How Rare is Rare? — Playing the NFT lottery with Neolastics.

Rules of the Game

  • The price curve is linear, starting at 0.001 ETH for a Neolastic piece. Each new piece increases the price by 0.001 ETH.
  • 99.5% of the price is kept in the bonding curve reserve. 0.5% goes to the creator.
  • There exists 6 colours, with white, black, red, blue, and yellow being equally likely (~20%).
  • Green is rare (~1/256).
  • The colours are chosen from a psuedo-randomly generated 32 byte hash.
  • A maximum of 10,077,696 (6⁹) potential combinations can thus exist.

The elusive Green Square

First thing everyone sees is the ~1/256 and tries their luck. With 9 squares to hit the jackpot, there is ~1/29 chance to add one to your collection. If you have minted less that 29, consider yourself a winner! But did you burn something much more valuable along the way?

Putting a price on rarity

Now how much is something ultra rare worth?

Looking for Gems

There are a number of other combinations that much rarer and probably worth keeping besides just a green. Just as you wouldn't throw away four 4’s chasing another Ace in poker, or that a full house is better than a flush, we can do the same for our Neolastics. Well go through some of the probability, save you from the scary math and let you know if it is better than getting a green, and if you should hold onto it.

5+ of a Kind

Neolastics: 5 of a kind

Green Combos

Is this rarer than a full house? It starts to get interesting if you consider combining something rare, with an already rare green square.

4 of a kind + green.

Combos

4 of a kind + green = ~1/612
5 of a kind + green = ~1/2448
6 of a kind + green = ~1/14,688
7 of a kind + green = ~1/138,312

Full House

Some of the more aesthetic combinations that have been minted, have only 2 or three colors. The following calculations are if you had two colors, in different ratios.

Full house 6:3 — Currently on sale for 32 ETH ($36,500)

Full house — 2 Colours

So far, the above full house with 6:3 is the rarest Neolastic minted.

Ultra Rare

2 greens = ~1/8680
7:2 greens = ~1/7,111,111
8:1 green = ~1/2,213,400

Connected squares

There is something aesthetic about symmetry and connected colors with these patterns. I’ll leave those calcs for another time, but every now and again, you’ll come across a pattern that you’ll need to keep. My rough numbers show a 2–10x increase in rarity for connected colors, much more so with some of the full houses combinations. Also worth looking into are full houses with 3 colors. Post your findings and corrections in the comments!

Full house 5:4 with a 1/775 chance

About The Project:

A few words about the project from the artist.

About The Artist:

I’m a creator at heart. I have created games, writing, music, code, companies, and new economics. Solving the problems of the creator has always been important to me. In the past I co-founded Ujo Music, working with Grammy-winning artists such as Imogen Heap and RAC to launch the first music royalty projects using smart contracts. I’ve helped kickstart wholly new markets and economies. I helped to create the Ethereum ERC20 token standard and token bonding curves, technologies that’s currently facilitating economies worth several billion dollars of value. I enjoy creating new forms of art and experimenting with ways to empower the creative industry.

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