john.kuhn
john.kuhn
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September 17th, 2020 at 2:33:48 PM permalink
Greetings,

My question is more a theory about gambling, specifically roulette, and the make things easier let's remove the greens from the equation, so just for this thought we'll say the wheel only has two options, black, and red.

Each individual spin has the same statistical chance to land on red or black, 50\50, right?

Gambler's fallacy tells us that some individuals fall prey to the belief that "past observations impact future outcomes"
Example, if you see the wheel spin twice black in a row, you may think the chances it spins red next time is increased, however it remains the same, 50\50 every single spin.
/wiki/Gambler%27s_fallacy

The Martingale System of betting, is where you double your bet each loss, so that when you finally "hit" you win back all previous losses + 1 betting unit.
/wiki/Martingale_(probability_theory)

I say all of this to ask, if you had a magical time machine, that could teleport you to ANY casino across the world, specifically to any roulette wheel, and allow you to place a bet, however the door to the time machine ONLY unlocked after there had been either 10+ reds in a row, or 10+ blacks in a row, and you would be betting on ONLY the 11th+ spin and onward, at these casinos.

Do you think you would find that your win rate would budge at all from the 50% W\L rate if you're ONLY making bets after an "anomaly" of 10+ red\black spins in a row have occured?

I know the odds are always 50\50, I get that, however if you spin the wheel 1,000,000,000 times, or whatever it may be, there should be some level of "error" however there has to be limits? Things should generally speaking, within some level of error, be "about 50\50, right?

Things should regress to the mean over time shouldn't they? IF we spin the wheel and it somehow lands on red 50+ times in a row, we KNOW that it will be black at some point, because 50% of the wheel is black, so aren't we moving closer and closer, on the "timeline" towards a guaranteed black spin? making it theoretically "more likely"?

In our betting scenario where we are ONLY betting after 10+ red or blacks in a row, aren't we being opportunistic, to the spins "regressing" to the mean, because we know that it must return back to the rough average at some point? we know that it is IMPOSSIBLE for the streak to continue, it MUST be broken, and therefore we are getting closer and closer to our win each spin.

Am I way off base here?

Thanks for any contribution!
ThatDonGuy
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onenickelmiracle
September 17th, 2020 at 2:46:44 PM permalink
You have to take into account two things.

First, "eventually" can take a very, VERY long time.

Second, as you continue to lose with a Martingale, the amount of money you have to bet increases dramatically. If you lose 15 in a row, the 16th bet is 32,768 times what your first bet was. Did you remember to bring that much money? Have you exceeded the table maximum bet yet?

I like to joke that I have a guaranteed can't-miss sure-fire 100% system:
1. Come up with a maximum number of consecutive spins for a particular result - for example, "red won't come up more than 25 times in a row."
2. Wait for the result to happen that many times consecutively.
3. Bet against it.
4. If you lose, don't blame me; you're the one that claimed that (in this case) red won't come up 26 times in a row.
gamerfreak
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Mission146
September 17th, 2020 at 2:54:35 PM permalink
This is actually a pretty good question, and I think itís at the heart of why the gamblers fallacy is so prevalent and hard for people to get over mentally.

I am going to quote Wikipedia because they explained it perfectly, and I will only make it worse by trying to use my own words.

Quote:

Regression toward the mean simply says that, following an extreme random event, the next random event is likely to be less extreme. In no sense does the future event "compensate for" or "even out" the previous event, though this is assumed in the gambler's fallacy (and the variant law of averages). Similarly, the law of large numbers states that in the long term, the average will tend towards the expected value, but makes no statement about individual trials. For example, following a run of 10 heads on a flip of a fair coin (a rare, extreme event), regression to the mean states that the next run of heads will likely be less than 10, while the law of large numbers states that in the long term, this event will likely average out, and the average fraction of heads will tend to 1/2. By contrast, the gambler's fallacy incorrectly assumes that the coin is now "due" for a run of tails to balance out.



Here is an exercise using your Roulette example....which of these two sequences of Roulette Spins are more likely?
RRRRRRRRRR
RBRRBBBRRB
john.kuhn
john.kuhn
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September 17th, 2020 at 3:07:55 PM permalink
Quote: gamerfreak

This is actually a pretty good question, and I think itís at the heart of why the gamblers fallacy is so prevalent and hard for people to get over mentally.

