Theoretically that is actually correct and that is how probability is calculated. But that sample size of 2 flips obviously isn’t big, but theoretically according to the laws of math (minus chaos theory) there is indeed a 100% chance to get at least 1 head.
Anyway, I understand the difference in our calcs. I was assuming there are 2 separate rolls for devour one after the other each with a 20% chance. But it is most likely a single roll on 2 targets with 20% in which case your calcs would be correct as it would incorporate a hit:hit into the equation.
But that sample size of 2 flips obviously isn’t big, but theoretically according to the laws of math (minus chaos theory) there is indeed a 100% chance to get at least 1 head.
Incidentally, if you generalize your question to “n tosses of an n -sided die,” as n approaches infinity, the probability of one or more occurrences of a specific number approaches:
No. You are again excluding independence. I understand whete you’re coming from but It’s not a board state. Look, you have a 1 in 100 chance of rolling a 19 (or any number for that matter) each throw. You have 100 chances. You have 100 x 1/100 chances.
Yes. My answer does not change, assuming each trial is independent. What value are you expecting here? It’s self-evidently not 100%, since you can clearly fail 100 times.
Whilst this digression into basic probability math is entertaining (@moons give it up, @lyya is right) - perhaps we could talk about troops and maybe some spoilers?
The Beargarok thing annoys me. Fails the @jainus test (now copyrighted). It’s a lot of mana for single nuke, with a marginal chance of extreme swing devour crap. Means: too unreliable to use much when attacking, but with potential for pure mindless RNG to win games for the AI. Cue Rage. That annoyance factor aside, this thing’s just not as good as Kraken.
Edit just to add: yeah I did @mention myself. I think that’s a new level of metanarcissism. And breaching the sixth wall.
Also: @moons you are confusing expectation value and probability. @lyya is correct on the probabilities. Both my wife (maths teacher with a PhD in maths) and me (long time game designer with a masters in maths) agree… and we rarely agree on anything
You have obscured the problem by not entirely correctly defining the problem. To find exact solution, you have to specify whether all dice are thrown simultaneously or sequentially, If dice are thrown sequentially, ideal solution should involve dynamic probabilities. For example, if the first 10 throws did not produce number 19, there are only 90 throws left to produce number 19 and the probabilities have to be recalculated after results of each throw are known to the observer.
For GoW, it is more relevant, for example, to the question about how many keys are needed to pop a mythic/legendary card or specific card. In this case, cumulative probability slightly increases after opening of each sequential chest that does not have mythic or that specific card you want to get.
Err, why are we assuming that opened keys affect the result of keys opened thereafter? Isn’t that exactly what the Gambler’s Fallacy entails?
The Birthday Paradox also has little to do with the question of probability of independent events happening together. The Birthday Paradox would more closely answer the question of how likely is it that two of my mythics are duplicates of each other if I have a certain amount of mythics. (e.g. 5 mythics of the current 18 will have a 44% chance of having at least 1 duplicate.)
It’s quite easy to prove that 100 chances at 1/100 isn’t 100%. If you have 1/100 chance to roll 19 (or any number), then you must agree that you also have 1/100 chance to roll any other specific number from 1-100. If you conclude that there is 100% probability that a specific number will show up in 100 chances, then all other numbers have that same probability, meaning that 1, 2, 3, 4… and so on will 100% appear at least once in 100 chances. In other words, for that to happen, you have to also assume that each number will appear exactly once in 100 chances. I’m sure at this point common sense will make it obvious that this conclusion is wrong.
To make an example more palpable, assuming mythic drop rate is 1/100 VIP chests, as dozens of players here will tell you, there isn’t 100% chance that opening 100 VIP chests will drop a mythic. Assuming 1/100 drop rate is true there is only a 1-(1-0.01)^100 = 63.4% chance at opening at least one mythic after 100 VIP chests. [1-(1-X)^Y = Z; Z is chance of something occurring at least once in Y chances, X being the chance of event occurring independently]. The same logic applies to Doomclaw devour. There is 1-(1-0.2)^2 = 36% chance at devouring at least once.
ANYWAY, on the topic of how useful Doomclaw would be, I think it’s a decent troop that can be tacked onto the 4th slot for any of the decent exploder teams. I’d like to have the opportunity to give Gorgotha/Infernus/Doomclaw/Elemaugrim a try. Having Doomclaw just for the random Enraged skull matches and as a backup finisher (even though Infernus works as a great finisher by itself.)
I wish I could add something of value here, but everyone said it, RNG’s knack for being 100% on defence will be horrible but I was rather enjoying Moons’s ‘juatification’ of a 100% chance, I’d love that logic in roulette. I wonder if he also thinks the world is flat.
I would use the trrop for the enrage other quality solely the fact that is I have a few team ideas already since its colors are very conducive toward transformers and synergistic with other “op” cards that frankly people don’t use.
(100% in GW)