Orb Statistics

Project Psiens

Orb Statistics 101

random2

While some of the statistical properties are easy to explain, others are much more tricky to describe.

Let’s start with the basics concepts:

  1. Players make a Guess against a given range 2,3,4,5,6,7,8,9,10,50,100 and 200.  Only these 12 ranges are supported.  So a player cannot make a guess against a range of 49 for instance.
  2. Every few seconds a new random number is created per range and published for public view and use.  
  3. All guesses are evaluated against the NEXT (after the guess has been submitted) random number of the used range
  4. When a player makes a correct guess, against a given range, a HIT is recorded and likewise if the player did NOT guess the correct number a MISS is recorded.
  5. Sequential HITs (multiple HITs in a row) give Orb Points while a MISS will reset Orb Points to zero.

  6. A Psiens.IO player has some key attributes:

    1. Hit Score:  Every Hit (correct guess) adds the used guess range to Hit Score (Internal)
    2. Guess Attempts: Every guess increases this by 1. (Internal)
    3. Guess Score: 100 * Hit Score/Guess Attempts.   So most Players Guess Score should hover around 100.
    4. Monthly Guess Attempts: Like Guess Attempts but resets to 0 at the start of every new month.   Players can max make 10k Guesses in one Month!
    5. Player Rank: When Guess Score reach Rank Thresholds the given Rank is achieved (102,105,110,140 for Rank 2,3,4 and 5 respectively)

Orbs are the core entities in the Psiens.io and understanding how Orbs are created is important but also not That simple.  For a detailed description of the Orb see: The Anatomy of an Orb

The Orbs have their own key attributes:

  1. Orb Points updates for current Staked Orb (more on this later) only::  
    1. For the first Hit: Orb Points = Guess Range
    2. Every subsequent Hit: Multiply Orb Points with used Guess Range.
    3. For the Miss: Orb Points = 0 (zero)
    4. When a Staked Orb is used to create a new Orb the Staking Orb’s Orb Points will be deducted the Orb Points which corresponds to the Type of the ‘newborn’ Orb.  The deducted Orb Points will be added to the Soft Orb for use in a later upgrade to Hard Orb.
  2. Energy  Orbs can be Energized or Depleted based on the amount of Energy they have left
    1. Newborn Orbs always start with 0 Energy.
    2. Orbs  can be Energized via the Psiens Admin App by paying a small fee
    3. When an Orb is Minted it uses it Energy.  the amount of Eneregy used to Mint depends on the Orbs Type,Level and Family.
    4. Orb Energy can be used by the various Psiens Games.  Some may not use it at all while other Psiens Game heavily rely on the Energy of played Orbs.  Besides the Minting process only Psiens Games may deduct Energy from Orbs.

Statistics of Orb Creation

Orb_circuit_duo

A New Orb can be born when the following criteria are fulfilled:

  1. A Staking Orb is used which will become the Parent of a new Orb.
    1. New Players will initially Stake a Dummy Orb but once their first Minted Orb is created they can no longer Stake this Dummy Orb.
  2. A Player has made a number of Hits in a row which have resulted in the Staking Orb’s Orb Points reaching a Orb Creation Threshold.  These Orb Creation Thresholds are critical to understand:
    1.  The Orb Creation Thresholds are set in the Players account will work across all Psiens Games.  If the Player chose not to set a Threshold (= 0) then the Player must manually trigger a Soft Orb Spawn when this is possible.
    2. Once a Statking Orb’s Orb Points reach the minimum Orb Points Threshold of 100,  the Player can chose to either cash in and Create a new Orb OR take the chance that the next Guess will also be a Hit and thus potentially allow for the birth of an Orb with an even higher stats.
    3. Orb Points are used duing the Upgrade process to determing the Hard Orbs Type, Level and Family.  This  gives the Player many options to create new Hard Orbs.
    4. The following Orb Points are needed for Type 100,500,2500,15000,45000 for Type 1,2,3,4 anf 5 respectively.
    5. The following Orb Points are needed for Level 0,100,500,2500,15000 for Level 1,2,3,4 anf 5 respectively.
    6. The following Orb Points are needed for Family 0,100,200,400,800,1600,3200,6400,12800,25600 for Level 1 to 10 respectively.
    7. Example:  If a Player has a Staking Orb with 3000 Orb Points and chose to Spawn a new Orb this Orb will inherit all the 3000 Orb Points which they can use (during upgrade) to create a Type 3,Level 3, Family 0 Orb.  Or a Type 3, Level 2, Family 4 Orb.  Or any other combination with the 3000 Orb Points.   After Upgrading the new Hard Orb might not have used ALL of its Orb Points and these remain on the Orb and will be used for any future sequential hit with this Orb.
    8. There is ONE small difference between Staking a Hard Orb  and a Minted Orb and that relates to the fact that when a Staked Hard Orb Spawns a new Soft Orb this Soft Orb will Maximum inherit 3000 Orb Points from the parent.  This also means that while a Minted Orb always will Spawn ONE Soft Orb will ALL of its available Orb Points, a Hard Orb parent might Spawn multiple Soft Orbs each with 3000 Orb Points or less.
    9. The ‘sequential Hit’ approach also means it is expected that most GameApps will use the guess ranges 2-10, but it is possible to use range 50,100 or even range 200.
    10. Orbs also belong to a Family, which are normally inherited from the Stake (parent) Orb.   However Soft Orbs can max inherit a Family of a level equal to the Parents Orbs Type and Level combined.   So a Type 2, Level 2 and Family 5 parent will let a new Soft Orbs inherit a Family 4 (2+2) and not the full Family 5.   Duing upgrading the Player can chose to pay Orb Points to increase the Family from the inherited level.   Orb Points are not returned if the Player upgrade the Soft Orb to a Hard Orb with a Family less than the inherited one.
    11. At birth new Orbs are also given 5 random Stats each within the  range of 1-99.   However the combined pool of Stat points are given by the Family Leve225600

Table 1

Simulation Results

Learn-Blockchain

As it might be understood from the concept above it is not trivial to ask questions like “How many Orbs will I create” or “What will it cost me in Depletion Fees”.

