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Suppose Boss Media provides completelly fair software (which I doubt that too). Are you saying that none of the casinos using Boss Media sotware, are cheating, because they are under the full supervision of Boss Media? Or because it is impossible to add a program on the initial program of Boss Media?
I am not implying anything, I am just asking.
I expect that games are similar between different casinos using the software, and it would be difficult to add a program on top of the software that would modify game decisions. I've never heard of a case in which a software was unfair at one casino, but fair elsewhere.
The Casinos using Boss Media aren't even able to cheat, because they don't buy the software and host it (IMO the real RNG isn't even implemented in the Boss Media Software).
All random numbers (for every casino customer) are created on Boss Media's server and after the outcome has been determined the data is sent to the casino client software...
Achievements:
Sure, rogue providers exist, and I believe this is referencing Casino1x2, although I'm not positive. Other examples were the software provider for Lucky Trump and Luck N Roll. That does not mean that longtime, RNG-certified, fair payout report-getting software providers like Boss, RTG, Microgaming, Playtech, Chartwell, etc etc are rigged. Quite frankly, if they were, they would not make it very far in an industry that only exists because of the copious amount of oversight of fair play.
Achievements:
Risk of ruin calculations incorporate house edge, which is only accurate when you play perfect strategy, which you've already admitted, you don't.
Your calculations therefore, are irrelevant, barring recalculating ROR to incorporate the increased edge of your incorrect play.
Suppose a player plays 5000 hands in blackjack, and places 1$ on each hand.
What is the average lowest point a player's bankroll will reach, during the course of these 5000 hands?
Or, in other words, what is the average greatest loss a player will meet during a course of 5000 hands?
(this could be, e.g. -100$)
Suppose that the bankroll is infinite.
(I am not talking about the average loss at the end of the 5000 hands)
I want the whole procedure which gives the result.
Do you know any math-blackjack forums I can ask this?
I mean that after the end of the 5000 hands, one might end up having lost -40$, but the greatest loss he met during these 5000 hands, was at the hand No 3524, where he was losing -150$. That's what I mean by lowest point of his bankroll during the play of the 5000 hands. So what is the average value for the lowest point? This does not refer to a loss AFTER the 5000 hands are completed. This loss corresponds to the -40$.
Always flatbetting 1$, basic strategy, reshuffle after every hand.
Player 1, ends up with a balance of -40$ after 5000 hands.
But the lowest point his balance reached, was -150$ at hand No 3524
Player 2, ends up with a balance of -15$ after 5000 hands.
But the lowest point his balance reached, was -70$ at hand No 2026
Player 3, ends up with a balance of +17$ after 5000 hands.
But the lowest point his balance reached, was -65$ at hand No 3730
... and so on. So when the number of players-samples tends to infinity, the values of the ending balances tend to an average value, and the values of these lowest points tend to another average value.
So how can we find the average value for this lowest point?
I am NOT asking how probable it is for the ending balance (after the completion of the 5000 hands) to deviate that much or that much from the average value of the ending balance.
I think these are two different things.
My problem has the condition that 5000 hands must be completed.
Achievements:
Based on your unpredictable strategies as opposed to optimal play, it would be impossible to speculate.
It is also impossible based on your calculations because there is no theoretical limit to a potential loss. Mathematically, it is possible to lose all 5,000 hands although hugely improbable. A more accurate way of looking at hands would be to look at the probability that a specific event occurs and what the standard deviation is:
Buttttttt..........
For the sake of argument:
Assume house edge of blackjack game is ~.5%:
A win/loss of about 60 bets would fall within 1 standard deviation (roughly 68% of all betting sessions would fall under 1 standard deviation of win/loss).
A win/loss of about 135 bets would fall within 2 standard deviations (roughly 95% of all betting sessions would fall under 2 standard deviations of win/loss).
A win/loss of about 220 bets would fall within 3 standard deviations (roughly 99.7% of all betting sessions would fall under 3 deviations of win/loss).
A win/loss of about 400 bets would fall within 4 standard deviations (the chance of something falling outside of four deviations is so improbable it would almost certainly suggest something other than bad luck).
As a general rule of thumb, I'd consider any result within three deviations of expectation to be a reasonable result for a gambling session.
Again though, this only applies to perfect strategy being played, which you've already admitted you do not adhere to.
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