bonus gold people are actually getting on average for 5/6 wins then it will be easier to tell.
It's obvious, just grind out arenas. If you hit even 50 gold you break even if you include the pack, unless you're having a horrible win streak, Arena is always the option.
It does get a little tedious, and sometimes you just want to rip packs open, but I try to be moderate
http://www.youtube.com/user/vtxaishi
You're not going crazy, I edit 2~3 times each post
The reward changes definitely favour Arena, unless you hardly ever achieve 4+ wins.
Even winning only 4 times is hardly a deficite. 5+ always had 50G.
Did 15 Arenaruns yesterday, worst session was 2-3 with a really bad deck, had one 8-3, rest was 5+.
Due to bonusrewards (had a bonus golden rare once and a "normal" common) I netted way better than having just bought 15 Packs.
Plus I was entertained for the whole day.
Add in the Funbonus and Arena is the winner :)
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I've done three arenas since the patch. First arena with 2 wins I got 40 gold (basically a pack and ~40 dust cost me 110), second I got 3 wins and 50 gold (broke even), third I got 4 wins and 60 gold. Arena is definitely the better way to go and way more fun too. I defintiely recommend it, even if you're new/mediocre
Your math is faulty, your statistics are meaningless and not based on anything other than pure speculation. The average win rate could be 4 or 5 or 6.
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Max of 3 losses
Max of 9 wins
For someone to win, another person has to lose
For the average win rate to be 5, for example, then then you would expect there to be another 5 losses from another person, which is impossible because the loss caps at 3 and the losses carry over to a second player, therefore, you can never expect a balance of winners:losers
This is twofold:
- One, there are more losers than winners. Losers are those who fail to be reimbursed, winners are those who win back the entrance fee. This leads to $1.99 or making use of other resources for gold. Blizzard likes $. This equation will always favor the $1.99 while allowing for room to grow and push for returns, satisfying both sides of the party.
- Following, you cannot expect to always gain net value investing gold in arena because there are more losers than winners. Higher chance of entrance fee being reimbursed are still at 7 wins, with gains on net gold slightly above at 5~6 wins, raising the overall re-entries in arena and balancing out the curve ever so slightly. The rewards are still RNG below the 7 mark and you can't expect to get 50 gold to break even on net gold while including the pack.
Now, to bring Enchanting Dust into the equation, the issue is that it has no real conversion rate, but I think a somewhat generous baseline would be 260 Dust = 100 Gold or a 2.6:1 ratio. The price of one pack put against the minimum amount to craft a pack with 4 commons and 1 rare, which we all know to be the minimum you can pull. With that said, it will take you
*Edit: Accidentally a decimal
All things considered, I still prefer Arena as a means of getting the most out of my gold because I can trust my skill enough to do so.
http://www.youtube.com/user/vtxaishi
You're not going crazy, I edit 2~3 times each post
That would be true if you had to play 6 matches no more, no less as well as a small and finite player base. With Hearthstone you have neither. The format is 9 wins OR 3 losses, whichever comes first.
The dataset includes: 9-0, 9-1, 9-2, 9-3, 8-3, 7-3, 6-3, 5-3, 4-3, 3-3, 2-3, 1-3, 0-3
3-3 is not the automatic default average win:loss ratio.
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If you think about it, for every win there is a corresponding loss. Therefore, for every 4-3 run there is a 2-3, for each 5-3 there is a 1-3, etc. So the average arena run across all the board will be 3-3. Now individual players can and will exceed that win rate for their personal average, but for each of them there will be others who win 1-2 games in an average arena run.
9-3 is not part of the dataset, the arena would end at either the 9th win or 3rd loss. That aside, each outcome in the dataset is not equally likely to occur. As many others have pointed out, there are an equal number of wins and losses as a whole within the Arena, for every game there is 1 winner and 1 loser (therefore a 1:1 win:loss ratio). This ratio makes it so that the number of 0 to 3 win runs will occur much more frequently than 4+. As pointed out, it makes it impossible for the average win ratio in arena to be higher than 3
I have no problems admitting I'm wrong when I'm wrong. Math is not my forte unless it's discrete. But something just seems really off about that 3 win average when you're playing out of a possible 11 matches. I asked Theck if he can math it out for me, hopefully I get a reply. Not arguing for arguments sake.
