Disclosure: I own Dice tokens!

The beauty of statistics is that the more samples we have, the more we can see how the future will look. Using this data we can accurately predict the rate of return of a known function and from that derive the value of the proposal.

We must make many assumptions (and, yes, we know what that leads to) but using maths we can try to accurately determine the value of the dice token that Etheroll offers. If everything goes according to plan; Maths might even make us rich!

For those that aren’t aware of Etheroll, it’s a simple dice rolling game that lets the player pick a number from 2 to 99 and then rolls a dice that must be below the user’s chosen number to pay out. The payout is weighted in the house’s favour, by 1%, the edge. The roll is provably fair, but for our purposes we have already assumed no one is cheating and the system is able to process as many bets as can be requested.

Etheroll is currently rolling around 1000 dice a day. It’s been as high as 2365(8th August 2017) and in the last month, the lowest moving average was 779 (23rd July).

The average value of each bet floats around 1 ETH although it is not unusual for the highest bet of the day to top 25 ETH.

I wanted to see what the EV and payout terms would look like under various assumptions so wrote some quite ropey java code to take a look at the possibilities. The code correctly simulated the bankroll skimming (which I was originally quite skeptical about). Etheroll takes any profit over the initial bankroll and distributes it to the token holders, resetting the bankroll back to its original size after 12 weeks. Should the house run at a loss the bankroll is not adjusted and there are no payouts. It is hoped that future profits will make up that short-fall. I was concerned about the asymmetric nature and wondered whether I could prove this might be an issue.

Assumptions

Without further ado, here are the assumptions for our initial “as is” scenario:

Number of bets per day: 1000

Average bet: about 1.3 ETH

Bankroll size (and cap): 2500 ETH

Gas per roll: 0.005 ETH

Simulations

I ran a loop that ran simulating 50 periods (12.5 years) and outputted the EV, change in bankroll and generated payout per dice token.

It should be noted that there is a reasonable variance in each test, so here are 5 consecutive outputs from the final period:

(Read this as Period 50, start -> end bankroll, total profit over the full 50 periods, [number of periods that had a payout, number of times the bankroll dropped too low to process bets] Eth bet =total eth bet in the period and the EV for that period, average bet amount and then the total amount of eth payable per dice token for 50 periods and the average dice payout per period.

P: 50 2500->3399 Total Profit: 36613 [39,0] Eth bet:114084 (EV:1140 av bet=1.36 total=0.0052292726460778 av.eth: 1.04585452921556E-4/dice P: 50 2500->3491 Total Profit: 43949 [47,0] Eth bet:114972 (EV:1149 av bet=1.37 total=0.006277033227205932 av.eth: 1.2554066454411862E-4/dice P: 50 2500->3410 Total Profit: 42553 [43,0] Eth bet:114539 (EV:1145 av bet=1.36 total=0.006077644024899536 av.eth: 1.2155288049799071E-4/dice P: 50 2500->3977 Total Profit: 34592 [44,0] Eth bet:115085 (EV:1150 av bet=1.37 total=0.004940660293364403 av.eth: 9.881320586728805E-5/dice P: 50 2500->4093 Total Profit: 36063 [43,0] Eth bet:115218 (EV:1152 av bet=1.37 total=0.005150668557582156 av.eth: 1.0301337115164312E-4/dice

These numbers look broadly right from what we’re seeing today. Approximately 1200 EV (our first payout was 1400 ETH or so).

The bankroll skimming issue

As can be seen above using the above numbers doesn’t guarantee a payout each period. In fact there were between 6 and 11 periods in the above tests that didn’t generate a payout at all. It should be seen that this didn’t actually affect the profitability and I did not take into account any profits that were not taken (around 7% in the first payout period) which are automatically added to the next period’s bankroll.

The other important point was that during each of these tests the bankroll did not drop to an unworkable amount, although this obviously doesn’t guarantee a similar result in the future.

Valuing the token

The important number above is the final number in each of the snippets. How much, on average, does each dice token generate. We might see between 0.000125 and 0.0000988 ETH each quarter per token. On average 0.00011 ETH/token.

What does this equate to, as far as the value of the token? Well, this really depends on what we expect as a return on ETH invested. I’m going to be conservative and suggest a 5% return is reasonable, so we can derive this value by dividing the year’s expected payout by 0.05.

Per year, our average payout per Dice token is 4 x 0.00011, or 0.00044 ETH. So, a reasonable investment price per token would be 0.0088 ETH, which is actually less than half what we are seeing the price sell for currently.

What’s going on here? Are people inherently overvaluing Dice tokens today or are they looking for some movement in the other numbers?

Increasing the number of bets to 1500 a day, a typical result is:

P: 50 2500->4476 Total Profit: 64688 [48,0] Eth bet:172209 (EV:1722 av bet=1.37 total=0.00923905107985155 av.eth: 1.84781021597031E-4/dice

Or in summary dividends of 0.000185 ETH/Dice/period -> 0.00074 ETH/year: 0.0148 ETH value per token (still below the price we see today).

So, what are we missing? The bankroll is due for a boost, but I’m skeptical that this will actually increase the profits all that much. Using the above numbers but increasing the bankroll to an initial 10,000 ETH does almost nothing to the figures (I averaged 0.000186 ETH/Dice/period). This is largely due to the effect it has, or doesn’t have, on the average bet placed- although our maximum bet can rise we are working with a constant average bet so little changes. This however, turns out to be the key piece of data. Increasing the average, up to around 2.3 ETH/bet gives results of: 0.0004 ETH/Dice/period or a token expectation price of 0.032 ETH, well above the generally accepted high of around 0.027 ETH/dice price. However, it really isn’t reasonable to consider players staking over $600 on dice rolls, as an average.

The other critical value is the number of bets placed (it should be noted there is only a minor difference in either doubling the average bet or the average number of rolls per day, with the former having the advantage due to the lower total gas spent each day by Etheroll). Where can a large number of new rollers come from? Almost certainly the mobile integration with Status.im that is planned for the new year will be important.

The final simulation

This final simulation ran 3000 rolls a day, averaging 2.3 eth per roll (high, but with a maximum roll of 2.5 this is actually simulating a few very high value rolls rather than the median which would be much lower)

P: 50 10000->10790 Total Profit: 237643 [50,0] Eth bet:597964 (EV:5979 av bet=2.37 total=0.03394120677889088 av.eth: 6.788241355778175E-4/dice

Here is where we start to see the likely potential of the Dice token: 0.000678 ETH/Dice/period, leading to a valuation of 0.05424 ETH/Dice, or in today’s money $16/Dice token.

Summary

In summary I believe that with a relatively low push for more rolls on the site and a modest rise in the average bet; Dice tokens can expect to see a 3 x multiplier over the next year to peak at about 0.05 ETH/Dice. It should also be noted that Dice tokens generally remain pegged to the ETH/Dice ratio which suggests that there is no significant risk on missing out on a strong Ethereum rise should you hold Dice tokens. Of course, others should do their own due diligence; this doesn’t constitute investment advice, etc.