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So I have a magic system in which Magic Practitioners cultivate Magic Energy. Grants super strength, regeneration, and the associated powers to make them work. There are nine levels to the system. Every person starts at level one. As you progress further you are granted more power as well as an increase in size.

Each level has a threshold to entry that allows for a possibility of Magic Energy deviation. At the threshold to level two, it's a 40% chance to deviate. However, as you go further up the levels, the chance you'll deviate decreases. Deviating causes you to skyrocket in power but turns you into a rampaging monster of a human basically allowing for a jump in power level by two or three. These rampaging monsters still need to eat and drink but only live for a year.

Does the chance of deviation create too high a barrier of entry and cause the abandonment of the magic system?

I don't want something like an opinion based answer. I need something more like game theory.

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    $\begingroup$ If you want a probability-based answer you'll need a lot more data. Psychology plays a big part. Size? Do you mean the higher-level wizards become giants? People who are dying might not care, governments will discourage anything where 40% of users become wild super-monsters. Preselects for people with nothing to lose and disregard for the safety of others. How quickly does the chance of going wild decrease as you go up? $\endgroup$ – DWKraus Oct 26 '20 at 13:10
  • $\begingroup$ This depends on the power of a maximum-mage. Can a level 9 mage win against 9 level 1 mages? How about against 90? If the end reward is high enough, military forces/clans/cults would be willing to push people all the way through even if there's only a 1% chance of gaining a peak-practitioner so long as that practitioner could then theoretically beat the 99 people who didn't make it. $\endgroup$ – Dragongeek Oct 26 '20 at 13:50
  • $\begingroup$ Following the "cultivation-manhua/wuxia" formula, Are there any ways to increase the success rate of levelling up? In it's current state, the number of people who would want to level up is low and those who do would want a partial army on standby to kill them in the event of a deviation. Level ups seem more like a terrorist act than a way to get stronger in this system. $\endgroup$ – IT Alex Oct 26 '20 at 13:50
  • $\begingroup$ True I'll get back to you guys when I have more stats then. Until then it might be best to close the question or something. I see where it's lacking. $\endgroup$ – BIGBOLDWORDS Oct 26 '20 at 23:58
  • $\begingroup$ When you go monster, do you keep your morality and alignment? Or do you turn on your friends? If you keep your morality you can do a super powered suicide attack - that is valuable. $\endgroup$ – Ash Oct 27 '20 at 9:08
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Is the progression purely voluntary? Can it be imposed?

I can easily see a military that drafts thousands of recruits, puts them through forced training and advancement, and have the forces on-hand to kill any who get corrupted by the advancement on the spot, before they do damage to anyone but themselves.

Who cares about the multitudes of "failures" that get eliminated? You few survivors are the ELITE. The best of the Best. You deserve to RULE over the plebs like the Gods you are.

How's that for a recruitment speech?

Yeah, it does sound a bit of a Fascist's Paradise. But think of the elite force of loyal SuperMages you will end up with, eventually.

Perfect representative example: Pug/Milamber's training to become a Great One, in the Magician(Riftwar series) by Raymond E Feist. The trainees are not given a choice, they are drafted. It is stated that less than 1 in 10 survive the training. And the graduated "Great Ones" are a law unto themselves, above ALL but service to the Empire. Which loyalty is deeply brainwashed into their very being.

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Only crazy, dying, or coerced people will do this.

To advance even one level, there's a 40% chance that a person will kill themselves (immediately in a methaphorical sense of becoming a rampaging monster, or within a year in the more literal sense). And this is just to get to level two, which may not be all that useful in the first place, depending on how fast power levels scale.

If the failure rate remains at 40% for each level, there's only a 1.7% chance that an individual would survive 8 level transitions. Of 100 people that attempt to achieve Level 9, 98 will become rampaging monsters. Even if the failure rate is only 10%, you'd still have 57% of people being killed by this process. You may have some people who want to do this, but for for most, the tradeoff seems far too high unless low-level magic is very useful. Is Level 2 magic really worth a 40% chance of losing your life as you know it?

Think about it this way - is there any amount of money that would get you to play a 60-40 game of chance, where you get the money if you win but die if you lose? For me, I don't think there's any amount of money where those odds become worthwhile.

