By Stéphane Reverre and Chadi El Adnani @SUN ZU Lab
November 2022
Crypto will always fascinate us. Who would have thought that we would manage to find a link between a famous 60’s American television game show, a Kevin Spacey poker movie, a heads or tails game and crypto market liquidity transparency? But here we are at SUN ZU Lab, always striving to push the boundaries of common perceptions.
The Monty Hall problem is a probability puzzle named after the host of the American game show “Let’s Make a Deal”. The problem was initially posed and solved in a letter by Steve Selvin to the American Statistician in 1975. It became famous after Parade magazine columnist Marilyn vos Savant responded to a reader’s question regarding it in 1990. Professor Micky Rosa (Kevin Spacey) later uses it to clarify his point about the Change Variable’s importance in the famous movie Las Vegas 21, released in 2008 (link).
It goes as follows:
Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?
Counterintuitively, the odds are not at all 50-50. You have a 2/3 (67%) probability of winning by switching doors!
We would not explain why this is true using conditional probability and Bayes theory (interested readers can check the paper in the reference section). Let’s instead see the problem from the following perspective:
- There are 10 doors to pick from at the beginning
- You choose one door
- Monty looks at the 9 others, finds the goats, and opens all but 1
Do you remain with your original door (1/10 chance of winning) or the other door, which was filtered out from 9 other possibilities?
Monty is improving your 9 choices set by removing 8 goats. Once he’s done “cleaning”, you are left with the top door out of 9 for you to choose from.
The question asked differently is: Do you want a random door out of 10 (initial guess) or the best one out of 9?
Now coming back to our initial pain point, crypto liquidity transparency, the question becomes:
As a professional crypto user, do you want one random liquidity venue to execute your trades or the best of 9 liquidity venues, carefully analyzed and filtered by an independent entity?
We give another example to illustrate our opinion better. Let us consider a game with three coins: one is two-headed, the second is a biased coin that shows heads 75% of the time, and the third is unbiased. One of the three coins is chosen randomly and tossed. What is the probability that it was the two-headed coin?
Without additional information, the chances of getting the two-headed coin are 1/3 (33%). Knowing that the tossed coin showed heads, the probability becomes 4/9 (44%)!
The previous probability is computed using Bayes theorem. Let E1, E2 and E3 be the events of choosing a two-headed coin, a biased coin and an unbiased coin, respectively. A is the event that the coin shows heads:
P(E1|A) = P(E1).P(A|E1) / [P(E2).P(A|E2) + P(E3).P(A|E3) + P(E1).P(A|E1)]
P(E1|A) = (1/3) / (3/4) = 4/9
Without this crucial information, the player would be at a clear disadvantage, as it is not “fair” to play against a game master that dissimulates essential information.
What we refer to in the previous example is non-other than information asymmetry. This problem has been studied thoroughly in contract theory and economics, and regulators try to eradicate it as much as possible. Information asymmetry creates an imbalance of power in transactions, leading to severe market inefficiencies such as moral hazard risks or the establishment of monopolies of knowledge.
The general idea, put simply, is the following: Information is King! The more you know, the better (crypto investment) decisions you make. That’s why transprency is key.
Between an opaque liquidity venue on which no information is available and another independently audited for a significant period, the chances of taking the best decision are far from 50-50. While past performance is not a guarantee of future results, you should at least be able to tell if your crypto liquidity venue is sharing necessary information with you. We are convinced at SUN ZU Lab that as the crypto market matures, the need for transparency-enhancing players will materialize to the point of absolute necessity.
We would be happy to hear your thoughts about transparency in crypto markets!
Questions and comments can be addressed to: founders@sunzulab.com
References:
About SUN ZU Lab
SUN ZU Lab is a leading data solutions provider based in Paris, on a mission to bring transparency to the global crypto ecosystem through independent quantitative analyses. We collect the most granular market data from major liquidity venues, analyze it, and deliver our solutions through real-time dashboard & API stream or customized reporting. SUN ZU Lab provides crypto professionals with actionable data to monitor the market and optimize investment decisions.
