Long run:
In the long run, luck is not a relevant factor. Basically on average every hash is going to give you some return. This is the same for pools and solo mining. Here is the problem. The pool has a fee, which reduces your overall return. In addition the pool is not 100% efficient. To reduce fraud, pools send out the same task to more than one miner. This overhead further reduces the efficiency of the pool and the associated return. The end result is that pools are not as profitable in the long run.

Short run:
In the short run pools are more profitable. Let's say you only mine for 1 second.
The likelihood of solo mining a coin is very low, but you can at least get something out if the pool.

The next question is when is solo mining more profitable than pool mining?
To answer this question we are also going to take luck out of the equation.

Given: The net hash rate is 10,000kh/s
Given: Your mining rig does 10kh/s
Given: 500 coins mined per day
(Yes I am using simple numbers to make the example simple, you can plug in the actual numbers)

((Net hash)/(your hash))/(hash per time period)=(time it takes to earn a reward)

((10000)/(10))/(500)=2 days

The code compiled for the pool does not support AVX512, as a result the rate was significantly less  than the native wallet's hash rate.
Basically if your CPU supports AVX512 instructions, the pool is a non starter until they upgrade their capability.

We know that pools are less efficient so in our example it is more efficient to run a solo miner if you mine for a little less than 2 days or more.

For DYN it is actually less than 2 days because the reward amount is 675 a day (going from memory). For BTC it is in the years or decades depending and therefore pools are viewed as better for BTC.