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[Review] Analysis of the Probability of Hall of Immortals in Infinity Kingdom

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Article Publish : 04/07/2024 14:04

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💠Introduction

What’s up, folks? New immortals were added to the game in recent patches, most notably, Pakal the Great and Artemisia. Currently, the only way to get these immortals is through the Hall of Immortals. Let’s take a closer look at the chances of pulling them through the hall and then see how those percentages hold up in practice.

💠Table of Contents

Overview
Hall of Immortals Percentages
Methodology
Result
Summary

💠Overview

For simplicity’s sake, I will only focus on some of the high-priority, newer, or immortals you have to get through the Immortal Glory bundles. We’ll use a relatively large number of Philosopher’s Stones and afterwards, we’ll compare the results to the stated percentages and see how close we can get. We can then determine whether trying to max an immortal through the Hall of Immortals is a viable strategy.

💠Hall of Immortal Percentages

In Hall of Immortals, the chance of drawing an Epic immortal is 2.76%. The chances of pulling their fragments is 9.88%. Pakal the Great, Louis IX, Toyotomi Hideyoshi, Trajan, Yi Sun-Shin, Ragnar, and Mehmed II are all 0.04%. The probability of getting their fragments is 0.15%. The chances of getting Artemisia, Margaret I, Matilda, and Seondeok are 0.06%, and getting their fragments is 0.22%. The probability of pulling an Elite immortal is 7.32%.

💠Methodology

For this experiment, I’ll pull 1,000 times, nine Philosopher’s Stones at a time to guarantee an Epic or Elite immortal to maximize the chances of getting one of the eleven immortals in each pull. Since every 10 pulls will cost 9 Philosopher’s Stones, it will cost a total of 900 Philosopher’s Stones or 270,000 Gems. In theory, I should get about one of the 0.06% Epic immortals in about 166 pulls and one of the 0.04% Epic immortals in 250 pulls.

💠Result

After 1,000 pulls, the results are fairly in line with the stated percentages with a small deviation. The probability of pulling an Elite immortal was 7.60% which was in range of what we would expect. The result for all the Epic immortals was 2.40% which is pretty close to the 2.76% that we would expect. All the target epic immortals were within 0.06% of what we would expect. As you do more draws, the percentage for each category will get closer and closer to the stated percentages with a lower standard deviation.

💠Summary

As you can see, it’s not feasible to max, say, Seondeok or any other Epic immortal via draws from the Hall of Immortals. You can definitely supplement it when you’re purchasing bundles, but you would need hundreds of thousands of Philosopher’s Stones if you wanted to rely on this method.