I'm at 209, and I dare promise you that I will have far from all the epics I'd want by the time I get to the guaranteed champion. It isn't about volume, it's about specifics. I have more legendaries than I can use at the moment because I don't have the books for all of them. Even so, like I said, at worst it's a 4* chicken or a book, so even in the worst case they are not wasted.

The cumulative chance of opening 12 shards and getting a legendary (or rather the chance of *not* getting a legendary) is not particularly relevant since we are talking separate events. You could get 0, or you could get 12. The expected results out of 12 shards at 12% chance is 1.44. Some will get more, some will get less. You may opt to open shards at 6% chance which would bring the expected total down, but then it's presumably because you're trading it for something you value more, which will no longer be an option.

Plus, that missing shard might end up being the one piece you need to complete a summon rush for a fusion, or to get you an extra legendary book or something, so it's not like its potential content is the only value it has.

Again, that is already there before this announcement. Also, I don't have the ability to get one from DT yet. I have just made it as far as I ever have at normal 110, and haven't tried hard in a while but couldn't even get to the first boss (though I probably could now). I have been too focused on getting champs to finally be able to consistently do all dungeons at 20 and get a team to 4 key UNM. currently buidling budget unkillable (just got my first maneater) and/or SkullTower ( Mercy was up yesterday and tried my hand at getting Bad El, not dissapointed at all getting Roshcard though).

I say I have been playing for a year but it has been on and off and at certain points I would just log in to get the daily reward.

I won't deny someone may need more epics over legendaries, or that some people may want different free login rewards.

I will say it is not 1.44 though as that's not how differing statistical events add up. You have just multiplied 12% by 12 times. But random chance events that you do back to back, over and over work differently.

See, each pull is it's own 12% chance.  Each shard opening is independent of the others, with a new 12% chance, and they don't sum together. That math is, again, 1((1-.12)^12).  The 12 shards give you a .78 chance. of succesfully pulling a legendary, that's just how the math works. 

As far as chickens, for me, I just have more energy than I know what to do with at this point, and wouldn't mind specific champ fragments. I can see how someone would prefer epics for their login rewards, especially if you're short on legendary books. 

It is 1.44. What you're calculating is the chance of opening 12 and getting no legendary (and from that inferring the inverse, which is to say 1+). That may be interesting when you want to evaluate the misfortune of someone who got no legendary, but it does very little when we're looking at a large population and try to objectively evaluate the value proposition.

The expected value is something else, which is more useful in this case since we're comparing the expected value of two separate scenarios, in which one has 3 events at 100% chance (which gives the expected value of 3) and the other 12 events at 12% chance. For example, tossing 100 coins gives you an expected value of 50 heads. Throwing a d6 dice 100 times and counting the 1s gives you an expected value of 100 * 1/6 = ~16.67. Opening 12 shards at 12% gives you an expected value of 12 * 0.12 = 1.44.

The chance to fail gives you the same answer. 1-(.88^12) gives you a 78% chance of success over 12 attempts. :D

Now, with the way math is, it's easy for anyone to get things wrong and mixed up, so I'm not willing to say I get 100% of every math problem correct. Could be the case here! I often get rightfully corrected while teaching! :D

Have a good day!

actually most of them are.

Pray tell me where exactly are you using the follwing S tier champs - Yaga, Lordly Legionaire, Dark Athel and Dark Elhaine?

Yes Ninja is great, Scyl is great and ther are 2 moer good ones. Ninja being limited time and result of an epically failed marketing campaign, which given the scope of the fail wil lprobably never ever again repeated.

I am also interested to know in how many areas of the game you are currently using or will use the S tier champ Cleo.

Very interested in your answer.

Yes I have no info on which future legendaries will appear. Given however the information, that Plarium chose a trash tier one for the first round doesn't bode well for the future, don't you think? It's not like Plarium has a history of generosity or has it and I have missed it somehow?

Let's try this again with the quote...

