The miner loops through all eligible UTXOs essentially every 16 sec (it is actually every 8, but there is a quantum of 16 sec applied to the transaction times, so it is effectively every 16) and tests for whether the candidate hash is less than the target * coinweight.

This is a series of Bernoulli trails with probability p for each trial where p = target * coinweight / maxhash.

If you have a small balance, such that you are going to stake only once every few days, it makes little sense to have more than a few UTXO’s for staking, because the expected TTS is beyond the 16 hour staking cooldown.

What happens if you have one UTXO originally and then take your coinweight (i.e. balance * 80) and chop it up into 10 UTXOs? Then for each miner loop you are going to run up to 10x as many bernoulli trails with 1/10 of the probability for each one compared to the original. And you have to remember, the probability for each one of these is pretty small...

For an expected TTS of 1 day (10000 GRC), that is 24*3600/16 quanta, or 5400 trips through the miner. So with one UTXO, the “coin toss”will have been thrown 5400 times, and with 10 the “coin toss” will have been done up to 54000 times over that day when the success (stake) happens.

Note that the probability of success after k trials of a coin p is geometricallly distributed.

Let’s put it together. For Bernoulli trials, the expected value of the number of throws is 1/p.

So for a one day expected TTS for one UTXO, this would be 24*3600/16 throws=5400. So p=1/5400. If you split your balance into 10 UTXO’s evenly sized, then p for each UTXO goes down by a factor of 10. So each p is now 1/54000. Now asking the question of what the expected number of throws is for that p? It is 54000! What? ten times as long? No. Remember that the miner every 16 seconds loops through ALL UTXOs very quickly and then goes back to sleep, so 54000 trails are done as 5400 groups of 10 spaced at 16 sec intervals. This gets us back to 1 day.

The bottom line is that from an EXPECTATION perspective, chopping up UTXO’s into finer ones results in the same expected time to stake, IGNORING the 16 hour cooldown effect.