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  • $\begingroup$ Your answer is, statistically speaking, incorrect and otherwise opinion-based. A 98% chance of turning does not mean that 98 out of 100 people do turn and for the magic to be used, one does not need to reach level 9 so other levels have to be taken into consideration too. Also, coercion is just another "player's" way of influencing your chances - what about those players? And finally, "crazy" has nothing to do with game theory. $\endgroup$ – hajef Oct 27 '20 at 9:59
  • $\begingroup$ @hajef Er, that's exactly what a probability is - if you have a 40% chance of failure at each transition, you only have a 2% chance of succeeding in 8 transitions in a row. Of 100 people that attempt 8 transitions, 2 will succeed. You're right, you don't need to go all the way to level 9, but the odds of failure are awfully high right out of the gate. But if you're coercing people anyway, the consequences don't really matter in the first place. And "crazy" is another word for "irrational", which is absolutely related to game theory - a "crazy" person will make irrational decisions. $\endgroup$ – Nuclear Hoagie Oct 27 '20 at 12:56
  • $\begingroup$ But 2% chance does not mean that 2 out of 100 will turn. While the average is the most likely scenario, it is still less likely than "anything else". Also, OP says that the chance reduces with each level. And the game theory is about the rationally best way to "play a game". Being irrational means leaving game theory. $\endgroup$ – hajef Oct 30 '20 at 9:59
  • $\begingroup$ @hajef You're missing the forest for the trees in the probability calculation. Yes, 2% chance does not mean that only 2 people will succeed every single time, due to the random nature of success. But with 95% probability, no more than 4 people of every 100 will succeed. With 99% probability, no more than 6 will succeed. If 100 people attempt this, at least 90 will die with 99.999% probability. Without knowing how fast the odds drop, there's not really any other numbers that can be evaluated without guessing. Also, the field of behavioral game theory absolutely does deal with irrational agents. $\endgroup$ – Nuclear Hoagie Oct 30 '20 at 13:44
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If you are asking for a game-theory answer, there are a few things to consider:

  1. How do we rate the usefulness of the magic at a given level?

This is mainly based on in-world opinion and depends not only on the actual power and usefulness of the magic but also on the alternatives and the situation. If a group of people see themselves outnumbered and low on resources, gaining more individual power will be much more appealing than gaining more strength even though there are machines that can be operated with ease anyway.

  1. How do we rate the damage of deviation?

Terrorists and soldiers on a suicide mission might consider turning in an overpowered, mindless monster a good thing, in those cases even the worst outcome is positive so go for it. If "rampaging monster" is meant metaphorically, even normal people might consider it a risk worth taking if they need to fight for their life, family or similar, if they can achieve their goal even if they deviate, it is like going to war knowing that you might die. In a civilised society where the majority of the population lives in cities with no external thread, turning into a monster and dying within a year might be as bad as it gets.

  1. How many mages are required to continue the magic system?

If magic comes from within and there is no specific knowledge required to use and level up magic, the magic will always be used by some people for one reason or another while if a level-up requires a ceremony including the help of several mages that have mastered the new level, the highest obtainable level will go down over the ages even if everything else aligns perfectly. The truth will be somewhere between these extreme examples.

  1. Who has a say in who levels up?

Is there a mages association that has to grant permission or help? Can a superior force someone to level up? Are level-ups an inevitable result of using the powers? No way to sort these questions out without knowing the specifics of your world and magic but they will affect the use of the magic. If using the magic results in level-ups, it might get discontinued altogether, if someone else than the user has a say, it will subject the issue to someone else's game-theory possibly with more concern for public safety or less concern for the user's life.

  1. What is the chance of deviation at a given point?

Chance of success times value of success minus chance of deviation times cost of deviation. If a deviation is the wanted or at least an acceptable outcome, this is redundant but otherwise, the result must be positive for an individual to risk it and considerably positive for a society to keep doing it without losing the knowledge due to natural fluctuations in the perception of risk and reward. If a deviation is a gam-over, there will be no content people who want to live a peaceful life and still use the magic unless the chances are extremely low.

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Shadow of the Conqueror by Shad M. Brooks has a similar mechanic where one type of magic can only be obtained by conducting a ritual that has a one in three chance of killing you. On the other hand, you get powers that are orders of magnitude higher than anything a normal human can do and the other two kinds of magic can be forced upon you but are deviation 100% of the time or are granted, not obtained, after years of dedication. Even the characters do discuss that it is only worth risking your life in the ritual if you are either extremely power-hungry or there is a strong external thread that is worth risking everything to fight against.

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  • $\begingroup$ Thanks for pointing out the problems and asking more directed questions I'll clarify at a later date most likely tomorrow. $\endgroup$ – BIGBOLDWORDS Oct 27 '20 at 0:03

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