Look, the problem is that you're making a problem that is not binary into a binary problem. If the question was if you'll get at least one legendary, then you would be correct, but the question is not if but how many. You have the answer for 0, which is about 22%. Rounded, it's then 35% to get 1, 26% to get 2, then 12%, then 4%, then 1%, then we're down to ~0% the rest of the way to the max of 12, the sum of those probabilities being about 78%. If you want to get the expected outcome for the average case, you can either do as I did before and just multiply the chance by the number of trials, or you can calculate the average from those probabilities, which is to say 0.35*1 + 0.26*2 + 0.12*3 + 0.04*4 + 0.01*5, which happens to be 1.44 despite the rounding. 

That is only true if all you value is legendaries.

12 sacred shards means 12 chances of getting something useful for general use or a specialised area. Compare that to the quality of the first thing plarium hands out, which is exactly useful...where?

I mean, none of us know what the next champ will be after Cleopterix. Just like everyone, I hope the one after her is awesome and helps my account!

There have been some very very solid free champs in my opinion. I used Scyl, High Khatun, Grush and Visix all over the place, and Scyl still gets in my teams a ton even now. Ninja looks very helpful, especially for new and mid accounts, but I just finished his masteries so I'm going to start trying him out for myself.. And Dark Elhain makes me very happy to fight Tormund teams and farm Ice Golem, although I'm at the stage to farm Fire Knight now pretty much exclusively. :D

off the top of  my head these are the free champions I am currently using  in the game that Plarium gave me access to aquire without summoning them directly from a shard

All of these I use  in Faction Wars as I continue to combat the end  boss  in all factions

Rhazin / Broadmaw / Drexthar / Akoth / Archemage Hellmut / Scyl / Visix / Elegaius . Cleo will join my faction wars skinwalker team

Scyl and Drexthar I also use periodically in DT

The  only reason I am no longer using the other free champions is because I have bought and summoned many shards aquiring many legends which replaced the others I no longer use

Forgot to add Arbiter. she was a great addition

Do you count Arbiter as free? I mean, technically she can be but she's so very hard to get I don't even think of bringing her up, even though she is basically the champ for me in arena. :D

And Archmage! How did I forget him? Gosh he slaps!

at the stage of missions I was approaching arbiter it was the one thing that gave me a kick in the pants to finally make a unkillable NM team

I suspect I may not finish my UNM unkillable  until the next mission makes me do so

But yes I love missions. It motivates me. Especially when such amazing FREE legends await you at the finish line. Much like faction wars. But Faction wars has so many other great reasons to play and such a important part of the game for account development. 

It's  ok  to  disagree  with  someone  and  post  your  own  thoughts  on  the  issue,  but  I  would  ask  you  to  become  more  civil  in  your  responses.  

If  you  are  unsure  how  to  do  that,  I   recommend  that  you  read the  responses  from  harleQuinn,  Priestguardian,  and  Egdnit  in  this  thread  as  they   are  making  valid  points  while  being  respectful   or  responding  in  kind.  

Just wanted to confirm that you are correct in saying that the chance to get a legendary after 12 sacred shards is 78%:

• Chance to get a legendary after 1 shard = 12% (88% of no legendary)
• Chance to get a legendary after 2 shards = 22% (1-(88^2))
• Chance to get a legendary after 3 shards = 31% (1-(88^3))
• Chance to get a legendary after 12 shards = 78% (1-*88^12))

That said, as mentioned before the value of the sacred shards are not only for the legendary chances.  It's much more as it brings so much additional context and choice into the game.

Benefits of 12 sacred shards including any of the following:

• 12 additional champions of at least epic level
• 6000 points for a summon rush (plus all of the tier rewards this brings)
• Between 1200 and 3000 points for Champion Chase (plus all of the tier rewards this brings) 
• +12 shard counts towards a guaranteed champion opening event
• Additional Increment to the mercy counter to help the other 12 sacreds you get from monthly quests
• The choice to participate in any of the 12 fusion/fragment events that year, which also gives a guaranteed legendary
• The choice to participate in any of the 2x or x10 events that occur

Benefits of the 4 free legendaries

• 4 additional legendary champions
• Don't need to play the game for them (I guess this is a benefit?  Who actually wants to play Raid?)

