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[Slacker]

All combinations that are of same length are equally likely and they almost happen equally too.

That's not correct. All permutations are equally likely in a string of outcomes of fixed length.  So RRRRR is as likely as RBBRB, taking order into account. But RRRRR is not as likely as RBBRB ignoring the order and just looking at the number of R versus B. That's why a long run of one color is less likely than a run which contains a mixture of R/B.

A combination is not a permutation. Combinations don't take order into account, permutations do. So "all outcomes are equally rare" only applies to permutations, not combinations.

Probability of 0 reds in 5 spins = 3.1%
Probability of 1 red in 5 spins = 15.6%
Probability of 2 reds in 5 spins = 31.3 %
Probability of 3 reds in 5 spins = 31.3%
Probability of 4 reds in 5 spins = 15.6%
Probability of 5 reds in 5 spins = 3.1%

So where is the equality?

Take one sequence "at random", say RBRBB. Sequential probability says the chance of this arising is (1/2)⁵ = 3.1% but this is the same as the probability of 0 reds or 5 reds in 5 spins. What's going on? is there a contradiction?

Nope. It's just that in one case you're looking at outcomes in terms of order and the other case you're not. So the "mystery" is solved. The reason why you think a 100 reds in a row is possible is because you're looking at each possible sequence as a permutation.

And as for memory, try the following little thought experiment. Suppose you work in a roulette wheel factory and it's your job to test each wheel as it comes off the production line. You spin the wheel only once for each wheel and record the outcome, then do the same for the next wheel. Now, clearly these wheels, being brand-spanking new, have no "memory" of any past spins: your spin is the first. Do you still think it's possible to get 100 wheels each generating red in that one spin? if you do, you have to admit it can't have anything to do with past results, because none exist.

[Albalaha]

I got some good, some average and some great answers.  Let me simplify the answer of this query, in my own way to sum up.


Let's take a coin flipping game. I enter a game of coin flipping, not being aware that in past 15 flips they were all heads. Now, if I want to make one decision/ one bet, betting head or tail would be equally wise or unwise because both have 50-50% chance to appear in this flip but if I need to make 5 bets to get a net win, it will be wise to bet that a tail will come in next 5 trials,  considering both the sequential probability of 20 hits of heads in succession and 5 consecutive failures of tails(after you start betting). Getting 5 consecutive failures of Tails is 1/32 and getting 20 wins of heads is one in a million probability. Now, if someone loses here, he is an unlucky gambler who just saw a one in a million probability working against him.
           Say, I lost. Now, a guy looking at this, started a 10 step martingale that a tail will hit is next ten flips. Now, if we consider a sequential probability of 1 hit in 30 attempts of an EC bet, the last man doesn't only have a probability of 1 hit in 10 trials working for him but also 1 win in 30 trials sequential probability at run. If he loses his 10 bets, it would be an almost impossible 1 in a billion event but if he just tries to win in 1 single flip after even 20 losses, he is having only 50% chance to win then and there.


        Just to clarifying, I am not advocating playing after so many losses, because:
1. Say, if you decide to bet after 20 runs of an EC, against that, u may need to wait one million spins to get an opportunity to bet once
2. Every limit of consecutive win or lose of any bet is a virtual limit, we can't guarantee that there will be no 31st consecutive win of an EC or loss of an EC bet.


  To clarify further, I am not advocating playing Martingale either, in any form or condition because I consider it to be the most foolish approach to try to win the least (1 unit is the max we can earn) risking the max we can afford or that table allows.




We haven't seen 36 reds in a row ever or maybe we will never see this because it will be a once in many billions event.  Every single spin is free to deliver anything but if we talk of succession, it is a very part of a running sequence and has a virtual limit. I think 1 in a billion event can be safely presumed to be the virtual limit of the bet.

[esoito]

Seeing that Albalaha in his wisdom deleted posts and locked this thread, I've set  up a similar thread -- with the deleted posts restored -- so you can continue this interesting discussion.