Winnning a Splatfest = 50% Chance of One 'Ideal' Gear Item

[Box]

There are 13 possible sub abilities. Eleven of them have an equal chance of rolling compared to each other. One ability is half as likely while another is 5 times as likely. This means there are 33 possible outcomes when rolling a sub-ability. There are 2 outcomes for each of the 11 normal abilities, 1 for the less likely ability, and 10 for the more likely ability. So rolling the most likely ability on any individual slot is 10/33 or about 30%.

Getting 3 specific abilities of your choosing is easiest when trying to get 3 of the same ability that match that brand's extra likely ability. We could calculate for other ability combinations, but those combinations don't fit with my claim in the title. Getting 3 of the same ability on a full reroll is (10/33)^3 or a little less than 3%.

To calculate how many rerolls you can expect to use when you have a 3% chance of success, you can use a geometric distribution. The median of the geometric distribution with a (10/33)^3 chance of success is around 24. That means with 24 rerolls, there's about a 50% chance that you'll get that 3% roll.

Winning a splatfest gives you 24 snails. So if you want to think about what that gives you in terms of in-game value, it's a coin flip on getting on 1 gear item with 3 of the most likely sub-ability.

This factoid brought to you by Box.

 

[Gideonsmash]

I won and got only 10 sea snails...

 

[Ellocus]

It's also the equivalent of 720,000 coins and can be used to add slots and not just re roll. I'd say it's plenty fair enough, given that you can order gear off of others and have a decent chance of getting exactly the abilities they had.

I won and got only 10 sea snails...

The assumption was max rank in addition to winning.

 

[SquiliamTentacles]

Not all abilities have to be 3 of a kind to win. There is no individual bonus for multiple abilities, and the abilities with diminishing returns are detrimental to be stacked (and if you want more, you can stack with your other gear.) Unfortunately, that just makes is even harder if you want your perfect gear.

 

[Rellek]

Question: Is there a thread that outlines each piece of gear's specific 11 normal, 1 half and 1 likely abilities?

Furthermore, are those abilities tied to the brands rather than the individual items?

And lastly, is there already a thread about that stuff?

 

[Ellocus]

Question: Is there a thread that outlines each piece of gear's specific 11 normal, 1 half and 1 likely abilities?

Furthermore, are those abilities tied to the brands rather than the individual items?

And lastly, is there already a thread about that stuff?

It's tied to the brand.

There's a video talking about abilities here:

Shows how the brands relate to sub abilities about 5:30 as well as giving lots of useful information.

 

[Egregore]

Question: Is there a thread that outlines each piece of gear's specific 11 normal, 1 half and 1 likely abilities?

Furthermore, are those abilities tied to the brands rather than the individual items?

And lastly, is there already a thread about that stuff?

 

[Pareto]

.3^3=2.7% each roll.

Pr(Failing to get three in a row in 24 spins): .973^24 =51.84%.

Pr(Getting three in a row once within 24 spins): 1-.5184= 48.16%. Slightly disfavored but it's negligible I guess.

This way might be easier than having to deal with probability distributions.

 

[Rellek]

Beautiful pixels

You are an angel.