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I'm playing a game, and in the game you have the ability to trade your in game currency for opportunities at better players. I have 2 options:

  1. 5 Draws, each with a 2.5% chance of getting a really good player.
  2. 1 Draw with a 7% chance of getting a really good player.

Which is the better deal, and what formula can I use to figure this out in the future?

CSS Apprentice
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1 Answers1

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Let's compare the options by computing the probability that you get at least one really good player.

Option 1: For a given draw (out of the $5$ draws), the probability that you don't get a really good player is $1 - 0.025 = 0.975$ or $97.5\%$. Assuming the $5$ draws are independent, the probability that you don't get a good player on any of the $5$ draws is $0.975^5 \approx 0.881 = 88.1\%$. Thus the probability that you do get at least one good player during the $5$ draws is approximately $$ 1 - 0.881 = 0.119 = 11.9\%. $$

Option 2: You have just one chance to get a really good player at $7\%$.

However, this analysis is overly simplistic: getting a really good player on your first draw is (I assume) more beneficial than getting one on your fifth draw. Perhaps you could take this into account by using some sort of weight to give greater value to good players obtained earlier.

Viktor Vaughn
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