This is a "fork" of another thread, in which I made the following statement regarding virtual losses:

The reality is that no matter how many virtual losses you use (and it would seem that more is better, for "safety"), outcomes behave like a receding horizon. It seems to be there in the distance, but never gets any closer. This is because being selective about what you "take" from a continuous random stream of numbers doesn't change the fact that you will end up with another continuous stream of random numbers which are indistinguishable from the original stream. "Removing" some elements doesn't leave any less.

I appreciate that this is very counter-intuitive and hard to get your head around, but sooner or later you have to come to this conclusion.

Here is part of Kav's reply:

Imagine this scenario. Someone is observing a number repeat 8 times (or whatever the realistic upper limit) then another player comes to the table and for the next 8 spins he sees the same number repeats itself 8 more times (the repeats limit for the second observer). Then a third person comes to the table and it is perfectly possible that he will observe the same number repeat another 8 times because he has not reached his limit. The problem is that the first person who sits on the table all this time has now seen the same number repeat 24 times!

This apparent objection to my proposed "model" of a receding horizon is that it must break down at the limits, because no one will ever see 24 consecutive hits on the same number (or 100 reds in a row, or whatever). So if it isn't true "at the limits", then that calls into question its accuracy as model, so perhaps, just being a "theory", it shouldn't be taken too seriously.

palestis seems to agree with this:

That's basically what it comes down to.

Let's take a more realistic event rather then the almost impossible 8 repeats of the same number.

A streak of 5,6,8,10 or whatever black in a row. As you walk around among many active roulette tables you will find that it's not that rare to observe a situation like this. Whether it is red or black or odd or even or 3 same DS's. If this situation is a virtual loss for me, I count on the fact that there will be at least one streak break in the next few spins.

But if my virtual losses don't count and the distant horizon becomes even more distant, simply because of my arrival at this table, ( and the roulette read my mind), then all players that happen to be playing what I plan to bet on, will be forced to see a new record. Or be PUNISHED, simply because of my way of thinking as I came up to that table. Then if someone else thinking like me came up to the table, I will be forced to lose because A NEW STATISTIC has to be constructed specifically for the new player to push the horizon even further in a greater distance. Ignoring every player that has been there earlier.

If that was the case then we would be witnessing "horror streaks" a lot more often. But we don't. Fortunately.

Virtual losses count and count heavily. And there are a lot of players using them without realizing that they use them. In fact most players moving around from table to table that's exactly what they do. Some follow the streak, the others go against it. if those who go against it are doomed, then we would be seeing streaks that we never saw before. But we don't. Something, some higher power makes sure that things remain normal, most of the time.

As I see it, there are several things wrong with this assessment. In the first place, there's no need to invoke any mysticism of a "higher power", or the idea that the roulette table knows what you're thinking and changes the outcomes accordingly. The idea of a limit to randomness is connected with the fact that we're usually interested in

**one** particular sequence of outcomes selected from a staggering large number of possible outcomes.

In fact, each sequence of 24 spins has a probability of 1/37 x 1/37 x 1/37 ... up to 24 times, which gives a probability of 1 in 4.33 x 10

^{37}, a vanishingly small number. This is why we are never likely to see such an event, but each one of these possibilities is equally likely,

**so in choosing any one of them and testing for its "limit", the actual limit is not inherent in the outcomes themselves, but in the computing power at our disposal.**Thus, in testing for worst case scenarios, I've discovered that there seems to be a "limit" of about 5 standard deviations, no matter what the bet is. But is this really a limit? is there really some "higher power" which constrains the outcomes to conform to these apparent limits? I think it's an illusion, and that there really aren't any limits to randomness (which, by the way, is confirmed by the bell curve).

If palestis is correct, and that "virtual losses count and count heavily", then why do all simulations show that they don't count at all?

If outcomes (streaks, or whatever) tend towards a limit, then waiting for 4 virtual losses should give slightly better results than waiting for 3 virtual losses, waiting for 5 virtual losses should be better than waiting for 4, etc, but we don't see this. The actual results conform to the "infinite horizon" model which I suggested.

Here's another way of looking at it. Many are familiar with the technique of betting the opposite of the last X decisions (in fact I think this is dobblesteen's primary system on the even chances). So the idea is that you bet the opposite of the last 10 outcomes, and (so the logic goes) this is preferable to betting randomly because it would be a rare event for the last 10 outcomes to repeat exactly in the next 10 spins.

It also seems sensible to bet on the opposite of a longer sequence rather than a shorter one; betting against the last two outcomes is better than betting against the last 1, betting against the last 3 is better than betting on the last 2, and so on. Although this technique doesn't need to wait for losses, it's still a virtual losses type system because you're in effect taking those previous outcomes as your imagined bet selection, which has just lost X times in a row, and so some losses have been "removed" from the outcomes, thus giving a better than average chance that subsequent outcomes will give a win (or so the thinking goes).

I don't have the inconvenience of having to wait for streaks of 10, 15, or 20 in a row and then betting against them to continue, I can just bet the opposite of the last 10, 15 or 20 outcomes. But why stop there? I should be able to make success even more certain by just betting the opposite of the last 30, 50 or even 100 spins. In that case, I've found a bet selection which has lost 100 bets in a row - surely success in the next spin or two is guaranteed, right?

Sadly, no. I've tested this and similar ideas and the results are no better than just betting randomly, or on red. And it turned up some losses the like of which I'd never seen, like 30 losses in a row.

And the reason why it doesn't work is that there are no limits to randomness. The illusion that there are comes from not understanding that our choice of bet selection is only one of an infinite number each of which is equally like, and so it seems that events tend to a limit. It's not that there actually is a limit, but there are limitations in confirming what the theory predicts. It's not that probability theory breaks down or becomes invalid after a certain point.