Ephemera are obtained either through using credits or a random chance from Ephemera Level and The Dojo. While existing, they have a random chance to disappear. A user can only hold a limited number of Ephemera, dictated by their Ephemera Level.

Each Ephemera Level grants a 0.5% chance at the end of every Bowl the user votes in to obtain an Ephemera, known as Spontaneous Generation. This includes Autovotes.

Users may use the command !condense to convert credits into 1 Ephemera. The starting price is either 0.06% of Active Credits, 1.5% of the user's total credits, or 1989 credits, whichever is greatest. If more than 1 Ephemera is condensed in the same Bowl, the price is 5% more than the previous use.

You may also obtain Ephemera through The Dojo. Upon defeating an Album, you have a 2% chance to immediately obtain an Ephemera if you can hold it. If the Album is defeated at levels 7, 13, 22, or 89, you instead will get an Pending Victory Ephemera. Voting in a Bowl will consume one such Pending Victory Ephemera, giving a 33% chance to get an Ephemera. If you would have gotten an Ephemera from Spontaneous Generation, no Pending Victory Ephemera will be consumed. These will be reset when a Bot Restart happens.

Every Ephemera has an independent 0.75% chance to Disintegrate at the end of every Bowl. This also means a user could lose more than one Ephemera at a time.

If a user has used Reinforce, they also have a 20% chance to have 1 Ephemera Disintegrate at the end of each Bowl. This chance is calculated as an additional chance after the standard Disintegration. Each Ephemera first has a 0.5% chance to Disintegrate. Then, if the user still has Ephemera, a single 20% chance is rolled for only one Ephemera to additionally Disintegrate.

Delegate is used to transfer Ephemera from one user to another. The command !delegate user consumes 2 Ephemera to transfer all other Ephemera to the target. If the Ephemera delegated would exceed the target's Ephemera limit, all excess Ephemera are lost.

Delegate will fail if no target is specified. Delegate will misfire if the invoker only has 2 Ephemera.

An Ephemera Level is required to hold Ephemera. Each Ephemera Level allows the user to hold two Ephemera. Users start with an Ephemera Level of 0 and is increased using the command !exceed, which consumes credits. The price starts as 0.2% of active credits, or all credits owned by active users, and increases by an additional 0.2% for every Level higher. Ephemera Level has a limit of 20, so users can only hold up to a maximum of 40 Ephemera at one time, and have a maximum Spontaneous Ephemera chance from Ephemera Levels of 10%.

Each additional Ephemera Level also gives a user 40 more Risk and Anti-Risk rolls, and 150 more Paid Yahtzee rolls.

The main use of Ephemera is to perform Invocations, which are powerful commands that can affect many aspects of TaylorBowl. Shortened descriptions are listed here, with full descriptions on their relevant pages and/or the Invocations page.

!decompress: Uses 1 Ephemera to convert 1 other Ephemera into a percentage of equivalent credits. (Main article: Credits)

!succumb user: Uses 1 Ephemera to reduce a user's Risk and Anti-Risk counter by 80. (Main article: Risk & Anti-Risk)

!discount: Uses up to 8 Ephemera to reduce the invoker's Paid Yahtzee price by an equivalent number of credits. (Main article: Yahtzee)

!fortify user: Uses 1 Ephemera to prevent a user's vote from being influenced by Invocations for 30 minutes. (Main article: Votes)

!puppeteer choice user: Uses 1 Ephemera to make a non-voting bot vote for a specified track. (Main article: Votes)

!ward: Uses 1 Ephemera to increase the Maximum Strength of the Blight by 120. (Main article: Farm)

!delegate user: Uses 2 Ephemera to transfer all other Ephemera to another user.