Both of these scenarios have the downside of being potential duplicate champions.

The biggest problem I have had with this is the removal of choice for a player to actually play the game.  I'd actually be slightly happer if the fragments given in the daily logins were generic fragments, and the player could choose where they wanted to spend it (i.e. during a fragment event, or for past champions, or even new ones).  

Do Plarium want us to play the game or not?

The point still remains. We did get a shard and chicken for free every month for just logging in, we no longer those rewards for logging in. 

I accept that you and others prefer the new log in rewards, but, ignoring the shard loss we are still talking about a lot of time and energy for the lost chicken... even if you can still get that reward from other content in the game. 

If they had removed the chicken from the logins and said, "hey, we have removed it but you can now get an extra chicken by doing this" that would be different and is not what they have done. 

I don't understand your argument at all.

1. How does the shard make u play the game more than the fragments? 

2. You completely overvalued the shard, and undervalue the fragments. 

This is well put point I was trying to get across.

Sure we can get 5* chickens in other areas of the game, Advanced quest, DT and if you can manage it events, tournaments and CVC (though currently I am only able to aquire them from the advanced quests) but we could already get them from these areas before they removed it from the daily login. There is no added alternative as of yet to get a 5* chicken on top of those places mention. Except through the clan shop, but you have to be in a clan that's ranked 16. and it costs 3000 clan gold which is in itself rediculous since 100 energy costs 100 gold and essentially 1500 energy=5* food making it not worth it.

I think you've shown with your post all the ways you can get chickens playing the game: advanced quests, dt progress, clan shop, cvc, tag shop, constant tournament events.... all added over the last year. You also get 1000s of free energy each month, and they continue to add more and more. Everything about the game is far more f2p friendly than when I started.  I have like 4 weeks of 2xp, I used to have to spend gems often for that. Never need to anymore. The clan shop prices are very reasonable, I think you can easily get enough energy and small chickens to make multiple 5star chickens each month.

and lets  not forget the clan shop frags for yet another free lego

I currently do not have that one either and plan to collect those free frags as well :) along with the daily login legos

I am saying that a shard allows you to participate in the game more than the fragments.  Providing a player with a sacred shard gives them a choice.  Do they use it straight away, or do they save it.  If they save it, what will they save it for?  A summon rush?  A champion chase?  A fusion/fragment event?  A guaranteed champion event?  A 2x event?  A 10x event?  

Now the player has to identify what is best for their account and make a plan.  If they use their shards in this 2x event, then they won't have enough shards for the next fusion event.  But if the next fusion event is crap anyway, then maybe it's better to just use them all now.  Maybe instead the player needs books, so will wait for a summon rush and aim for the top tiers. 

Everything I listed above are features the game offers, but to participate in them you need shards.  The shards provided by these daily logins are not enough to do them all, but are enough to give a player a chance to choose what they want to do

A similar example is gems, which also gives players choices.  They can use them for masteries, for energy, for shard parks, for gem mine, for Marketplace slots, for sparring pit slots, etc.  They are a currency that is given to players to then allow the players to choose where they use them in the game.

Providing 25 fragments a month does not give the player any choices.  If a player logs in and get 25 fragments, then until they finish the 4 months they don't get any additional drive to action.  They can't use those 25 fragments halfway.  They can't use them in any of the numerous tournaments and events that are thrown at you.  This is why I proposed before that these should instead be generic fragments, that could be used for anything.  Now the player can choose where to use them, such as a current fragment event, or a previous fragment event, etc.

If this is how we want to collect champions, then let's just put all champions into the daily logins and rename this to: "Raid: the Login/Logout game"