I am going to quote Wikipedia because they explained it perfectly, and I will only make it worse by trying to use my own words.

Quote:

Regression toward the mean simply says that, following an extreme random event, the next random event is likely to be less extreme. In no sense does the future event "compensate for" or "even out" the previous event, though this is assumed in the gambler's fallacy (and the variant law of averages). Similarly, the law of large numbers states that in the long term, the average will tend towards the expected value, but makes no statement about individual trials. For example, following a run of 10 heads on a flip of a fair coin (a rare, extreme event), regression to the mean states that the next run of heads will likely be less than 10, while the law of large numbers states that in the long term, this event will likely average out, and the average fraction of heads will tend to 1/2. By contrast, the gambler's fallacy incorrectly assumes that the coin is now "due" for a run of tails to balance out.



Here is an exercise using your Roulette example....which of these two sequences of Roulette Spins are more likely?
RRRRRRRRRR
RBRRBBBRRB



They seem to contradict one another.
"the next random event is likely to be less extreme" - doesn't that mean exactly what i'm saying, and by "less extreme" in this case translates to things will be "closer to a 50\50 outcome moving forward" and "regress"?
RRRRRRRRRRR vs RBRRBBBRRB are exactly the same odds of occurring aren't they?

It's not RRRRRRRRR vs RBRRBBBRRB though, it's RRRRRRRRRRR vs alllll the other outcomes in the future 10+ follow up spins afterwards that may provide a slight edge when betting on black moving forward. Even if it's 1 singular more B spin out of the next 100, in the scenario I've laid out with no green spots, that would make you a winner
gamerfreak
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Mission146
September 17th, 2020 at 4:31:10 PM permalink
Quote: john.kuhn

"the next random event is likely to be less extreme" - doesn't that mean exactly what i'm saying, and by "less extreme" in this case translates to things will be "closer to a 50\50 outcome moving forward" and "regress"?


Yes, but knowing that the results of the wheel will eventually average out is not actionable gambling information.

Think of it in terms of BJ card counting.

Counting only works because the deck is finite. When a card is removed, the probability of the next card being a certain value changes. If the deck is shuffled, the cards that were previously drawn are meaningless.

Trying to make conjectures about the future based on previous spins is analogous to trying to count from an infinite deck or reshuffled deck.
OnceDear
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odiousgambitMission146
September 17th, 2020 at 5:32:52 PM permalink
Quote: john.kuhn

Things should regress to the mean over time shouldn't they?

NO NO NO NO. Why the hell should it?
The ratio of red/black will tend towards 50:50. that is true. But that is totally regardless of the fact that if Red is x spins greater than black, there will ABSOLUTELY NOT be any reason to trend to numerical parity.

Eg. let's say if the wheel has spun 100xred and 50xblack since it was created
red/total = 100/150 = 66.7% and black/total = 50/150 = 33.3% Disparity = 100-50=50
let's watch another 200 spins and we get 100 red and 100 black ( ain;t coincidence grand)
red/total=200/350 = 0.5714% and black/total =150/350 = 42.86% Disparity still = 50

So we already see that proportion tends towards 50% (66.7 and 57.14 is converging towards 50% and so is 33.33 and 42.86 )
without any move in numerical disparity.

Let's say we now observe 110 red and 90 Black
Red/total=310/550 = 56.36% Black/total=240/550 = 43.64% Disparity now 60

We have still tended towards 50% red ( we were at 57.14 last time we looked), but dammit, the numerical disparity has increased at the same time!!!

Time machines or whatever makes no odds. the NEXT spin after any event or sequence of events has 50% probability either way.

Quote: john.kuhn


I know the odds are always 50\50, I get that, however if you spin the wheel 1,000,000,000 times, or whatever it may be, there should be some level of "error" however there has to be limits? Things should generally speaking, within some level of error, be "about 50\50, right?

