How pathetic that the math community believe this! So, the math community unequivocally state the percentages that will eventually occur in each game, for the house, and the gambler.

But how can this be true, due to the Gambler's Falacy???? Another paradox!!!!

How can math say on one hand, you cannot give predictions re chances, but on the other hand predict future chances down to percentage points? Is the math community moronic???

Your post reveals more about your own inability to comprehend probability theory than about 'the maths community'.Quote:WellbushThe Gambler's Falacy states that every fair play in a game of chance, is independent, and has no better or worse chance based on past play.

How pathetic that the math community believe this! So, the math community unequivocally state the percentages that will eventually occur in each game, for the house, and the gambler.

But how can this be true, due to the Gambler's Falacy???? Another paradox!!!!

How can math say on one hand, you cannot give predictions re chances, but on the other hand predict future chances down to percentage points? Is the math community moronic???

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Since this forum represents a decent swathe of 'the maths community' especially of those who gave their time to politely educate you, I'll take your post as yet another insulting attempt to troll the forum. Penalty to be decided.

Who knows what I was betting, but the numbers are 6 figures.

Quote:ChumpChangeIf I could cash-in my comps, I'd be ahead after nearly 3,000 rolls of the dice. But the data says I've lost 666 bets, but I'm only down $897 or -0.33%.

Who knows what I was betting, but the numbers are 6 figures.

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Yet another complete Thread Hijack from ChumChange. I invite him to explain himself. Is it a cognitive inability to post in the correct or new thread?

Thanks CCQuote:ChumpChangeI was busy replying to Wellbush and hadn't noticed you hijacked the thread by suspending him before I hit Send. I was just trying to give Wellbush a taste of statistics that he so rails against. I'm not sure he didn't change the thread title while I was replying either. My PM service went down and it refused to let me check the "I'm not a robot box". Could just be a sporadic internet glitch..

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Explanation appreciated and accepted.

It was not clear to me that you were trying to give him a stats example. I doubt it would be clear to him.

With wellbush, such subtlety needs a lot more explicit explanation.

Quote:unJonThis thread is amazing in all ways.

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𝐓𝐇𝐄 𝐅𝐀𝐋𝐋𝐀𝐂𝐘 𝐃𝐄𝐍𝐈𝐄𝐑𝐒 𝐌𝐀𝐍𝐓𝐑𝐀

for the love of:

martingales and all its variations (reverses, Laboucheres, D'Alemberts, Oscar's Grinds)

betting streaks

stop losses and stop wins

hit and runs

leave cold tables - look for hot tables

𝙖𝙣𝙙 𝙞𝙩'𝙨 𝙧𝙚𝙖𝙡𝙡𝙮 𝙩𝙧𝙪𝙚

there are thousands, maybe millions in LV and elsewhere who've gotten rich from these techniques________they've made 𝑴𝑰𝑳𝑳𝑰𝑶𝑵𝑺

for people who are very, very shrewd like the Fallacy Deniers___________𝑨𝑵𝒀 𝑪𝑨𝑺𝑰𝑵𝑶 𝑨𝑵𝒀𝑾𝑯𝑬𝑹𝑬 𝑰𝑺 𝑳𝑰𝑻𝑬𝑹𝑨𝑳𝑳𝒀 𝑨 𝑮𝑶𝑳𝑫 𝑴𝑰𝑵𝑬

.

.

Quote:WellbushThe Gambler's Falacy states that every fair play in a game of chance, is independent, and has no better or worse chance based on past play.

How pathetic that the math community believe this! So, the math community unequivocally state the percentages that will eventually occur in each game, for the house, and the gambler.

But how can this be true, due to the Gambler's Falacy???? Another paradox!!!!

How can math say on one hand, you cannot give predictions re chances, but on the other hand predict future chances down to percentage points? Is the math community moronic???

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I guess someone should give this an answer---just in case someone is actually interested in this question:

https://en.wikipedia.org/wiki/Regression_toward_the_mean

Okay, so let's give a quick example of Regression Towards the Mean:

Imagine if a Craps Player is betting the Pass Line and it's the first time in his entire life he has ever done so---that person wins (49.29% probability), so now that person has won 100% of his Pass Line bets.

Probability says that event has already happened and that the next attempt is independent and comes with probabilities 49.29% and 50.71%, winning and losing, respectively.

