PRDX — risk without an intermediary

Risk without an intermediary

Some seek risk, others avoid it, and for centuries an intermediary has stood between them: the broker, the lottery, the insurer. It keeps part of the money for itself.

The PRDX token has no intermediary, its rules are written on the blockchain: those who seek risk spend PRDX on tickets to mine PRDX by the rules of the 1738 St. Petersburg game, and those who avoid it hold PRDX.

The paradox: the open risk of some adds up to a steady average growth of the token.

How It Works

Карта Vault: баланс PRDX и его цена в монете резерва

Issuance

PRDX needs no exchange: a participant issues it and backs it at the same time. They put coins into the reserve and receive new PRDX* at the current price. The reverse exchange burns PRDX and pays out coins from the reserve; it is available at any time.

Issuing and exchanging go at one price: the reserve divided by the number of PRDX issued. They change the reserve and the number of PRDX in the same proportion, so they do not change the price; the protocol withholds a 1.5625% fee on each operation. Only mining tickets change the PRDX price.

* On TON PRDX is issued under the Jetton standard, on Solana under the SPL Token standard.

Mining

A ticket* is bought for PRDX and gives the right to mine new PRDX. The payout follows the rules of the St. Petersburg game: a coin is tossed until the first heads. If heads comes at once, the payout is the smallest, and with each toss without heads it doubles up to the largest. The number of possible payouts equals the ticket level, and all of them with their chances are written in the contract before the purchase. At the same ticket price, the higher the level, the larger the top payout and the rarer it comes.

For example, a level 8 ticket with one attempt costs 51.43 PRDX; its smallest payout is 10 PRDX, and its largest is 1,280 PRDX and comes once in 128.

When mining starts, the PRDX paid for the ticket burn, and the protocol issues the payout as new PRDX. For any ticket settings the average payout equals exactly 87.5% of its price, and the other 12.5% burns on average while the reserve stays the same.

* On TON a ticket is issued as an NFT; on Solana it is kept in a separate account of the protocol's program.

Two strategies

PRDX is held or spent on tickets, and these two strategies can be combined. Both can be tried for free in the app's test mode (TRIAL), without a wallet.

Alice, less inclined to risk, holds PRDX.
On average more PRDX burns on tickets than is mined, and the reserve does not change. So each PRDX is backed by more and more reserve coins, and the PRDX price grows on average. The more tickets, the closer the burned share comes to 12.5% (the law of large numbers), and the steadier the growth.
Alice takes the growth by selling (Burn). The protocol withholds a 1.5625% fee on purchase and on sale, and the sale returns more coins than Alice paid only if the price growth covers both fees. The fees protect against arbitrage: the price growth goes to those who hold PRDX, not to those who buy and sell at once.
Bob, more inclined to risk, spends PRDX on tickets.
On average Bob gives up 12.5% of each ticket's price. In return he gets a chance to mine many times more: for a level 12 ticket with one attempt, the largest payout is 276 times the ticket price and comes once in 2,048.
Bob chooses the ticket level himself, and the outcome is computed by a protected protocol: no one can pick it.

History

PARADOX rests on two ideas of 1713, and both came from the Bernoulli family. Jacob Bernoulli's book, published that year, proves the law of large numbers: the more trials, the closer the frequency of an event comes to its probability. His nephew Nicolaus proposed a problem about a game whose payout doubles until the first success.

In 1738 Daniel Bernoulli wrote this game down with a coin in his paper “Exposition of a New Theory on the Measurement of Risk”: a coin is tossed until the first heads, and the payout doubles with each toss. The expected value of such a game is infinite, yet people are willing to pay only a few coins to play. Bernoulli explained this by the value of a gain depending on a person's wealth, and by the same argument worked out when a Petersburg merchant should insure goods shipped from Amsterdam. The paper appeared in the journal of the St. Petersburg Academy of Sciences, so the game is called the St. Petersburg game, and the gap between the expectation and the price of playing is called the St. Petersburg paradox. PARADOX is named after it.

The original game cannot be run: its payout is unbounded, and there is nothing to pay it with. In PARADOX the number of tosses is limited by the ticket level, and the protocol issues the payout as new PRDX, so the reserve is not spent on it. The rules and the random numbers are written on the blockchain, and no intermediary is needed to hold the money and pick the outcome. And Jacob Bernoulli's law of large numbers makes the average growth of the PRDX price steadier the more tickets there are.

Benefits

Risk without an intermediary

The protocol does not take the payment for risk: the average shortfall on tickets burns and, through the price growth, goes to everyone who holds PRDX. The protocol withholds only the Mint and Burn fees.

Open rules

The possible mining payouts and their chances are written in the contract and known before buying a ticket. The payout is computed from two random numbers, and anyone can recompute it.

Price by formula

The PRDX price equals the reserve divided by the number of PRDX issued. Mint and Burn go at this price and do not change it; only mining tickets change it.

Full backing

Every PRDX is backed by the reserve in the contract: Gram or USDT on TON, SOL or USDT on Solana. The four pairs of network and currency are not linked to each other, and neither are the two pairs on one network: each has its own PRDX, its own reserve and its own price. Burn cannot be paused.

FAQ

What are the fees on issuing (Mint) and exchanging (Burn), and what are they for?

1.5625% on each operation. The protocol takes the Mint fee in coins and does not add it to the reserve, and takes the Burn fee in PRDX and does not burn it. Neither operation changes the PRDX price.

