The same was done for the batch method and plotted in green.Īs an example, let’s look at Epic Commander Sculptures. These expected percentage values are plotted below in grey for each reward type.Īdditionally, I took every item received from the single method and calculated the proportion (percentage) of the total number of items for each reward type. My interpretation of this value is that if you look at all of the items you’ll ever receive from gold chests, 3.023% of them will be legendary sculptures.
For example, ‘Legendary Commander Sculpture’ has a probability of 3.023%. The rewards list (probability section) in the Tavern tells us the expected distribution of items from a gold chest. After opening everything, the individual singles method gave me a total of 1297 items, and the batch method gave me a total of 1304 items. Then I saved another 201 gold keys and used them individually. To test this, I saved 201 gold keys and opened them in batch. The central question is: do you get better rewards by saving gold keys and opening everything at the same time (batch method), or by opening the same number of chests one at a time (single method)? Keep this in mind when interpreting the rest of the graphs below. The key is to look at the statistical test. Just because one bar looks larger than another on a graph doesn’t mean that it actually is. This is a very very simplified overview of sampling (apologies to anyone that is already familiar with statistics), but I see incorrect conclusions being drawn all the time. We need a larger sample and to conduct a statistical test that accounts for error in sampling. To put this into the context of Rise of Kingdoms, if you open a gold chest and see 3 legendary sculptures and only 1 resource item, would you conclude that gold chests in general are highly likely to give you sculptures? I’m sure you’ve seen that situation happen, but you would never conclude that you’ll be drowning in legendary sculptures just because you received a lot of them from 1 gold chest. Just because it looks larger in one sample, doesn’t mean that is generally true in the overall population. The key point I want to get across is that we should avoid that temptation. When looking at a sample distribution like the one above, it is tempting to say that the coin is biased towards heads just because the heads bar is larger than the tails bar. So we have this intuition that there is always some amount of error whenever we take a sample of something. If we flipped another 100 times the proportions may be completely different. Just because in this particular sample we saw 60% heads, intuitively we know that this coin won’t always be 60% heads. The graph above on the right shows our observed sample of coin flips. So lets say we flip a coin 100 times, and see that 60% of the time we land on heads, and 40% of the time we land on tails. However, we clearly can’t perform infinite coin flips.
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