Many of us are probably familiar with the accounting equation of national income, Y = C + I + G + NX, which relates national income to a country's expenditures in the form of consumption, investment, government spending and net exports. Most of us have at least heard of GDP in which Y is empirically measured at monthly, quarterly or annual frequencies. A few of us have had the pleasure of seeing this simple equation used to develop and debate deep theorems in economics and public finance. Lord Keynes himself, Marxian economist Kalecki, and Nobel laureate Simon Kuznets all worked their theories out of this common framework. It is about time we develop a similar framework for the tokenized economies of social slots.
Due to the hard work of engineers and data science, we often have complete daily information on individual players that allows us to connect all the relevant variables at a high level. We can begin with an individual player and build up from there. A player starts her day with Wt-1 coins in her wallet. Over the course of the day she is given F free coins, earns E coins through engagement, purchases P coins and wins Win amount of coins. She will have bet B coins throughout her day and holds Wt coins at the end of the day when she stops playing. The change in her daily wallets Wt-Wt-1 combined with her total bets must equal all the inflows the player accumulated:
F + E + P + Win = Wt-Wt-1 + B.
Basically, a player can choose to keep coins in her wallet or bet coins, but only from the stock pile of coins she had at the beginning of her session, from the coins the game gives her, or from the coins she wins by betting. This equation holds for every individual player, but also holds when players are summed up. So we can take this equation as an aggregate accounting identity when considering the economy as a whole or large subgroups of the economy.
After aggregating, let's make a few more transformations to make it more useful. Subtracting total wins from bets is called RAKE, but let's also divide all variables on both sides of the equations through by bets:
F/B + E/B + P/B = (Wt-Wt-1)/B + B/B - Win/B,
or,
f + e + p = (Wt-Wt-1)/B + 1 - Win/B.
The lower case letters are shorthand for free credits normalized by bets (f = F/B), etc. But maybe it doesn't look too helpful yet? Well, ask any games mathematician about Win/B. For large numbers of players, although volatile, Win/B will on average equal the return to player RTP.
f + e + p = (Wt-Wt-1)/B + 1 - RTP,
or,
f + e + p = (Wt-Wt-1)/B + rake.
In this last equation, rake means the rate of coins lost to the house when coins are bet on the slot machines. To summarize in words: adding free, earned and purchased coins normalized by total daily bets equals the change in wallets normalized by bets plus casino's rate of rake. All of these variables are likely already stored somewhere. They may even be sitting on the same Tableau dash, waiting for you to precisely and accurately connect them. An immediate lesson we can learn from these equations is that chance wins in machines will push plenty of noise into the other variables.
Let's analyze a basic scenario to understand how to really use the equation. For a month's worth of data you look at all these variables at daily frequencies. You have a problem, purchases have fallen so much that p has fallen over time. You notice wallets stayed constant so (Wt-Wt-1)/B = 0, and of course your economy is tuned to 92% RTP so the equation is simply:
f + e + p = 0.08,
or,
F + E + P = B*(0.08).
If purchases decreased, by pure accounting, this could have been because free and/or earned inflows increased, total bets decreased or some combination. What is important is that this is a very precise equation and scaling the effects of inflows on bets by RTP or vice versa is often neglected.
If total bets also stayed constant, then the change in purchases was likely caused by an increase in inflows. If however purchases fell such that total inflows fell 10%, we know that any compensating rise in free and earned credits did not fully offset the drop in purchased credits and total bets also fell 10%. But, if we intervened by changing RTP, things get more complicated! As an exercise, assume RTP was tightened 1%, what happened to total bets to have balanced the equation?
True empirically driven economics begins by being able to look at these scenarios, reducing them down to accounting truths, postulating how players are financing their changes in behavior and making bold educated guesses as to how all the variables will play out given your interventions. There is no reason for data analysts, product managers, or economists to just wing it when guessing how much of a change in RTP they should use, if they should use it at all.
In subsequent posts, I hope to explore these identities in relation to common industry practices like price inflation, periodic sales and making earned credits a function of past bets or wallet sizes.
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