Hi /r/DuelLinks,

Intro/Background Info

I noticed a while back that a post was made with some data that someone gathered regarding how often they got the same card back. This data was met with the conclusion that there was a 25% chance that Switcheroo would automatically fail, which is now being memed across the subreddit.

I was a little concerned by that statement, so I decided to attempt a rudimentary statistical analysis of the data with what little I remember from Statistics 101.

I started by calculating how many standard deviations away from the target % each trial (here used to mean each set of 10 attempts with X cards remaining) was. And, well, that was the end of my analysis, however, it comes to a different conclusion than the one the community drew.

As a reminder, if you look at a population on a normal bell curve, 68% of the population falls within one standard deviation of the mean, 95% of the population falls within two standard deviations, and 99.5% of the population falls within three standard deviations. This lets us say that if the target percentage (or alternatively, the 25%) is within one standard deviation of our actual, then at least ~15% of people who conducted this same test could have had more egregious results than this without eliminating the possibility that nothing is wrong with the RNG (or alternatively, that the 25% figure is correct).

The Data

My Spreadsheet

Original Data

• Cards Remaining - Self explanatory
• Uses - How many times Switcheroo was used at each Cards Remaining level (it's always 10)
• Same Card Returned - How many times the player got the same card back
• Target % - What the percentage should be, in an ideal world
• Actual % - What the percentage actually was in these trials
• STD Dev Away - How many Standard Deviations each trial is from the target %.
• That table at the bottom - the calculations for standard deviation, the top row is an index so I can look it up in the above tables, the second/third rows are the distance away from the mean squared and then multiplied by how many instances there are, the last row then is the corrected average (sum of 2nd and 3rd rows divided by 9)

Analysis

Of the 20 trials, only three are more than one standard deviation away from the target percentage. OTOH, only four trials go against the 25% guaranteed chance of failure. In short, there is little enough data that it is inconclusive as hell. With OP's data, we can disprove neither that the RNG system is perfect and working as intended nor can we disprove that the 25% guaranteed chance of failure exists. That being said, with such a disparity existing, for the love of god, stop spreading the rumor that a 25% guaranteed chance of failure exists for sure.

tl;dr- We probably don't have enough data to say for certain that the RNG is/isn't working properly, so stop treating the 25% guaranteed chance of failure as fact.