Notes. Alan Zhong

24 Game

I played 24 for the first time last weekend. The game is pretty simple, you’re given 4 cards from a deck, 1 through 13, and must make 24 using a combination of basic operations or additional operations. For example if we drew 5, 10, Q, K, that would translate to 5, 10, 12, 13 which we could make 24 doing (10+5-13)×12.

Computationally there are two straight forward ways of solving this.

  1. Iterate through all bracket and operation placements until you find the solution
  2. Solving for 4 numbers is the same as solving for 3 given every pair in the original 4.

However these strategies are ineffective in real play because not only do you have to solve for 24, you have to be the fastest. The median solution time for all solvable draws is 9 seconds.


In general, draws with more solutions tend to be easier and solved faster.


Looking at a subset of skilled players, the median solution time for all solvable draws drops to 3 seconds.


Fortunately for mere mortals, draws with more solutions tend to be easier and solved faster even for skilled players.

solved rate vs skilled players.png

At a median of 3 seconds per draw, a skilled player would beat another player trying to enter combinations of numbers into a computer. Anecdotally, I’ve seen players call out the solution within a split second of the cards being turned over, sometimes by the dealer themselves. One possible strategy is to watch for tendencies in players to be better at specific operations, choose to give up those, and focus on other operations. Even skilled players have difficulty with harder operations:


Augur v2 Thoughts

v1 of Augur seemed uninspiring with betting volume topping just $1 million. A few of the biggest issues have now been addressed in the Q1 2019 planned v2 release, but there’s still a lot more work to be done before the ecosystem is ready for mainstream use.

1. Currency volatility is more than prediction market volatility

YTD in 2018, the daily volatility of REP/USD (only trades on Kraken but still representative) is ~7%. YTD on PredictIt, the median daily volatility of all listed contracts has been ~0.3%. You could very feasibly win a bet, but lose more just on currency moves. Furthermore, since Augur bonds are also posted in REP, market makers have been mainly limited to long term crypto investors rather than traditional book runners. Augur aims to solve this by adding support for stable coins.

2. Bad user interface is an opportunity for book runners

Betting on Augur markets is unintuitive and time consuming., a third party alternative to downloading a node frequently disconnects and has a transparency issues. While third party offerings like help with searching through markets, the platform lags far behind traditional betting offerings. Augur does provide a reasonable backend for individuals and institutions to build upon though. Although no UI changes have been mentioned for v2, I think that’s actually not a mistake on the foundation’s part. That work can be divvied amongst Augur users who probably in the next 1-2 years will move more volume through their own respective channels than users betting directly on Augur.

3. Duplicate markets divide liquidity

Augur lacks dedicated book runners/market makers. Aside from a few practical hedging crypto hedging contracts and options, the vast majority of betting markets are illiquid with sparse orders (the median tick frequency is in days). A big issue here is that market fees are lower-bound at zero. The result being many zero fee markets, that divide liquidity between the same bet. The hope here is that as more users join Augur, book runners would have a larger incentive to actively provide liquid markets. There is room here for improvement with a mechanism forcing market consolidation, ex. if two markets have the same verification source the markets are merged with fees split by share of total bond posted.