Refutation of an Article on Shuffling in TCG

• Restatement
• Rufutation
  • Invalid Evaluation
  • Poor Experiments
  • Unjustified Results
• Conclusions
• Appendix
  • Recommended Material
  • My Implementation

Months ago I came across an article on the methods of shuffling cards in TCG tournaments. Given limited time in a match, the author, hyakkoTCG@hyakko_tcg sought a way to mix a deck thoroughly by shuffling three times. However, at least to me, it is obvious that the methodology proposed is fundamentally flawed. Later I found out in surprise that the article was widely disseminated: it got 2.3k retweets and 3.1k likes on twitter. It also began to spread on Weibo, so I wrote a short refutation in Chinese immediately. Though it was a bit late, I still decided to write another one in English so that I can send it to Hyakko.

Side Note: Information Entropy, Cross-Entropy and KL Divergence

我们考虑一个事件 , 它发生的概率是 . 假设我们观测到事件 发生, 我们希望定义一个信息量 来衡量 " 发生了" 这件事给了我们多少信息.

1. 是关于 的递减函数. 如果事件发生概率高, 而且它发生了, 我们得到的信息应该比较少, 因为我们认为它确实容易发生, 这不稀奇.
2. 考虑另一个独立的事件 , 它发生的概率是 , 则 . 也就是说我们希望独立事件同时发生时提供的信息量应该是他们分别提供的信息量之和.

Lights-Out

Each employee of MegaCorp has a separate office in the MegaCorp office building. Each office is equipped with one overhead light and one toggle switch to turn the light on and off.

Every day, the employees turn on all lights when they come to work. Each evening they turn off all lights when they go home.

One day, the employees arrive to discover that someone has played a rather elaborate hoax on them. Though all looks fine when they come in (all lights are off), every time an employee flicks the switch in her office, this not only toggles the light in her office, but also the lights in the offices of all of her friends. (Friendship is a symmetric relationship.)

The question: does there necessarily exist an arrangement of the switches that will turn all lights simultaneously on (so that work can begin)? Prove your answer.

Super Egg Drop

You are given eggs, and you have access to a building with floors from to .

Each egg is identical in function, and if an egg breaks, you cannot drop it again.

You know that there exists a floor with such that any egg dropped at a floor higher than will break, and any egg dropped at or below floor will not break.

Each move, you may take an egg (if you have an unbroken one) and drop it from any floor (with ).

Your goal is to know with certainty what the value of is.

What is the minimum number of moves that you need to know with certainty what is, regardless of the initial value of ?