The fees protect against arbitrage. The PRDX paid for a ticket burn when mining starts, and the payout is issued later, so between these moments the PRDX price is higher. Without fees, a participant could buy PRDX before someone else's ticket starts mining and sell before the payout is issued, and the price fall from the payout would land on those who hold PRDX. With the fees, a sale returns more coins than were put in on purchase only if the PRDX price growth between the purchase and the sale covers both fees.

How does PRDX differ from stablecoins?

A stablecoin's rate is pegged to the dollar or another currency. PRDX is backed by the reserve and can be exchanged for reserve coins at any time, but its price equals the reserve divided by the number of PRDX issued and grows on average while mining goes on.

The PRDX price is expressed in the reserve coin, so against other currencies it moves together with that coin.

How is PRDX different from a pyramid scheme?

In a pyramid scheme old participants are paid with the money of new ones, and the payments stop when new ones stop coming.

In PARADOX issuing PRDX for coins does not change the price, so new participants joining pays nobody by itself. Only the average shortfall on tickets raises the PRDX price, and miners give it up for a chance to mine many times more.

If mining stops, the PRDX price stops growing but does not fall. All PRDX together are backed by the reserve and can be exchanged for reserve coins at any time at the same price.

Does PRDX need an exchange?

No: a participant issues PRDX by putting coins into the reserve and can exchange it back for reserve coins at any time. Both operations go at a price equal to the reserve divided by the number of PRDX issued.

PRDX is still an ordinary token of its network: wallets show it, and it can be transferred.

Are TON, Solana and the reserve currencies connected?

No. On TON PRDX is issued for Gram or USDT, on Solana for SOL or USDT, and each of the four pairs works separately: it has its own PRDX, its own reserve, its own price and its own tickets.

PRDX of one pair cannot be exchanged for PRDX of another.

Which standards are PRDX and tickets issued under?

On TON PRDX is issued under the Jetton standard (TEP-74), and a ticket as an NFT (TEP-62). The NFT's description records the ticket's level and state, and TON wallets show the ticket among other NFTs.

On Solana PRDX is issued under the SPL Token standard. A ticket there is not an NFT: it is kept in a separate account of the protocol's program and can be transferred with a command of that program.

On both chains a ticket can be transferred to another owner only before mining starts.

What is PRDX mining?

A ticket gives the right to mine PRDX. When mining starts, the PRDX paid for the ticket burn, and the protocol issues the payout as new PRDX. A ticket has three parameters:

LVL from 2 to 32: the number of possible payouts.
MIN from 1 PRDX: the smallest payout of one attempt.
DRAWS from 1 to 8: the number of attempts.

In each attempt a coin is tossed until heads, but no more than LVL − 1 times, and with each toss without heads the payout doubles. The average payout equals 87.5% of the ticket price for any parameters.

Who decides the payout, and where does the word “mining” come from?

No one chooses the payout: it is computed from the miner's random number (the secret) and the number of an independent service (the oracle). The protocol records the secret in hidden form before the oracle's number arrives. The miner can no longer change the secret, and the oracle sees only its hash. Both numbers are kept on the blockchain, and anyone can recompute the payout.

The word “mining” comes from the similarity with Bitcoin: mining costs money, and the payout is random. Otherwise mining works differently: the chances are set by the ticket level, one ticket's payout does not depend on other tickets, and mining confirms no transactions.

Can you lose PRDX on mining?

Yes. On average a ticket returns 87.5% of its price, so the miner loses 12.5%.

With one attempt on a high LVL the payout is most often below the ticket price and rarely many times above it: on LVL 24 the payout is below the ticket price in 15 cases out of 16, and the largest payout exceeds the price 587 thousand times.

How large can one ticket's payout be?

Up to 12.5% of all PRDX issued, that is, up to a ninth of the reserve in coins at the price after issuing. This limit grows with the number of PRDX issued: the more PRDX are issued, the larger the payout one ticket can bring.

The limit protects those who hold PRDX: the protocol issues the payout as new PRDX, and a payout at the limit lowers their price by about 11%, not more. A ticket over the limit can be bought now and mined when there are more PRDX, or its level can be lowered (RESHAPE).

Can I change my mind after buying a ticket?

Yes, while mining has not started. A ticket can be canceled for exactly 87.5% of its price, and the other 12.5% burns.

A ticket can also be given away or transferred to another address, and a ticket over the limit can be moved to a lower level (RESHAPE).

Can the PRDX price fall?

Yes. The protocol issues mined PRDX, so a large payout increases the number of PRDX at the same reserve, and the PRDX price falls; large payouts on several tickets at once lower it more. The fall from one payout is limited: about 11% at most.

If mining goes on, such a fall is temporary: the number of PRDX shrinks again on average, and the PRDX price grows. In prdx-sim simulations with 100 to 100,000 participants the PRDX price fell in 1–4% of years.

Can anyone freeze or take my PRDX?

Not on the protocol's side. Governance cannot change PRDX balances and cannot pause Burn, so PRDX can always be exchanged for reserve coins. Governance can pause Mint, ticket purchases and the start of mining and change parameters for new tickets, while a ticket already bought keeps its share of the average payout.

A USDT reserve carries an outside risk: USDT is issued by Tether, which can freeze USDT on any address, including the reserve's, for example at a regulator's request. Gram and SOL are the networks' own coins and cannot be frozen this way.

What are the protocol's risks?

The protocol is experimental and runs on test networks.
On average a miner loses 12.5% of a ticket's price.
After a large payout the PRDX price falls.
The PRDX price grows only while mining goes on.
The PRDX price is expressed in the reserve coin and moves against other currencies together with it.
The issuer of USDT, Tether, can freeze a USDT reserve; a reserve in Gram or SOL has no such risk.