###
Overview

#### Summoning Inputs

Select your summoning options in the input box:

- Summoning showcase "banner"
- Desired ★5 target (adventurers, dragons, etc.)
- Number of summons (round down to the nearest increment of 10)

The calculator can also be used to automatically convert wyrmite/diamantium the no. of summons that you can afford, in terms of ten-folds.

Below the inputs, the colored boxes display the total probability of summoning your target(s) at least once, based on the selected number of summons. For details on summoning mechanics and other assumptions, please refer to the **FAQ & Contact Info** tab in the menu. For more complex summoning inputs, you can also try **Custom Calculations** in the menu; this tool opens up advanced options like single summons and custom ★5 rates.

#### Info Table

The info table box shows converted summon costs, in terms of 10-fold summons. These values assume a rate of 1,200 wyrmite or $22.86 per 10-fold; of course, your actual costs will likely be lower with free summon vouchers or diamantium package deals.

Additional statistics for the target ★5 are shown to the right of the table. The *median* is the value required to achieve at least a 50% chance of success. The *average* is the expected cost of success. Note that these two values are not the same, because the distribution is strongly skewed (you could pull your target on the first summon, but there is no theoretical maximum).

#### Probability Chart

The chart plots the probability curve for the target ★5, by number of summons. This is also known as a cumulative distribution function. Your selected number of summons is shown as a red dot.

###
Showcase Analysis

###
Inputs

###
Calculator

###
Table

###
Chart

###
Custom Calculations

###
Frequently Asked Questions

### Contact

Last Updated: Mar 2019

Discord (DM): **@Proof#8868** and **@Archaic#0001**

Reddit Posts: Prooof

### Overview

App Link: http://canarycraft.net/shiny/dl-summon/

This tool is intended to help you estimate your chance of successfully summoning ★5s in Dragalia Lost, a mobile game published by Nintendo.

To get started:

- Open the menu bar and select Showcase Analysis
- Select the desired ★5 target option (adventurers, dragons, etc.)
- Select the number of summons (slider), or use the calculator
- Check your probability of success or failure (colored value boxes)

### Pity Rates

All calculations shown account for "pity rate" mechanics used in-game:

- For every ten pulls without any ★5 summons, the individual ★5 summon chance increases by 0.5 points, up to a cap of 9.0%
- The summoning rates are reset after any ★5 is pulled, including wyrmprints or other ★5s that you don't want
- If a 9.0% "pity rate" is reached, the next summon is guaranteed to be a ★5; this takes 100 consecutive summons on a typical banner (4% base rate), or 60 summons during Gala Dragalia (6%)
- "Pity rates" do not carry over to different banners, so you always start at the base rate

### Single vs Tenfold Summons

The **Showcase Analysis** tool assumes that you *only summon using 10-folds,* including the calculator inputs & table stats.

Pulling single summons instead of 10-fold is typically a disadvantage, even if you ignore the guaranteed ★4 from a 10-fold. This is because ★5 probabilities are fixed for each 10-fold summon, i.e. the rates do not increase or decrease for individual summons within a 10-fold, only after that 10-fold is completed. Of course, this won't make much difference unless you are sitting on an extraordinarily high pity-rate.

If you do plan on using single pulls (e.g. the daily deals or single summon vouchers), you can still estimate your chances by adding them to your total number of summons, rounded to increments of ten. This should still give you reasonably accurate (but not exact) results.

The **Custom Calculations** tool allows you to input single summons. The calculation assumes that only ten-fold summons are pulled first, then any remaining summons are pulled individually at the end (i.e. with 64 summons, 6 ten-folds are pulled, then 4 singles). Your actual summoning strategy and number of single vouchers may vary from this assumption, but results are not materially affected; the tool will still calculate a reasonably accurate probability.

### Methodology

The cumulative probability calculation is implemented as a recursive function F(p, n) that returns the following:

F(p, n) = A + (1 − A) × [(1 − B) × F(p + 0.005, n − 10) + B × F(p_{0}, n − 10)]

- A = Probability of pulling the target(s) in a particular tenfold at the particular pity rate
- B = Probability of pulling a
*non-target*★5, given that the*target*★5 was not pulled in the same 10-pull at the particular pity rate - p
_{0}= Base ★5 summon rate - p = ★5 summon rate
- n = Number of tenfold summons

Credit for this methodology and JS code goes to R9K-IC (Archaic). Prior Monte Carlo mass summon simulations also validate the statistics produced by this formula.

### Featured ★4s

Although this tool only calculates ★5 rates, probabilities for pulling ★4s are relatively straightfoward to produce. A ★4 calculator may be considered for a future update.

Below, you can find a table of the typical cumulative rates for pulling at least one copy of the featured ★4 (1.75% displayed rate) on standard banners. This assumes that you only summon using ten-folds (to get the guaranteed ★4 and up). Note that increasing ★5 "pity rates" typically do not impact the odds of obtaining featured ★4 units.

N | P % |
---|---|

1 | 23.6 |

2 | 41.7 |

3 | 55.5 |

4 | 66.0 |

5 | 74.1 |

6 | 80.2 |

7 | 84.9 |

8 | 88.5 |

9 | 91.2 |

10 | 93.3 |

11 | 94.9 |