An MPQ Math Problem

Unknown

I love reading the game theory and statistics posted by our forumites. With that said, I was thinking about something last night and I need your help.

Some argue that putting all the 3* into their own token will help with transition, but I am not sure. So I ask, how many draws would you need to get a fully covered 3* under the following hypothetical conditions.

- There are 50 3* characters
- All 3* have 3 skills
- All the covers for each 3* have an equal chance of being drawn
- Only 3* covers are in the token

If the answer can be found, here is the next conundrum. Just because you pull 13 covers for a 3* doesn't mean you are done. You may have built a Hood with 3 blue, a Thor with 3 green, or a Hulk with 5 Red. Not optimal choices, so now you need to keep drawing. So back to the "drawing" board........sorry, couldn't help it.

Anyway, I hope some of you have some fun with this. Thanks.

Killinstinct

I don't think you can calculate this, but you can definitely simulate it.

Unknown

Hadn't thought of simulation. I don't have experience with it, but I will do a google search to see if there is something I can use to find an answer. Thanks.

FierceKiwi

After running a dirt simple simulation 50000 times I got an average of 768.68928.

After running it another 50000 times I got an average of 768.7891.

A few more runs gave 768.03472, 770.03862. So 769 average seems pretty likely unless I completely screwed something up.

Unknown

FierceKiwi wrote:

After running a dirt simple simulation 50000 times I got an average of 768.68928.

After running it another 50000 times I got an average of 768.7891.

A few more runs gave 768.03472, 770.03862. So 769 average seems pretty likely unless I completely screwed something up.

Is that having a fully covered 3* (the distribution doesn't matter) or just pulling 13 covers, because if it's just 13 covers it should be very close to just 50 * 13 = 650. If it's to get some kind of full cover 3* that number looks about right because I was calculating the odds to get a specific cover and started with trying to get 5 in a particular color which is just 50 * 3 * 5 = 750, and you're expected to get 10 covers of the other two colors so that has a high chance of giving you a covered character, and the extra 18 token seems reasonable to account for those rare cases where you got more than 7 of some other color or you got less than 10 covers of the two other colors.

FierceKiwi

Yeah it's to get a fully covered 3*.

Unknown

Thanks for the help. So once we hit 50 3*s, even if they had their own token, it would take 769 tokens to cover max any given 3*. At this point you would have pulled 756 other covers, which with good luck COULD have some if not all the other 3* at 12 covers. Then it would be a 150-1 chance of drawing the much needed 13th cover.

Thoughts? When this point comes, if no other solution has been presented, could this be viable? Or would another step need to be taken as well, such as splitting the 3* into subgroups as mentioned by others before me.

Sandmaker

I think the problem with looking at it this way is that, realistically, nobody uses tokens to full cover a character. At some point it become much more efficient to buy the cover straight up.

FierceKiwi

Sandmaker wrote:

I think the problem with looking at it this way is that, realistically, nobody uses tokens to full cover a character. At some point it become much more efficient to buy the cover straight up.

Eh not really I'd say it's more efficient to just win the character in an event.

Paintsville wrote:

Thanks for the help. So once we hit 50 3*s, even if they had their own token, it would take 769 tokens to cover max any given 3*. At this point you would have pulled 756 other covers, which with good luck COULD have some if not all the other 3* at 12 covers. Then it would be a 150-1 chance of drawing the much needed 13th cover.

Thoughts? When this point comes, if no other solution has been presented, could this be viable? Or would another step need to be taken as well, such as splitting the 3* into subgroups as mentioned by others before me.

I guess that depends on how many tokens you'd end up getting each week and how long would be reasonable to fully cover a character. I think it took me something like 6 months before I had a fully covered 3* (I'll use that as a reasonable amount of time since I don't have anything better to go on).

6 months = 24 weeks
769 tokens / 24 weeks = ~32 tokens/week

That seems like way more Heroic or better tokens than you'd typically get in a week so my guess would be no you'd probably need to do something more unless the target time is alot bigger than my 6 month guess.

EDIT: This ignores the fact that you'd probably win at least a few covers in that time but trying to model that with any accuracy seems like a mess.

Unknown

If you have 50 3*s and if there's an event every 2 days it'd take an average of 100 days before the 3* you need shows up as a reward, and that's of course assuming you can always get top 5 since the cover you need might be the one for finishing top 5.

This is why you should consider using HP to upgrade covers because there's no guaranteed the character you need is even going to show up in an event as a reward in the next month, provided you really need that guy.

Unknown

Putting all of the 3*s into a single token would *not* help the transition from 2*->3*. In most realistic cases, it would make the problem *worse.*

1) The devs want to keep the flow of 3* covers approximately constant over time. (This is basically reasonable; the problem is that they are clueless about how to manage the other issues.)

2) The 2*->3* transition has become much much more difficult because the increasing number of possible 3* covers has diluted the pool. Nine months ago, a player with 75 3* covers was probably deep into the transition with a couple of viable 3*s. Today, a player with 75 3* covers probably has a roster that's 15 characters larger, and none of them have more than 6 or 7 covers.

3) Most of the available 3* covers in game come from progression or placement rewards (and more from PvP than PvE, since PvP events are shorter and run constantly). A minority come from token drops. This means that player roster development will look universally similar, and will depend on the scheduling of fixed rewards by the devs. (The fixed rewards come in "chunks", which is very good for transition purposes, but you need a minimum of 2-3 chunks to have a viable character and the increasing pool means chunks for a *given* character will likely be spaced farther apart over time, which is bad for transition.)

4) A solution that might work better would be to replace some of the fixed 3* rewards with tokens that have a mix of only 5-6 3* characters, and each player chooses Token A/B/C/D/etc. whenever they hit one of those reward points. The total number of 3* covers released is unchanged (one-for-one), but players can exert a bit more control over the direction of their roster development by choosing a token that might give them a more useful cover.

5) The point is that the *only* way to counteract the longer and longer transition time *without* considerably increasing the number of 3* covers released is to restrict the field of covers. Vaulting characters is one solution, though it hurts players who are on the edge of viability with a character that disappears for a month. Having the players choose from a mix of equivalent token types accomplishes the same goal, but with several added benefits, in my view.