Cheers!
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if you hate arena go there only if you can get at least 6 wins if not better buy packs you get good enough gold in constructed now, 4 and lower wins rarely give more than 10 gold now in arena.
1 gold = 2.5 dust
20 dust = 8 gold
50 gold = 8 gold?
>:
I think you mean 125 Dust, which skews your analysis a bit heavily. There's a decent chance you won't break even around 2~3 wins
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I stand corrected, here's the data: (tldr avg # wins 2.9546 and avg # games is 5.9092 ASSUMING 50/50 odds of winning)
@TheckPhD Hearthstone math ? Arena round ends at 9 wins or 3 losses. Avg wins given 1 mil players would be?
@ZalbarTheMad General soln: mean N = sum_{n=3}^8 n*nchoosek(n-1,2)*p^{n-3}q^3 + sum_{i=0}^2 9*nchoosek(8,i)p^{8-i}q^i ; q=1-p, p=win chance
Average wins? Or average games? Complicated problem either way, but avg # games should be 5.7773 if 50/50 chance of winning
that's for number of games; number of wins is a slightly different calculation (the 9 in the second sum has to change)
avg # wins =sum_{n=3}^8 (n-3)*nchoosek(n-1,2)*p^{n-3}*q^3 + sum_{i=0}^{2} nchoosek(8,i)*((9-i)q^i*p^{9-i)+(8-i)q^{i+1}p^{8-i})
Looks like average number of wins works out to be 2.8887 for 50/50 odds of winning
Actually, I take that back. I misread that as 9 *games*, not 9 wins. That changes things slightly
Updated values: avg games = 5.9092, avg wins = 2.9546
games=sum_{n=3}^{11} n*nchoosek(n-1,2)*p^{n-3}*q^3 + sum_{n=9}^{11} n*nchoosek(n-1,n-9)*p^9*q^{n-9}
# wins = sum_{n=3}^{11} (n-3)*nchoosek(n-1,2)*p^{n-3}*q^3 + sum_{n=9}^{11} 9*nchoosek(n-1,n-9)*p^9*q^{n-9}
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I appreciate all the math, fun read, but that's so much overthinking for this situation.
It's a closed system with two situations - 9 of x or 3 of y where one begets the other. Average of the y is the cap because x exceeds it.
I suppose on the flip side you can call it oversimplified, but theory is made so that you don't have to go the whole 9 yards.
http://www.youtube.com/user/vtxaishi
You're not going crazy, I edit 2~3 times each post
No, theory is made so you can accurately model things. Whether or not you have to go the whole 9 yards depends on how well you want to model something.
In any case, this is a closed system with an analytical solution that's easily arrived at via combinatorics. I've written up the results in a pdf here:
https://sites.google.com/site/theckhd/other/Hearthstone_Arena.pdf
That also contains a link to an m-file that you can run in MATLAB (or FreeMAT or Octave, most likely, it doesn't use any fancy functions) that will calculate the average number of game you'll play and the average number of wins you'll rack up per deck for a user-definable probability of winning (first line, p=0.5, change the 0.5 to anything from 0-1).
If you have a 50% chance of victory per game, then you'll play an average of 5.9 games per deck and win 2.95 of those games. If your chance of winning is higher than 50% (i.e. a very good player), then of course those numbers go up.
No cutting corners in most cases, but where you can, referencing them replaces most of the dirty work because it's already substantiated by most of the community in question. Sure, shoddy work in the strictest sense, but as for how accurate, there's a nice number 3 that I can use in the scope of this situation without exiting my realm of comforting laymanliness to traverse into the world of combinatorics nor being technically incorrect as far as I understand.
Cheers, thanks for the link, appreciate the work.
http://www.youtube.com/user/vtxaishi
You're not going crazy, I edit 2~3 times each post