VirtuallyVB, first, atheists do not have opinions relating to what god thinks or knows. I am sorry I included the last paragraph in my previous post. I thought it would convey a mood or an attitude.

I do not understand your distinction between "open" & "closed" probabilities. Are you saying that the "closed" type situation is a one time, unrepeatable process? Like if you had 50 white balls and 50 black balls, you could pull 100 balls out of the bag, and that would be the end of the process? Would your "open" process involve replacing each ball before drawing again? This would allow you to keep it up indefinitely. If this is your concept, then both situations are considered to be probabilistic processes. Of course in one case (the 100th ball) the probability is know to be one, or a certainty. I personally have never heard the terms "open" & "closed" used in this context. Of course, I paint with "colors," while my British friends use "colours."

For pulling balls out of a bag, the usual terms are "sampling with replacement" ( "independent Trials" events) and "sampling without replacement" ("dependent trials"). Dice tosses are independent trials events (history does not change odds), while Blackjack involves dependent trials events. Blackjack causes a lot of quibbling. Once the cards have been shuffled, the game could be considered deterministic and predictable. When viewed from the laws of physics, you can inspect the deck and know what is going to happen. If conforming to casino rules, your strategy must view it as a probabilistic dependent trials game.

Following are some remarks about deterministic systems, giving some idea of what is meant by deterministic or predictable.

Newton's differential equations can be integrated for "2-Body" problems, resulting in exact equations ("analytic functions") describing circular, elliptical, & parabolic (maybe hyperbolic also) orbits for two objects influenced by their mutual gravitational attraction (and under no other influences). You can use the exact equations to calculate where each object will be at any given time (future or past). Everyone agrees that this is a deterministic, predictable system (or process). In principle, you can restart such a system with exactly the same initial conditions and expect it to be repeatable. The initial conditions seem well defined and obtainable in principle. In practice, there is some limitation on how accurately all the required values can be measured.

When there are 3 or more objects, exact equations cannot be obtained (except for some special cases). However, the differential equations can be solved "numerically." The initial conditions consist of the position, velocity, & mass of each object. Given these, the positions, velocities, and masses can be calculated at the end of a short time interval, resulting in what can be treated as initial conditions for another calculation. You can keep this up, calculating positions and velocities for a long time into the future (or the past). Note, however, that there is some inherent inaccuracy in the calculations. If you use one second time intervals, you will get more accurate results than using one day intervals, but it will require 86,400 times as many computations. In principle, you cannot obtain exact results. In practice, you can get results so accurate that you cannot measure the difference between the calculated results and the actual behavior of the system. This last statement is an exaggeration. It is only true if you do not want to calculate "too far" into the past or future. The meaning of "too far" depends on the characteristics of the system.

Some claim that gravitational systems more complex than 2-Body systems are not deterministic. Personally, I think that is being too picky. In principle, the differential equations define a deterministic (or predictable) system. It is in practice that difficulties arise.

Some claim that rolling dice under casino conditions is a deterministic, predictable process, others say no. Superficially, it seems like you could collect the necessary data and decide on the necessary equations or algorithms. If you think deeply about the problem, you start having doubts. I personally lean away from determinism on this one, but am not sure. An argument could be made for quantum world processes affecting dice rolls. A dice roll in which one die almost balances on a corner, might roll one way or the other depending on quantum level events. Interactions between the dice and the cushiony table seem difficult to calculate, and might be affected by quantum events.

Now start thinking about cooking food with the boiling water in a pressure cooker, the biochemistry of a living creature, the interactions of all the living creatures on the planet. If the experts tell me that quantum world processes are involved here, I believe them. These processes
just do not seem deterministic (or predictable to me).