The authors claim people make a "mistake". In a very small amount of transactions, this may be true, but you cannot base a model on every transaction containing a mistake. But let's look at the math. The authors use an example where every transaction that costs $1 nets either $1.2 or $.83. Over ten transactions, the net is less than $10. But this assumes that the person puts their whole net worth on every transaction. This is false. Each transaction costs a $1. So, the first one costs $1, and the second costs $1, etc. You cannot accumulate the past values of the previous transactions into the current one. This is the coin toss fallacy. If you flip a coin and get 99 heads in a row, the coin toss fallacy says the odds are greater the next flip will be tails. But, each flip is independent of the previous flips, so the 100th flip has a 50/50 chance of being tails, regardless of the results of the previous 99 tosses. So there is no "loser" in every transaction as the authors posit. Both parties win, or the transaction would not occur.
Their next claim is that becoming a billionaire is just "luck" and could happen randomly to anyone at any moment. Bill Gates is a billionaire because he created Microsoft. Mark Zuckerberg is a billionaire because he created Facebook. John Smith a fast food worker in Hoboken, Nebraska doesn't just wake up a billionaire one day by luck.
And what is bad about being a billionaire. Gates and Musk are doing wonderful things with their money that disbursing it to a million people would not accomplish. The authors never give a reason why income equality is bad. In fact, inequality is the natural order. They never mention the Pareto Principle, popularly manifested as the Bell Curve, which is found everywhere in nature.
The authors claim income equality is destabilizing and must be corrected by redistributing all the wealth in equal amounts. However, as stated, income inequality is the stabilized form. It might be increasing slightly now due to faster movement of information, but class mobility is highly dynamic. Yesterday's billionaires are not today's, and today's billionaires might not be tomorrow's. Income inequality is the stable distribution of scarce assets in a free market economy.