!falsify choice : Uses at least 1 Ephemera to make a random non-voter vote for a specified track in a Bowl. (Main article: Votes)

!inhibit: Uses 2 Ephemera to stop the natural Blight Strength increase. (Main article: Farm)

!kickstart user: Uses 3 Ephemera to increase a user's current Streak. (Main article: Votes/Streak)

!invert: Uses 3 Ephemera to switch the votes of all bots to the invoker's choice. (Main article: Votes)

!reinforce: Uses 3 Ephemera to prevent the invoker's vote from being influenced by Invocations for a period of time. (Main article: Votes)

!fertilize: Uses 3 Ephemera to increase the Commons Multiplier per Expected Bloom. (Main article: The Commons)

!expedite track1 track2: Uses 4 Ephemera to remove the Recency value of two tracks. (Main article: Tracks)

!expel choice: Uses at least 5 Ephemera to remove two random votes from a specified track in a Bowl. (Main article: Votes)

!enhance: Uses at least 5 Ephemera to increase credits earned from Voting. (Main article: Streak)

!exempt user: Uses 6 Ephemera to re-allow a user to harvest. (Main article: Farm)

!attune: Uses 7 Ephemera to allow a user to automatically harvest upon the Warning Bloom. (Main article: Farm)

!flourish: Uses 9 Ephemera to force a Bloom. (Main article: Farm)

!trick: Uses 10 Ephemera to force a fake Warning Bloom. (Main article: Farm)

!collect: Uses 12 Ephemera to conduct one round of taxes. (Main article: Credits)

!delay: Uses 16 Ephemera to force all Farmers to weed the Farm. (Main article: Farm)

!delay: Uses 20 Ephemera to increase the Maximum Strength of the Blight by 20 000. (Main article: Farm)

!abandon: Uses 24 Ephemera to remove all farmers' ability to harvest. (Main article: Farm)

!reap: Uses 28 Ephemera to force all Farmers to harvest. (Main article: Farm)

!decimate: Uses 32 Ephemera to destroy 10% of all credits. (Main article: Credits)

There are 2 Evocations that affect Ephemera and Ephemera Levels.

Disintegrate is used to instantly gain Ephemera. The command !disintegrate consumes 1 Perpetua to grant the evoker 32 Ephemera, while also destroying all other Ephemera in existence. This ignores the evoker's Ephemera limit.

Submerge is used to reduce all Ephemera Levels. The command !submerge consumes 1 Perpetua to reduce the Ephemera Level of all users by 1. This cannot reduce a user's Ephemera Level below 0.

The base price for condensing is given by the formula: Since the cost increases by 5% multiplicatively for each additional condense in the same Bowl, the price for condensing in general is given by the formula: where \(n\) is the number of previous condenses in the same Bowl.

Thus, the total price to condense multiple Ephemera in the same Bowl is given by the formula:

Let the event an Ephemera Spontaneously Generates and Disintegrates in a given Bowl be \(X\) and \(Y\) respectively. The probability for an Ephemera to Spontaneously Generate is given by: The probability for an Ephemera to Disintegrate in a given Bowl is given by: Since each disintegration is independent, \(Y\) can be described with a binomial distribution: where \(n\) is the number of Ephemera on-hand.

Thus, the probability that a certain number of Ephemera disintegrate in a given Bowl is given by: where \(r\) is the number of Ephemera that disintegrate and \(n\) is the number of Ephemera on-hand.

And the expected value of Ephemera disintegration is given by: The disintegration of Ephemera can be described with an exponential decay function: where \(N(t)\) is a function of \(t\) for number of Ephemera on-hand, \(N_{0}\) is the original number of Ephemera on-hand, and \(t\) is the number of Bowls that have elapsed. Note that this formula assumes no new Ephemera generate.

Assuming no new Ephemera generate, the probability of having at least a certain number of Ephemera after a certain number of Bowls is given by the formula: where \(k\) is the ending number of Ephemera, \(t\) is the number of Bowls that have elapsed, and \(N_{0}\) is the original number of Ephemera.

Equilibrium Ephemera refers to the number of Ephemera a user will have on-hand, given they vote in every bowl for a sufficiently long time.

This value is reached when there is an equal probability for an Ephemera to Generate as there is for it to Disintegrate. When there are less Ephemera than Equilibrium, the probability for Generation is higher than that of Disintegration, and vice versa. Thus, equating the probabilities: which simplifies to: where \(N_{eq}\) is your Ephemera Equilibrium.

The average number of Bowls needed to reach your Ephemera Equilibrium can also be calculated. The average number of Bowls required to gain 1 Ephemera is given by the formula: where \(t\) is the number of Bowls required and \(N_{0}\) is original number of Ephemera.