Imagine that our fortunate first-time player wins his next five bets in a row, so he now has six consecutive Pass Line winners: (.4929)^6 = 0.01434012407

Thus, he has experienced an event with 1.434% probability, but it is 100% since it has already happened.

For the next trial, his probability of winning remains 49.29%, which nobody disputes.

However, let's suppose that he loses just that one attempt, so he goes from:

Win 6, Lose 0---Win 100%, Lose 0%

TO:

Win 6, Lose 1---Win 85.7143% (Rounded) Lose 14.2857% (Rounded)

Critically, his winning percentage can never be 100% again, which is a short-run example of how Regression Towards the Mean works in the long run. In other words, the Gambler's Fallacy is relatively focused on the notion that a short-run phenomenon (usually many consecutive losses) will not happen based on the fallacious position that, after a particular series of losing results---the next result(s) to be losing becomes less probable.

Regression Towards the Mean, on the other hand, describes what happens in the long run. Simulations bear this out, but more importantly, relatively long-term real world results will also bear this out. You can win 80% of your total bets on the Pass Line at Craps, for example, but not for particularly long.

Regression Towards the Mean also does not mean that there will be a series of six losing results in a row to offset the six winning results that happened before. However, in a long-term series of results...long winning AND losing streaks will not be uncommon.

Let's imagine that after our first-time Craps players' first loss the results go W-L for the next ten results, which makes him:

Win 11, Lose 6---Win 64.7059% (Rounded) Lose 35.2941% (Rounded)

Despite the fact that the player opened up with six consecutive wins and has never lost more than once consecutively, we see that his winning percentage is now down from 100% to 64.7059%.

I'm obviously cherry-picking short-term results here to try to do a short-term illustration of a long-term concept. The point is that every loss (when the actual winning percentage is more than 50%) will have a greater impact on the overall percentage than every win. Let's take our 11-6 and see what happens to the winning percentage if the next is a win and if the next is a loss:

Win (12-6): 66.6667% (Rounded)

Difference: 66.667-64.7059 = 1.9611%

Loss: (11-7) 61.1111% (Rounded)

Difference: 64.7059 - 61.1111 = 3.5948%

As you can see, Regression Towards the Mean doesn't require that a long run of winning results is offset by a long run of losing results---though you would expect to see long runs of both in a large sample anyway. Regression Towards the Mean relies on two components:

1.) In a large sample size, any long runs of results are mostly going to be offset by running relatively as expected for a very long time.

AND:

2.) If a result is coming up either more, or less, than expected---then the result that is not yet running, "As Expected," will be moved more towards the mean for every time it DOES happen than it is moved away from the mean if it fails to happen again.

Another example is that of a Video Poker player who has never had a Royal Flush in his first 60,000 hands, which means he has run more than one, "Royal cycle," without getting it. He currently has 0.000000% Royal Flushes, but as soon as he gets one, then he is above 0.000000% and can never be at 0% again just by virtue of that one Royal Flush.

The Royal Flush will also pull his overall return percentage up on the game as significantly as any hand could, or more, with only a few exceptions such as Four Deuces with a Joker on DJW (somewhat rare game) which actually pays more than a natural Royal.

Specifically, it will pull it up by 800x the bet, assuming full coins, so let's imagine that he has played 60,000 hands at an overall return of 96.9% before that Royal:

Credits Played: 300,000 Credits Won: 300,000 * .969 = 290,700

Okay, so let's imagine that he hits the Royal Flush and also what would have happened if the hand had paid nothing instead:

Credits Played: 300,005, Credits Won: 294,700---Actual Return Percentage: 98.232% (Rounded)

NO ROYAL---LOSING HAND:

Credits Played: 300,005, Credits Won: 290,700---Actual Return Percentage: 96.8984% (Rounded)

What you will notice here is that, as anyone would expect, the Royal has a much more profound impact on the player's overall return percentage than does having a losing hand, which barely moves the percentage. Another thing that you will notice (pretend it's JoB or Bonus Poker) is that a 10 credit return on Two Pair:

Credits Played: 300,005, Credits Won: 290,705---Actual Return Percentage: 96.9017% (Rounded)

Has a slightly more pronounced impact on the overall return percentage (simply because 0% is closer to 96.9% than 200% is) which we also expect to work itself out in the long-run.

