"

Whoever created this doesn't understand what independent outcomes means.

If every gaming result were truly independent, then it would be possible for a roulette table to fail to produce the number 7 in twenty million consecutive spins, because there would be nothing to enforce that occurrence.

But in the real world, unless the world is biased, there is a 100% chance that won't happen.

... the only logical conclusion that can be drawn is that it is not possible for gaming results to be truly independent.

He said, "unless the wheel is biased". But even if the wheel is biased the outcomes will still conform to expectations, just a different expectation to what it would be if the wheel wasn't biased. It has nothing to do with outcomes being independent.

**dependent** outcomes means that past results

**affect** future results. If you record enough spins you can find the distribution of outcomes, but once you know that, whether or not you know the spin history doesn't help to predict future spins, and that's what independence means. In roulette past results aren't affecting future results even though you can find the distribution of outcomes from past results; how else could you find the distribution?

He's just playing with semantics and it doesn't change things in any practical way. If the fact that expectations do work out the way they're expected to then you can call those "non independent" outcomes if you like, but how does it help? It's not the same dependence that you get when playing blackjack, for instance.

If you stick to the statistical definition of independence you wouldn't make the mistake that he has.

Two events are independent if P(B) = P(B | A).

Logged

Whoever created this doesn't understand what independent outcomes means.

He said, "unless the wheel is biased". But even if the wheel is biased the outcomes will still conform to expectations, just a different expectation to what it would be if the wheel wasn't biased. It has nothing to do with outcomes being independent. **dependent** outcomes means that past results **affect** future results. If you record enough spins you can find the distribution of outcomes, but once you know that, whether or not you know the spin history doesn't help to predict future spins, and that's what independence means. In roulette past results aren't affecting future results even though you can find the distribution of outcomes from past results; how else could you find the distribution?

He's just playing with semantics and it doesn't change things in any practical way. If the fact that expectations do work out the way they're expected to then you can call those "non independent" outcomes if you like, but how does it help? It's not the same dependence that you get when playing blackjack, for instance.

If you stick to the statistical definition of independence you wouldn't make the mistake that he has.

Two events are independent if P(B) = P(B | A).

**How about fixing the programs which I've paid you for?**

Hey everyone, this person took payments by Paypal and sent me a program with technical issues and another which was NOT what I had melticusly instructed over and over again, it was just his understanding after ALL those DAYS of instructions, explanations and examples!

This person never even replied my emails when I've informed him that he has to fix those 2 programs!

Now, at this forum, pretends the honest and educated programmer, people be aware!!!

Logged

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