In other words, to go from \(N_{0}\) to \(N_{0}+1\) Ephemera, \(t\) Bowls are required. Thus, the number of Bowls required to go from 0 to your Ephemera Equilibrium is given by taking the summation from 0 to your Ephemera Equilibrium of the above: where \(t_{\text{total}}\) is the number of Bowls and \(N_{eq}\) is your Ephemera Equilibrium.

This can be generalised to start from and end on any number of Ephemera as such: where \(t_{\text{total}}\), \(N_{0}\) is your original Ephemera on-hand, and \(N\) is your desired Ephemera on-hand.

You may use the EsteBot command /ephemeraequilibrium to determine your Ephemera Equilibrium, and the average number of Bowls required to reach a number of Ephemera below or equal to your Equilibrium.

Expected Ephemera refers to the average number of Ephemera a user will Spontaneously receive given a certain number of Bowls voted in consecutively.

The formula derived earlier for the number of Bowls required to go from one number of Ephemera to another can be repurposed for this calculation, but to solve it is extremely difficult: where \(t\) is the number of Bowls you can vote in consecutively and \(N\) is the number of Ephemera that you will end with.

The summation function cannot be simplified to solve for \(N\). Instead, we can approximate Expected Ephemera using differential equations. The average rate of change of Ephemera is given the sum of Spontaneous Generation and Disintegration: where \(n\) is the number of on-hand Ephemera, \(t\) is the number of Bowls, and \(EL\) is the Ephemera Level.

Solving this seperable variable differential equation: Let \(f(t)=n\) to express the number of on-hand Ephemera as a function of the number of Bowls. Then, \(f(0)=N_{0}\) where \(N_{0}\) is the starting number of Ephemera such that we have an initial condition to solve for the constant. Thus, substituting \(t=0\): Therefore, the number of on-hand Ephemera as a function of the number of Bowls is approximated by the formula: where \(f(t)\) is the number of on-hand Ephemera expressed as a function of the number of Bowls, \(t\) is the number of Bowls, \(EL\) is the Ephemera Level, and \(N_{0}\) is the initial number of on-hand Ephemera.

The reason this is an approximation is because the change in Ephemera occurs in discrete values and not smoothly like is required for differential equations. This means that the effects of Disintegration are slightly overestimated because of fractional values of Ephemera. However, based on graphical comparison, this is still a good estimate and is reliable enough for practical use where the randomness of Ephemera is more significant.

You may use the EsteBot command /ephemeraexpected to estimate the average number of Ephemera that will Spontaneously Generate.

1.1   Base price of condensing: 1.2 Price of condensing multiple times in : 2   Price of exceeding: 3   Minimum EL to see an Invocation: 4.1   Probabilities for Ephemera Generation: where \(X\) is the event an Ephemera generates.

4.2   Expected value for Ephemera Generation: where \(X\) is the event an Ephemera generates.

5.1   Disintegration distribution: where \(Y\) is the event an Ephemera disintegrates and \(n\) is the number of Ephemera on-hand.

5.2   Probability for Ephemera disintegration: where \(Y\) is the event an Ephemera disintegrates, \(r\) is the number of Ephemera that disintegrate, and \(n\) is the number of Ephemera on-hand.

5.3   Expected value for Ephemera disintegration: where \(Y\) is the event an Ephemera disintegrates and \(n\) is the number of Ephemera on-hand.

5.4   Ephemera disintegration over time: where \(N(t)\) is the number of Ephemera at the end, \(N_{0}\) is the starting number of Ephemera, and \(t\) is the number of Bowls.

5.5   Probability of having at least a certain number of Ephemera after a certain number of Bowls: where \(f(k,t)\) is the probability, \(k\) is the desired number of Ephemera, \(t\) is the number of Bowls, and \(N_{0}\) is the starting number of Ephemera.

6.1   Ephemera Equilibrium: where \(N_{eq}\) is the Ephemera Equilibrium.

6.2   Average number of Bowls to reach Ephemera Equilibrium from 0: where \(t_{\text{total}}\) is the number of Bowls and \(N_{eq}\) is the Ephemera Equilibrium.

6.3   Average number of Bowls to go from a certain number of Ephemera to another: where \(t_{\text{total}}\) is the number of Bowls, \(N_{0}\) is the starting Ephemera on-hand, and \(N\) is the desired number of Ephemera.