Video Poker has more variance than Pass Line bets on Craps, so you might need a more significant sample size of hands to see Regression Towards the Mean fully play itself out. A player could be running a couple Royals, "To the good," or, "To the bad," and resulting, could run well below (relatively speaking) or well-above, the Expected Return of the game for a very long time.

So, no, the math community is not moronic. The simple answer to this one is that the Gambler's Fallacy (particularly as relates negative expectation betting) is only concerned with short-term results (at least, in a given trial---perhaps some system players have trouble thinking long-term?) and the, "Math Community," primarily as it relates to concepts such as, "Regression Towards the Mean," is more concerned with the long-term.

Anyway, this has been a much longer answer than your post deserves, but there are many posters and readers here that do deserve an explanation of the difference, so there it is.

AND---It's for that reason that I defended something, such as the 18 YO's claim, as being theoretically possible. Do I think it happened exactly that way---probably not. If you're going to rely on the math, then it's very important to remain consistent---so nobody should say such a result is impossible. It has a non-zero probability, though not much above zero, but any specific string of 18 results has a very close to zero probability of occurrence (by virtue of the fact that so many combinations of events are possible), but the dice must do something.

In fact, the most likely string of 18 dice rolls, which is to say the highest single probability, is 18 sevens in a row:

(1/6)^18 = 9.8464004e-15

Which is to say 0.0000000000000098464004 or 1/0.0000000000000098464004 = 1 in 101,559,960,000,000

Virtually impossible, but technically the most likely specific sequence of 18 rolls of fair dice. If you go to a Craps Table and observe a series of eighteen rolls, then that specific series was (unless all 7's) less likely than the 1 in 101.56 TRILLION chance of them all being sevens.

Of course, if I come to the Forum and report that I observed a Craps Table with the following sequence:

7-7-5-2-3-9-5-7-11-12-3-7-8-4-4-5-9-7

Nobody would bat an eye, despite that specific series being substantially (well, relatively speaking) less likely than all 7's.

Conclusion

The, "Math Community," simply understands how numbers relate to each other and many betting system believers (and I am not saying you specifically) do not fully comprehend it. The math community's belief in a long-term concept does not debunk the math community's opinion of why gambling systems can fail in the short-term and would fail in the long-term on a negative expectation game.

The concept of a long streak does not change the concept of Regression to the Mean.

Why not?

Going back to the Craps Table----let's take into consideration every Pass Line bet that has been made in all of history; I can't even estimate how many that might be: How much do you think a string of 30 consecutive Pass Line losses would change the overall winning percentage of all Pass Line bettors in history?

Answer: It wouldn't even be enough to qualify as a rounding error.

The probability of rolling an 11 on any individual trial certainly does not change; nor the probability of winning a Pass Line bet on any one trial.

Quote:Mission146I guess someone should give this an answer---just in case someone is actually interested in this question:

...

I'm obviously cherry-picking short-term results here to try to do a short-term illustration of a long-term concept. The point is that every loss (when the actual winning percentage is more than 50%) will have a greater impact on the overall percentage than every win. Let's take our 11-6 and see what happens to the winning percentage if the next is a win and if the next is a loss:

...

As you can see, Regression Towards the Mean doesn't require that a long run of winning results is offset by a long run of losing results---though you would expect to see long runs of both in a large sample anyway. Regression Towards the Mean relies on two components:

...

So, no, the math community is not moronic. The simple answer to this one is that the Gambler's Fallacy (particularly as relates negative expectation betting) is only concerned with short-term results (at least, in a given trial---perhaps some system players have trouble thinking long-term?) and the, "Math Community," primarily as it relates to concepts such as, "Regression Towards the Mean," is more concerned with the long-term.

Anyway, this has been a much longer answer than your post deserves, but there are many posters and readers here that do deserve an explanation of the difference, so there it is.

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Thanks Mission.

I fear that your answer brought in too many opportunities for WellBush or others to choose to not understand.

Craps and VP stats also complicated things. My zod. you used lots of numbers and maths and dragged in the concept of regression to the mean. A noble effort wasted.

If Wellbush want's to say that he has debunked the Gamblers Fallacy, that he's debunked everything you ever posted, or that he derides that none of the maths community can debunk his paradoxes, then he's going to do so indefinitely. And 'The maths community' will bang their heads against the wall, getting nowhere.

He's already asserted that we are all unable to debunk his so called paradox. He can and will assert any old nonsense. I think it's time he found a new audience of his peers.