4 m uncollected bc
SHAYU
Member Posts: 78 ★
18
SHAYU
Member Posts: 78 ★
SHAYU
Member Posts: 78 ★
Comments
It’s called the Law of Large Numbers in probability.
For UC, you have a 33% of 225 units and 66% chance of 75 units. For an expected value per success of 125 units.
OP had 6,300/125=50.4 successes. Let’s just say 51.
51/382 is 13.3%. Less than the 15% the crystals provide.
The probability of at least 51 successes out of 382 trials at 15% odds is 83%.
Now, instead of 382 UC, one could have 1910 regular. Suppose one achieved the same 83% probability. That would represent 272 successes. 272/1910 is 14.2%. Closer to the theoretical probability of 15% (see also: Law of Large Numbers).
Regular crystals give 15 or 45 at the same 33/66% probability, making expected value per success equal 25 units. 125/25=5, so that matches the cost increase.
272 successes would yield 6,800 units.
Same probability across the board, yet more trials led to 500 more units.
You can RNG more units from UC/TB, but overall, most people will be better off going for more chances with the regulars.
The Law of large numbers in statistics simply states that the more trials you perform of a random outcome, the closer your measured result will be to the statistical average. Applying this principle here, opening regular arena crystals is more likely to generate the average result than opening UC crystals, because you open more of them. It doesn't say how often the result will be higher or lower than the average in either case.
There is some truth to the idea that the more expensive crystals are more risky, and thus you have a greater chance of getting a below average result if you open the more expensive crystals, but this averages out over long periods of time to the point of having a negligible impact. But this doesn't come from the law of large numbers, this comes from the specifics of how the crystals function.
The biggest issue here is you can't take one player's result which happens to be below average and use it to prove the cheaper crystals are better, because there's a hidden circular dependency here. You're taking a below average result to prove the alternative would have been better because it would have been closer to the average (and thus higher than the below average result). Suppose I were to post a TB opening where I got 3750 units out of one million BC. The exact same logic would prove that the cheaper crystals would have been worse (because once again, they would be calculated to be closer to the average, and now are being compared to a higher than average result).
So yeah, if you’re hoping for rare events more expensive crystals would be more beneficial.
But for most people, opening a lot of crystals, regulars will be better in the long run.
Throw it in a Monte Carlo if you wish.
I can apply OPs scenario because they did not achieve theoretical probability of 15%. Instead they hit 13.3%. Thus, they would have benefitted from more trials pushing them closer to 15%. Which is why I stated the law.
“Because you underperformed the actual odds this time, it would have been better if you opened the regular crystals instead.”
Thus he would have had more changes to narrow the gap towards the actual 15% odds.
Which “after the fact” or “in hindsight” of this particular case might be a valid argument. But would be the opposite for someone who overperformed at say 17% with the UC ones (switching to Normal would have dragged his over performance downwards toward the 15% instead). Exactly counter to your premise of Normal being better for units.
I believe it is the same bug as when opening lots of SigStone crystals, Daily's, 4-Hour's, etc, and the counts that show up are well above what you actually got (and indeed sometimes far above how many crystals themselves were actually opened)
Same bug, large openings has problems where it overstates how many you got.
However, achieving greater than 15% is slightly less common (43.2%) versus achieving less than 15% (45.7%).
So over time more people will be on the lower end. And those people will benefit from more trials.
It may be splitting hairs, but are there any crystals that technically get worse with progression? Kabam really needs to add some rare bonus to the higher crystals to offset this.
So he might have gotten less Units than the rates let us expect, but instead he must have gotten a better rate of something else.