Ticket Sales

The purchase value of tickets depends on the price in UNIT of the cryptocurrencies deposited and the probability of the outcome.

On day 1 of the round, tickets (yUNIT and nUNIT) are priced in UNIT at the rate of

$$1 \;\textrm{UNIT}= (1-p) \;\textrm{yUNIT},$$

$$1 \;\textrm{UNIT}= p\;\textrm{nUNIT},$$

for $p$ being the probability of "yes".

On subsequent days, ticket prices depend on the updated probability of the outcome on each day.

In the Ethereum network, for $V$ the price of 1 ETH in UNIT and $p$ the updated probability of "yes" we get that 1 ETH will yield the following amount of yUNIT and nUNIT tickets.

$$1 \;\textrm{ETH}= V * (1-p) \;\textrm{yUNIT},$$

$$1 \;\textrm{ETH}= V * p \;\textrm{nUNIT}.$$

Example of Ticket Sale Calculation (Day 1)

Question: Will coin A enter The UNIT this round?

Calculate the probability $p$ that coin A will enter The UNIT in this round given equal $0.5$ probability that it will satisfy the requirements in any given day.

$$p = \frac{1}{2^{13}}\biggl[\binom{13}{8}+\binom{13}{9}+\binom{13}{10}+\binom{13}{11}+\binom{13}{12}+\binom{13}{13}\biggr]$$

$$p =\frac{2380}{8192}= 0.29052734375.$$

Then, if 1 ETH is currently worth 1000 UNIT, then

$$1 \;\textrm{ETH}= 1000* 0.70947265625\;\textrm{yUNIT}=709.47265625\;\textrm{yUNIT},$$

$$1 \;\textrm{ETH}= 1000 * 0.29052734375 \;\textrm{nUNIT} = 290.52734375\;\textrm{nUNIT}.$$

Example of Ticket Sale Calculation (Day 2)

Same Question: Will coin A enter The UNIT this round?

Known Data: On Day 1, coin A met the requirements to enter The UNIT.

Again, calculate the probability $p_1$ that coin A will enter The UNIT in this round given equal $0.5$ probability that it will satisfy the requirements in any given day.

$$p_1 = \frac{1}{2^{12}}\biggl[\binom{12}{7}+\binom{12}{8}+\binom{12}{9}+\binom{12}{10}+\binom{12}{11}+\binom{12}{12}\biggr]$$

$$p_1 = \frac{1586}{4096} =0.38720703125.$$

Then, if 1 ETH is currently worth 1000 UNIT, then

$$1 \;\textrm{ETH}= 1000* 0.61279296875\;\textrm{yUNIT}=612.79296875\;\textrm{yUNIT},$$

$$1 \;\textrm{ETH}= 1000 * 0.38720703125 \;\textrm{nUNIT} = 387.20703125\;\textrm{nUNIT}.$$