Unfortunately I don't know the math behind
predicting the improved probability of getting
the production boost between 2x vs 4x. If I
knew this I could do the math and determine
which has a higher success ratio for getting
the boosted outcomes. If someone knows
the math behind this, we could find out what
truly offers the best odds: 2 chances vs 4
chances with the same win chance per attempt.
I've found a formula for probability that with multiple attempts the bonus occurs. This is
the source:
The formula is;
100*(1-(1-p)^attempts)
p = chance for 4x boost
So, we can only influencing the number of attempts, I'll calculate the probability for 1
attempt for reference, 2 for the representation of 2x 8h and 4 attempts for 4x 4h
representation. This are the results with 20% chance of the 4x bonus:
1 attempt
20% = 100 * (1 - (1 - 20)^1)
2 attempts (2x 8h)
36% = 100 * (1 - (1 - 20)^2)
4 attempts (4x 4h)
59,04% = 100 * (1 - (1 - 20)^4)
So, according to the math it's more
likely that you'll get the 4x bonus with 4x 4h. Now the
math for when you'll get a bonus with 4x 4h. Which is more likely to happening than with 2x
8h.
2 x 10 = 20
4 x 5 + ((5 * 4 bonus )-5 base prod) = 35
This scenario is
most likely to happen
most of the times. Which will deliver most likely in the
most cases 15 goods more.
Now let's assume your also lucky with the 2x 8h prod, than this is the production:
2x 10 + ((10 * 4 bonus)-10 base prod) = 50
4x 5 = 20
In this
less likely event which according to the math will most likely be less often. The 2x 8h
prod wil be massively more productive.
In conclusion the
4x 4h option has the
best odds. While the
2x 8h production
can offer higher production when lucky.
So, it's rather risk management and up
to personal preference to gamble with either
better odds, or
higher risk higher reward.
Taking chances into account for decision making brings two complex subjects:
chance calculation / estimations and risk management. Both are tricky and will lean
towards personal reference. What for some will be acceptable risk will be for the other
outrageously high. Math can in conclusion help making the decisions but ultimately it's up to
yourself.
@derdelyi beta yes but actually no, you did calculate under both favourable / equal
conditions and ignored chance calculations. Causing the math to confirm the known result
that both productions under the same conditions are the same. The discussion went
more to with which options you'll likely
get goods faster. Using the 4x bonus by
chance and which
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Regardless of the conclusions. I find it fascinating how deep and mathematically we
try to answer, explain and finding the best ways to achieving our goals in this game and trying
to convincing one another from our points of views.