In Capua Nor, there is a man in a corner who you can play dice against, for free! It costs nothing but your precious, precious life time. There are two games, and they are probabilistically identical, assuming no shenanigans on the part of the developers.

As noted above, both games are ultimately the same, and the same as guessing the results of three fair coin tosses.
The game can be modelled with a four state discrete time Markov chain (transition matrix below), from which the following (awful) statistics can be extracted.
It takes about 9 seconds per dice roll, so I'll use that to give a minimum time. It will feel a lot longer.

First, averages:
From the start state, it takes an average of 14 dice rolls, or at least 2'6" to reach a winning state.
From the first correct choice, it takes an average of 12 more dice rolls to win.
From the second correct choice, it takes an average of 8 more dice rolls to win. That's right: you're on average at least 1'12" away from victory when you're two up. Don't gamble!
The median number of rolls to victory from the start is 10, or a minute and a half.

Second, the awful (not quite exact, but close) probabilities, from the start state to victory:
You will win eventually, as long as you keep rolling dice.
There is a 1/8 chance of taking 3 rolls (straight to victory!) 18 seconds.
There is a 1/4 chance of taking 5 or fewer rolls. 45 seconds
There is a 1/2 chance of taking 10 or fewer rolls. 1'30".
There is a 1/2 chance of taking 11 or more rolls. 1'39".
There is a 1/4 chance of taking 18 or more rolls. 2'42".
There is a 1/10 chance of taking 30 or more rolls. 4'30" (!)
There is a 1/20 chance of taking 38 or more rolls. 5'42"
There is a 1/100 chance of taking 57 or more rolls. 8'33"
For the extremely unlucky, there is a 1/1000 chance of taking 84 or more rolls, or at least 12'36".

Bandai-Namco suggests 1580193 sales of this game over all releases as of 2019. From Steam's achievement statistics, we can estimate that about 1% of players got all the game's titles, so an estimated 15801 people wasted time winning this game at least once, for a grand total of more than 23 days of human life spent watching extremely slow simulated dice. The moral? Don't statistics either!

The transition matrix I used to get the distribution I wanted is given by
With state 1 being the initial state and state 4 being the victory state. Exact transition probabilities come from entries of powers of this matrix. "Markov Chains" by J.R. Norris is a good book on the details.