Event Free Play - Gold Chest

[Noeh23]

Hmm ... just did a quick run in the current event (Jim's formation, trying Omin with 4 champs in front of him).

Normally I would expect a silver chest for the free run. But I got a gold one!!! Is this because Kelemvor's Golden Luck, or was this because I went to lvl 500 or is there a random chance to get a gold chest?

[alo_obert]

Publicado originalmente por Phantom:

yeah but its 33% chance to get a chest with a 100% chance to get one if you fail 3 in a row which actually brings it to

40% or so of the time you get a gold... If my not well remembered math on percentages is correct

Breakdown of possiblities are

... [read original post for details]

so the chance of actually getting a gold chest is 40%

I think that's actually close, but not exact. In this case, I believe the fastest way to obtain the rate is as the inverse of the average number of chests separating 2 golds (including the last).

So, always after 1 gold chest, the probability that the next gold is at

1 chest = 1/3
2 chests = 2/3 * 1/3
3 chests = 2/3 * 2/3 * 1/3
4 chests = 2/3 * 2/3 * 2/3 * 1
+5 chests = 0

and the average distance is then 1/3 + 2 * 2 / 9 + 3 * 4 / 27 + 4 * 8 / 27 = 2.407...

The inverse of that number is the gold chest average rate = 41.538%

Would that be right?

[Coo Coo Pigeon]

40% or so is an "or so" but yea, seems about right.

[alo_obert]

Sure. the intention was just to show the mathematical exact way of calculating it. The mathaholic and pedagogic instincts have just jumped in and, although for this particular case the numbers are close, it doesn´t always happen that way.

I'm sure there are a lot of people that play that game and enjoy cracking the maths and probabilities or others that take advantage of some coments in this forum to learn or practice a little.

@Phantom,
If you are interested and you don't mind the explanation, the thing you didn't take into account is that the sequences G, S-G, S-S-G and S-S-S-G are not equiprobable in the series. A quick way to see this is that in your estimation the drop probability for the gold chests doesn't have influence in the result.

For example, if the ratio for gold chest were to be very high (close to 1) the total rate would be also close to 1 no matter the pity timer. If it were to be too low (close to 0) the influence of the pity timer would bring the total rate close to 25%. Your estimation method always gives 40%.

Also, if the pity timer were to be 1 gold for sure after 5 silvers instead of 3, your method would result in 6 / 21 < 1 / 3 (the pity timer would be reducing the total drop rate!! XD )

You were right that probability is favorable cases / total cases, but the tricky part is always adding them in the right way. Even physicist and mathematicians have problems in certain kind of problems. :)

[OldGamer]

Publicado originalmente por Coo Coo Pigeon:

Yup, but if you only have a few hours a week of active play. It might be worth spending it elsewise.

or been away for 7 days,

BTW there new automation stop after 1 hour :(

So instead of a 22k gem boost, I got 315 for 7 days.

[Coo Coo Pigeon]

Welcome back (& time for a ticket?)