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Leagues

CrazyWizard

Shaman
That´s of course true you don´t actually need money, just diamonds. So yes I could spend my 20k diamonds from the spire get into the gold league and not have to pay actual money, but that argument is the same all over. So using that argument pay2win doesn´t exist, because I can always use free diamonds to win...
To a certain degree that is correct, off course you can always throw more money at it than you can aquire free diamonds.
But yes since all the changes and generous diamonds payouts pay2win is not really applicable anymore.

I mean I bought some expansions before the change from 2000 diamonds max to the currenty 17500? I bought about 14K diamonds(80 euro) + 2 workers (10 euro) in my life for it. but right now I own 348450 diamonds worth of expansions, own 6 magic workshops and 14 magic residences.
So plenty of free diamonds there, in fact almost all of them are.

So yeah it's not really pay2win anymore. you can easily replace pay with effort these days.
It's just thay paying is quick, and free takes a lot longer but you get there.
 
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Pauly7

Magus
That´s of course true you don´t actually need money, just diamonds. So yes I could spend my 20k diamonds from the spire get into the gold league and not have to pay actual money, but that argument is the same all over. So using that argument pay2win doesn´t exist, because I can always use free diamonds to win...
Anyone can do that (well, anyone with enough diamonds). I had a team member in Beta do the same (Soggyshorts). He waited until the final hour of the event and then spent all his currency plus any diamonds he needed to in order to get the double set. I think he said it cost somewhere close to 5,000 diamonds. That figure is, of course, swayed massively by luck. On Beta I finished in gold having spent 600 diamonds.

Anyway, I'm digressing... The point I came here to make was that Inno still sees it as you spending money if you use your saved diamonds, because they will figure the more these stores can be depleted the more likely people will be to want to spend in the future.
 
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Sir Derf

Artisan
yes but I did not like it much.
most of the time you also have a 45% with return in the same pool.
Then it's 19SK, but if luck fails 27 per SK, or 19.6SK and 22.5 if luck fails.

45 with return is by far the less risky move
And if you throw the dice on luck, 80/89 has a far greater impact in your luck results. a few good dice rolls set's you up high (and none sets you low)

A few good dice rolls on 27 is nice, but it keeps you in average player land.
If you use the strategy everyone does, you get into everyoneland.


If thats the case, then they call this change a super duper amazing awesome change. (from innos point of vieuw)
and yes if you are only 32 below gold at the end of the event, it makes sense to maybe go for it. same for those close enough to silver.

Thats where they obviously hope for, enough edge cases to increase spending.
There is a reason these GP are pretty good ;)
It's too early in the morning to start doing semi-pointless math.

I think we both agree on where the relative humps of the respective probability curves are for the 27 and 80/89 chests, the question is what goes on with the tails. What are the odds and payoffs on 1, 2, 3 lucky rolls above average... Where is the crossover point, where the luckier players with 80/89 make out better than the luckier players with 27?

I'll get back to you.
 

Gargon667

Mentor
I think we are leaving maths behind and cross over into metaphysics...
 

Sir Derf

Artisan
Metaphysics - abstract theory with no basis in reality

I object! My semi-pointless math (tm) is still attempting to describe reality. Even a discussion of the likelihood of the unlikely is reality. Now, positing a semi-sentient capricious RNG...

Now, let the semi-pointless math begin.

Step 1 of analysis - What do you expect.

Round27 SK80 SK89 SK27 chests80 chests89 chests27 bonuses80 bonuses89 bonuses
1
6000.00​
6000.00​
6000.00​
222.00​
75.00​
67.00​
22.00​
4.00​
8.00​
2
1766.00​
1200.00​
1637.00​
65.00​
15.00​
18.00​
7.00​
1.00​
2.00​
3
571.00​
300.00​
435.00​
21.00​
3.00​
4.00​
2.00​
0.00​
0.00​
4
164.00​
60.00​
79.00​
6.00​
0.00​
0.00​
1.00​
0.00​
0.00​
5
82.00​
60.00​
79.00​
3.00​
0.00​
0.00​
0.00​
0.00​
0.00​
1.00​
60.00​
79.00​
0.00​
0.00​
0.00​
0.00​
0.00​
0.00​
Total Used856075008000317938932510

27 SK chests - 317 chests, 317 flags, 15 Grand Prizes, including 32 bonuses of 80 SK, for 2560 SK total bonus.
80 SK chests - 93 chests, 279 flags, 13 Grand Prizes, including 5 bonuses of 300 SK, for 1500 SK total bonus.
89 SK chest - 89 chests, 267 flags, 13 Grand Prizes, including 10 bonuses of 200 SK, for 2000 SK bonus.

Step 2 of analysis - Odds of getting different outcomes...

