Making things in a more complicated way, we could set up many different r.w.'s utillizing a pace different than 1.

After all the general law of independence of the results should work no matter how deep we want to classify the outcomes, right?

Thus a BPBBPPBPBBBBBBPBPPPPBPBBPPB succession could be

1-2-1-1-2-2-1-2-1-1-1-1-1-1-2-1-2-2-2-2-1-2-1-1-2-2-1 (1 pace) or

1-1-2-1-1-1-1-2-2-2-1-1-2-1 (2 pace) or

1-1-1-1-1-1-2-2-2 (3 pace)

Again summing the two adjacent numbers from left to right we'll get:

1 pace) 3-3-2-3-4-3-3-3-2-2-2-2-2-3-3-3-4-4-4-3-3-3-2-3-4-3 (runs: 12)

2 pace) 2-3-3-2-2-2-3-4-4-3-2-3-3 (runs: eight)

3 pace) 2-2-2-2-2-3-4-4 (runs: 3)

Skipping certain outcomes provides a better evaluation of the place selection impact, that is the main factor by which certain subsequences must be considered as collectives or not.

And naturally in this example the best indicator is the number of runs.

We should convert what others call "stop loss" or stop wins" cutoff points with the simple number of runs, especially if we want to disprove a real randomness.

Without boring to test many shoes, it's intuitive that a kind of asymmetrical force is acting along the way on the vast majority of shoes dealt, our task should be directed to spot the shoes where such asym force will be more likely to act on certain points.

Now let's sat we want to follow two opposite players, one player A wishing to parlay his bet up to 5 steps toward a new same number situation (being 2, 3 or 4) and the other one B wishing to make a progressive plan toward not getting same number clusters (up to 5 steps).

Player A will win anytime 5 or more consecutive homogeneous situations will show up (2-2..-3-3..-4-4.. 3-3, etc) and player B will win anytime a given number won't be clustered up to 5 times.

From a math point of view both players will get the same results getting different W/L frequencies.

In the practice things go quite differently.

as.