So to address this issue we create the Evil Robots which play a series of Simulator Games.   These are pseudo Players which cannot create real Orbs (Mint NFTs) but they do create ‘virtual orbs’ and gain Rank etc using the same rules as real Players.  We then let them run millions of Guesses and make ‘virtual orbs’

Each of the 10 Robots act differently in 3 areas:

  1. Target Orb Type: Some Robots target a specific Orb Type and only that.  So 5 means this Robot will keep going until he finally gets enough orb points for a Type 5 Orb.  This Robot will only have Type 5 Orbs in inventory.   Most Robots use a balanced (1-5) approach where they get a certain number of Type 1 Orbs it starts to target Type 2 Orbs and when he reaches a given number or Type 2 Orbs he moves to Type 3..and so on.    Players/Robots can opt to a variant of  Target Orb Type where the System will auto generate as many Soft Orbs as possible with the Orb Points available.  With this set a Player who got 3 hits with Range 10 in a row would have 1000 Orb Points which it would use to create 2 Level 2 Orbs.  IF this feature is not set the Robot would only create 1 Level 2 Orb in this example and thus continue into the next guess with 500 Orb Points remaining.
  2. Staking Orb Type: By default the server will select the lowest available Orb Type to Stake.  However some players may opt to Stake higher Type Orbs.  Most Robots opt to use any of their available Orbs randomly (1-5)
  3. Energy Strategy: The Player/Robot can choose to always play with Energized Staking Orbs Or just never Energize Orbs after Deplete their initial Energy balance.
  4. Player will probably use a mixture of these strategies and even make use of the Favorite features which will focus Staking specific Orbs over others or select Staking Orbs manually.

Table 2.  Evil Robots Simulation Settings

During a Simulation run the 10 Robots play 100K guess rounds.  Each guess round  will use a random range (2-10) and a random result within that range..   All 10 players play a guess round against the same random range and random result.

So we run 100K rounds and got the following AVERAGE results:

1. The first point is how many (virtual) Orbs did the Robots actually create?  Well, on average the Robots only created ONE Type 5 Orb per 100K guesses and the average  The monthly Orbs  (by Type and Level) created by a Player will look like table 3, assuming the Player plays 10K guesses/month.  An important point in this context is that Orbs are not created in strict accordance with the probabilities in table 1 but also very much based on the decisions by the Player/Robot.   Very often the Players will be faced with the dilemma: “Do I cash in now and create an Type X Orb or do I RISK another guess to potentially earn enough orb points for an even higher Type Orb?”.   Remember that a Miss will reset the Orb Points..so this is an ‘all-or-nothing’ decision.

Tabel 3

2. Looking at the simulation results we see that the average amount of Guesses used to create Orbs for each game (range) reflects the statistical data in table 1.  So if we use the Range 5 and as index 100 we can visualize how each range affects the number of guesses needed to create various Orb Types (table 4).  So for example Range 8 is not ideal to use when trying to get a Type 5 Orb as this requires approx. 6 times more guesses than using Range 5!.  On the other hand Range 8 on the other hand is slightly more effective than Range 5 when trying to get Type 2 Orbs.  Note that the Robots are not using the optimal Range which would yield  slightly better results.   Using an Optimal Range a Player who got 7 HITS with a Range 4 (= 16383 orb points) the next optimal Range would be 3 since this would give you the required 45000 orb points to create a Type 5 Orb.   As the Orb Type Thresholds have been optimized around Range 5 (see table 1) you would also expect to see more Orbs created when using Range 5 than other Ranges.  This is reflected in table 4, where we can see that for Orb Type 1 and 2 we are “Range 5 centric” (with a small uptick for Type 2 Range 8) These differences decrease for higher Orb Types.   As a validation of the simulated results which gives rise to the data in table 4 we can see we have a good match to the theoretical values (raw probabilities) in table 4.   One way to slightly offset this inherit ‘overshoot’ is to use the Target Orb Type (see above) concept with full Orb Points usage.

Table 4.

  1. All the settings/thresholds presented here are also used by the Psiens.io server and the entire set of settings are publicly available here (in json format): https://psiens.s3.eu-north-1.amazonaws.com/configs/psiens_settings.json 
  2. Valuation of an Orb is important if Players want so buy/sell Orbs.   Setting the right valuation for an Orb is very difficult.  Valuation is driven by:
    1. The Rarity of the Orb.  This is the “Collector Effect” and can range from nothing to skyhigh. 
    2. The Cost used to produce an Orb.   Let’s us take a Level 3 Type 3 Orb.  Statistically you need a minimum of 2400 guesses to get a Type 3 Orb and only approx 20% of Orbs would generate a Level 3.  This means you need approx 12000 guesses to make a T3L3 and if on average each or has 120 guesses this is equal to 100 Depletions of an average cost of 1.5JENJ = 150JENJ.   Now this a very rough estimation since real values will differ.
    3. The Mint Cost.  Not too important in valuation since this is reimbursed if Melting.
    4. The Energy Balance of the Orb.    Buying an Orb Depleted Orb is possible but to use it as a Staking Orb the Player would need to Energize it first.  Like Minting Costs the Energizing Costs are likely not very significant in the overall Valuation of an Orb.
    5. Halo Runes.   A very small number of Orbs will have the Halo Rune tag which makes these Orbs specially rare.