(Edit - had to correct the Total Used SK cells)
(Edit - changed Grand Prize payouts, 20 flags/GP, not 10)
 
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Sir Derf

Artisan
Hmmm, Excel doesn't like 317! Had to brute-force 317!/(317-n)!...

Okay, got the numbers, got the presentation, but as setup, let me first try and describe what I think the scenario at hand is...

So, yeah, sure, the 27 chest gives the best average payback, but look at that bonus payoff in those large chests. 200, 300 SK! If I'm lucky and get above average results, that'll be way better, right?

Well first of all, look at the above average numbers. The 89 and 80 chests scored 560 SK and 1060 SK fewer bonus than did the 27 chest. It's going to take 3-5 additional bonuses to almost match the performance of the average 27 chest.

Then, consider how lucky you have to be to get 3-5 additional on those chests, and ponder what the payout for the 27 chest would be for a similarly lucky player... or even a half lucky player...

Lets just look at first order effects from our previously established baselines of opening 317, 93 or 89 of each of the 27, 80 and 89 chests.

27 vs 80 vs 89 Chest
Bonus CountOddsCumulative OddsTotal SKFlagsBonus CountOddsCumulative OddsTotal SKFlagsBonus CountOddsCumulative OddsTotal SKFlags
210.05%14.20%6600
246​
76.92%14.84%7400
249​
264.45%16.53%8080
299​
275.33%21.86%8160
302​
89.67%24.51%7600
255​
286.14%28.00%8240
305​
316.04%30.24%6900
258​
296.80%34.80%8320
308​
911.87%36.38%7800
261​
307.25%42.05%8400
311​
317.46%49.51%8480
314​
418.99%49.23%7200
270​
1012.95%49.33%8000
267​
327.41%56.91%8560
317​
1112.68%62.01%8200
276​
337.11%64.02%8640
320​
517.79%67.03%7500
279​
346.60%70.62%8720
322​
1211.24%73.25%8400
282​
355.93%76.54%8800
325​
613.74%80.76%7800
291​
365.16%81.70%8880
328​
139.08%82.33%8600
288​
374.35%86.05%8960
331​
146.72%89.05%8800
294​
383.56%89.62%9040
334​
78.99%89.75%8100
303​
392.83%92.45%9120
337​
154.58%93.63%9000
303​
402.19%94.64%9200
340​
85.08%94.83%8400
315​

Getting an extra 33rd bonus 27 chest gives only 80 SK.
Getting an extra 11th bonus 89 chest gives an extra 200 SK.
Getting an extra 6th bonus 80 chest gives an extra 300 SK.

But
Getting an extra 33rd bonus 27 chest is only a 7.11% increase in luck.
Getting an extra 11th bonus 89 chest is a 12.68% increase in luck.
Getting an extra 6th bonus 80 chest is a 13.74% increase in luck.

32 Bonus 27 chests produced a total of 8560 SK.

Getting 3 bonus 89 chests for 8600 SK is a 33.00% increase in luck.
Getting 4 bonus 80 chests for 8700 SK is a 31.46% increase in luck.
That same increase in luck would produce 6-7 additional bonus 27 chests.



Bottom line, semi-pointless math shows that better math is still better.

27 chest is still the superior chest. You have to be more than one-off luckier with 80 or 89 chests to match the average outcome with 27 chests, and if you're going to be that lucky that you surpass average 27 chest, you would have been better served being that lucky with 27 chests.
 

Sir Derf

Artisan
BTW, the above numbers seem a little odd, because the question "What are the odds for number of bonus chests when opening 317 27 chests?" is different from "What are the odds of opening 6000 SK worth of 27 chests?" The second batch of computations, near-match across the three chests types at 49+% at 31, 4 and 10 chests, instead of 32, 5 and 10. If adjusted to that norm, the benefits of 27-chest strategy appear improved somewhat.
 

Gargon667

Mentor
27 chest is still the superior chest. You have to be more than one-off luckier with 80 or 89 chests to match the average outcome with 27 chests, and if you're going to be that lucky that you surpass average 27 chest, you would have been better served being that lucky with 27 chests.
While I personally rather take the 18er chest and certainly agree with 27 being better than the rest, I believe @CrazyWizards point was to go gambling seriously.

You are telling him his chances to win are better if he puts his money on red, but he is going to put his money on the 7 instead, because he doesn´t care about winning, he only cares about winning big!

So in terms of the calculations wouldn´t it make sense to say: What are the odds of making it to a total of 10000 SK (or whatever is deemed the limit for the gold league) from a starting point of 6000 SK?

Now without even intending to do the maths, my guess would be @CrazyWizard has a chance to be right, because you need fewer big chests to reach the goal, while the 27 would need a lot more chests to get there. And more chests always increases the likelihood of a more average result, which we don´t want in that case... So fewer big chests might have a higher chance of being off the average far enough to make the goal.

