The Bitcoin learning tournament.

Inspired by discussion on the previous article, it's my great pleasure to give you the world-famous Bitcoin Learning Tournament. Here's the details :

I. The Deux-Pez Machina is a device defined as follows :

1. To initialize, it generates a randomⁱ 256-byte ISRⁱⁱ. This ISR describes a total of 256 linear functions, indexed in a one-byte list. Each function is of the format a_i X + b_i, with i taking values from 0 to 255. For each byte in the ISR : the first bit will set a_i to negative if 1, and to positive otherewise ; the second bit will set a_i to either 1 or 2 ; the third bid will set b_i to negative if 1 and to positive otherwise ; the remainder five bits will set the value of b_i (from 1 to 32). For each player it further generates a UMMⁱⁱⁱ on the basis of randomly selecting one byte from the UIS, one byte from the ISR, concatenating them, MPFHF-ing the two byte product to obtain a one byte mask. The UMM will never be divulged to the players.
2. Every tick it prepares the function list, by multiplying each a and each b with the respective byte^iv in its ISR and dividing the result by 16.
3. Every tick it receives as inputs a 64-byte UIS^v, a one-byte UIM^vi and a positive double UBA^vii from each user participating that tick. To be accepted the UBA must be no lower than half the average UBA of the previous round -- all UBAs are accepted first round.
4. Every tick for each accepted UBA it XORs the UIM with the respective player's UMM. If a randomly-selected byte from its ISR is divisible by 8, it also XORs the UMM with that byte. It then selects the function in its list indicated by the XOR'ed UIM and applies it to the UBA. The result, capped at 2x the UBA, is returned to the respective UIS.
5. Every tick it XORs its ISR with four concatenated UIS randomly selected from the UIS received that turn and with one random 256 byte value thus becoming ready for the next tick. Once four UIS can not be selected, the Deux-Pez Dispenser ends the world.

II. All players start with capital in sum of 20999999.9769 to bid however they please.

III. Each tick each player may either

• Play, by specifying his own UIS, and providing correct values for UIM^viii and UBA^ix. Up to double his UBA will be returned and added to his capital ;
• Observe, by specifiying any other player's UIS^x, which will result in the Observing player receiving the UIM, UBA and payoff that other player realised) at no cost ;
• or Research, by specifying the magical UIS "Research", and a UBA the player will receive the Deux-Pez Machine UIM that would have provided him with the largest payoff for that UBA as wel as the numeric value of that payoff (nothing is added to his capital).

IV. To celebrate nine years since the original publication of the original paper at the foundation of The Most Serene Republic (the world's only sovereign), the first tournament will be run on November 2nd, 2017. You may submit your entry in the comment section below.

V. Prizes will be announced in this section up until the end of October 2017. The prize pool will be no less than 1 BTC in any case. Currently the proposal is in draft form and still accepts discussion, also to be contributed below.

1. TRNG random. [↩]
2. Internal state register [↩]
3. User Mode Mask [↩]
4. Byte values run from 1 to 256 for the needs of this multiplication. [↩]
5. User identification string, think of it as a sha512 output. [↩]
6. User intended mode. [↩]
7. User bid amount. [↩]
8. Single byte. [↩]
9. Positive value lower than his total sum. [↩]
10. All player UIS are published every tick, along with their current capital. [↩]