That is my metamatical explanation :)
 

Pauly7

Magus
You are telling him his chances to win are better if he puts his money on red, but he is going to put his money on the 7 instead, because he doesn´t care about winning, he only cares about winning big!
I'm not sure that is the best comparison as putting your money on red or on 7 have the exact same odds over time. What we need is a scenario where choosing red had slightly worse odds of winning, but you could go for it with the no-guts-no-glory approach.

On a side note - The best thing is to walk away and go find a game of French Roulette, which looks exactly the same, but gives you much more favourable odds... but I digress.
 

Sir Derf

Artisan
Well, for starters, my above table ends at bout 94 +/-% chance of opening 40 out of 317 27 chests for 9200 SK or 15 out of 89 89 chests for 9000 SK, so we were almost at the 10,000 level.

On the ridiculous level, both chests allow the possibility of infinite progress. All you need is better than 1 bonus every 2.96 27 chests (33.75%, or 3.375 times the expected rate) or better than 1 bonus every 2.25 89 chests (44.50%, or 3.71 times the expected rate).

Doubling isn't all that more impressive from where we left off, so let's shoot for tripling, 18,000 SK.

12,000 SK bonus means 150 bonus 27 chests, or 60 bonus 89 chests.

Uhmmmmm. Broke Excel again with my computation of 317!/(317-n)! Rather than rework my math, let's shoot for 16,000 SK total.

10,000 SK bonus means 125 bonus 27 chests, or 50 bonus 89 chests.

125 bonus in 317 27 chests represented a near 100% cumulative odds, out to something like 10 decimal places.
50 bonus in 89 89 chests represents 99.9989% cumulative odds.

And again, I'm talking first order effects, not including compounding on the above, or what is needed to reach our goal with compounding.
 

Sir Derf

Artisan
I'm not sure that is the best comparison as putting your money on red or on 7 have the exact same odds over time. What we need is a scenario where choosing red had slightly worse odds of winning, but you could go for it with the no-guts-no-glory approach.

On a side note - The best thing is to walk away and go find a game of French Roulette, which looks exactly the same, but gives you much more favourable odds... but I digress.
He gave a bad analogy. Our scenario is our scenario. Lower cost, lower odds, lower reward but overall better payout beats higher cost, higher odds higher rewards but overall worse payout. Mostly...
 

Gargon667

Mentor
I'm not sure that is the best comparison as putting your money on red or on 7 have the exact same odds over time. What we need is a scenario where choosing red had slightly worse odds of winning, but you could go for it with the no-guts-no-glory approach.

On a side note - The best thing is to walk away and go find a game of French Roulette, which looks exactly the same, but gives you much more favourable odds... but I digress.
I guess I didn´t do that one very well, see if I can save it somehow ...

What I was trying to say is: We have 100€ each, a roulette table and one chance.
Gargon leaves, because as an average over all the people playing they will come out with less than 100 €
Sir Derf puts his 100€ on red because it gives him the highest chance to win and get away with 200€ (yes I know he also wants to leave, but he can´t really run away now, can he?) Maybe Pauly wants to take his spot?
Crazywiz put his 100€ on 7, because he doesn´t care if he has 0 or 100 or 200€, he needs 1,000€ or the Gangster he borrowed money from to buy his latest alchemy kit (it was a fraud and didn´t make gold as promised) is coming to collect tomorrow and if he doesn´t have 1000€ cash, a few of his body parts will go missing.
 

Sir Derf

Artisan
Okay, thought I'd try something different...

Playing around with the spreadsheet for my first table (which factored in compounding), I tried changing the bonus odds on the original chests to get an equivalent outcome.

By raising the 89 chest payout rate from 12% to 16.66-16.67% (38.83% increase), I could get 103-107 chests total (an increase of 10-14 chests) for 309-321 flags, bracketing the average 317 flags from average 27 chest play, and achieving 15 Grand Prizes

If I raise the 27 chest payout from 10% to 13.74-14.18% (around 38.83% increase), I could get 376 chests total (an increase of 59 chests) for 376 flags, and get 3 Additional Grand Prizes.


If I doubled both odds (20% vs. 24%), I get 27 and 22 Grand Prizes, respectively.
Tripled (30% vs 36%), I get 81 and 48 Grand Prizes, respectively.
 

Sir Derf

Artisan
The problem with your analogy is that you picked possibly the worst game for your purposes; all payouts in roulette are the same.

The ball lands on 1 out of 37 spaces, your payouts are based on 1 out of 36. Every bet is about 2.7% in the houses favor. There is no highest chance. Bet on red and bet on 7 have the same odds. For a long term goal, the odds are the same no matter what bet you place.

Having placed numbers on your scenario, though, you have skewed the situation somewhat, as starting with 100 but looking for 1000 is not a long term goal. Winning the 1/37 7 bet (2.7%) gets 3,600, more than enough for the Gangster. Winning the 18/37 Red bet (48.64%) 4 times (5.60%) all in, will get 1,600, again more than enough, and with odds better than twice that of the 7 bet. But that is only because you choose such a small goal.

And as I keep pointing out, the math is the math. The payouts don't care whether you care if it pays out. Regardless of if you want to come out with taxi money or Gangster money, the best strategy is the best strategy, and given our two options, the 27 chest is better than the 89 chest. If you ignore luck, you'll do better with 27. If you are planning for luck, you'll do better with 27. It's only if you're going to invoke the magical special pleading of "I'll be luckier if I pick 89 than if I pick 27" that this works, but then you're stacking the deck (to mix my metaphors). And you would need to overstack the deck, because you need to be overly lucky with 89 just to do as good as 27.
 

CrazyWizard

Shaman
Crazywiz put his 100€ on 7, because he doesn´t care if he has 0 or 100 or 200€, he needs 1,000€ or the Gangster he borrowed money from to buy his latest alchemy kit (it was a fraud and didn´t make gold as promised) is coming to collect tomorrow and if he doesn´t have 1000€ cash, a few of his body parts will go missing.
Roflol,

What sir Derfs calculation did not take into account is the times you play.

There are 2 reasons why I disliked 27.
  • the cost per staff is not much better than 45 with return. this means that if I have 27 or 45 with return as an option the 27 has a much higher risk factor. when you are unlucky at 27, you loss is 27, if you are unlucky at 45 with return your loss is 22.5 per staff. so even of 27 is a tiny bit better on paper it's much more riskier, I do not feel the risk is worth it as it's reward ain't that amazing.
  • 27 is a small number, one of the reasons why in the past with other formats like the one event started with we always said grab the smallest chests for best results. it's like rolling a dice. if you roll a dice 6 times the result can be anything from very high to very low and anything in between. but the chance to get average is very slim. but when you roll the dice 50 times you get a lot closer to "average" the chance to roll 6 on a d6 6 times is slim, but the chance to roll 50x6 in a row is near non existent. if you want to aim high you should not do average, "average" is the thing everyone does. and this means your results will also be average. if you want silver or gold you need to do a lot better than average. the analogy with roulette is not that bad. you take a high risk but you need that high payout is you want to make it there. you decrease your win chances a lot, but it's the only way to get really lucky fairly easy. It's easier to get lucky 5 times and walk away with with a huge payout than getting lucky 50 times. because the more times you try, the closer you get to average.
 

Sir Derf

Artisan
I was describing the what I thought was the 'standard' single-zero, which is also easier to understand the math . I am curious as to how your French setup gives half the house payoff.
 

Sir Derf

Artisan
And both of those reasons are nonsense.

Both of your reasons are pure amathematical drivel.

Let me pick apart number 1 in pieces...

the cost per staff is not much better than 45 with return. this means that if I have 27 or 45 with return as an option the 27 has a much higher risk factor. when you are unlucky at 27, you loss is 27, if you are unlucky at 45 with return your loss is 22.5 per staff. so even of 27 is a tiny bit better on paper it's much more riskier, I do not feel the risk is worth it as it's reward ain't that amazing

Your argument consists of:
  • stating 27 is better. This is where the whole argument should start and end.
  • downplaying how much better, which is mathematically irrelevant, bigger or smaller, better is better.
  • Making a risk assessment looking only at the 'unlucky' side, and not at the whole opportunity. It would be equally improper to have said "when you are lucky at 27 you gain (80-27), but when you are lucky at 45 you only gain (80-35)."
  • Ultimately, letting feelings trump math.
Number 2 is longer, so I'm not going to pick it apart the same way. But I believe that you are overstating the way 'luck' can play a part in the 45, or the 89 and understating the the way the same 'luck' can play a part in 27. Also, I think your analogy with dice shifts the math to a different form than what we're talking about here. This kind of stuff really can not be worked out with 'feelings'... our intuitive senses just really aren't cut out to do accurate assessments of complex probabilities.

You talked dice, let's talk dice.


Which weapon do you want, one that does 20d6 damage, or one that does 6d20?

20d6 can do from 20-120 damage, with an average of 70.
6d20 can do from 6-120 damage, with an average of 63.

I believe that the math (not just the three data points I mentioned above, but the whole spectrum of options) shows the 20d6 is the superior choice.

Rather than blindly type further, are you suggesting that it is better to go with the 6d20, because with fewer rolls, it is easier to luckily make a 100+ damage with the 6 larger rolls than the 20 smaller rolls? I think that is the argument you are making, but before I go further, I wanted to verify that.
 
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Pauly7

Magus
I was describing the what I thought was the 'standard' single-zero, which is also easier to understand the math . I am curious as to how your French setup gives half the house payoff.
In French roulette if the ball lands on 0 the house pays back half your stake.