OK. take a wheel that has only spun once since it was created. It came up red,
It had 50% chance of coming up red and 50% chance of coming up black, but dammit, it was red. That's 100% red and 0% black. Each is 50% away from where it should be. But if it had come up black, they would still both be exactly 50% away. In fact after only one spin, the nearest that red can be to 50% is either 0 or 100% and the minimum is an error of 50%... so is the maximum. and at that point, the max numerical disparity is the same as the mini disparity of 1-0 or 0-1 is 1

After a lot more spins, the max numerical disparity can only increase and the percentage disparity can only decrease. Reconcile that!
Last edited by: OnceDear on Sep 17, 2020
Take care out there. Spare a thought for the newly poor who were happy in their world just a few days ago, but whose whole way of life just collapsed..
john.kuhn
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OnceDear
September 17th, 2020 at 6:14:22 PM permalink
This explanation is amazing, and this is exactly what I was hoping to get by posting here!

Thank you so much!
redietz
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OnceDearMission146
September 17th, 2020 at 9:08:43 PM permalink
That was a top notch and very understandable explanation.
"You can't breathe dead hippo waking, sleeping, and eating, and at the same time keep your precarious grip on existence."
Mission146
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rawtuff
September 18th, 2020 at 4:55:49 AM permalink
Great answers by both OnceDear and GamerFreak!

I also want to expand on GamerFreak's answer to the extent that probability is something that always comes into play, not just when something, "Weird," happens. For example, let's take a look at video poker (or any game with a starting five card hand) and look at a specific deal. I'll use the VP game here on the site and just tell you my exact cards:

Qs, 3h, 7s, 7c, 2d

Obviously, the hand is quite unremarkable. However, the probability of getting this specific hand (ignoring order) is:

nCr (52,5) = 1 in 2,598,960, which is just the number of possible starting hands.

On the other hand, a dealt royal:

1/(20/52 * 4/51 * 3/50 * 2/49 * 1/48) = 1 in 649,740

But, imagine you're a video poker player who is skilled enough to play quickly...If you caught the first hand listed twice in a row, you'd probably never notice...and even if you did, you might just shrug it off. If you caught two dealt royals (could be different suits) in a row, you'd have a remarkable story. Both would be remarkable, but getting the first hand listed twice in a row would be more remarkable...unless the dealt royal was the same suit, then it would be equally remarkable.

Anyway, that's just the nature of how our minds work. Our brains look for patterns and then think that these patterns lend themselves to predictability, which of course, is often the case in the natural world...but probability doesn't care about any of that, except in the extreme long-run.

We also have the problem of Confirmation Bias such that we come up with a hypothesis and then (semi-consciously) set about wanting that hypothesis to be confirmed...which satisfies the ego. Slot players do that all of the time with their different (not advantage players) weird theories about what a slot is, "Supposed to do," given a particular circumstance or series of spins.

It's been reported that the longest Roulette streak of all time saw Red hitting 32 consecutive times back in 1943, followed by Black at least once. Since you're giving me a time machine, I'm going to go there after the first ten Red results, bet Red 22 times, then bet black once and leave. Perhaps some of the bills I'll get paid when I cash out will be collection worthy and be more valuable when I take our time machine back than they were when I won!
Vultures can't be choosers.
OnceDear
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Mission146
September 18th, 2020 at 7:09:34 AM permalink
Quote: Mission146

Since you're giving me a time machine, I'm going to go there after the first ten Red results, bet Red 22 times, then bet black once and leave. Perhaps some of the bills I'll get paid when I cash out will be collection worthy and be more valuable when I take our time machine back than they were when I won!

He didn't give me a time machine, but you gave me an idea.... So, I looked in my bank account and there was 10 Billion dollars there. I knew straight away that I needed to invest 5 Billion in my time machine. It was finally built 100 years from now and I arranged to get it delivered today. I took it for a run, back to that remarkable event and placed many huge wagers. I arranged to have my winnings paid into my future bank account, and that's how I came to have that 10 Billion.
While flirting through time, I went and strangled that megalomaniac Henry Bobbins at birth, so he never went on to destroy half the civilised world. I'm the only one who remembers him doing it.
Spent a while following Alan M, and watched some guy throw four Yo's in a row. I didn't place any wagers on that and didn't stick around to see what happened.
Did a few short trips back and forth, playing Baccarat and bought a top of the range Casio with the winnings. It's the 2135 teleporter model in weightless Tanzanite and mock stainless steel case.
I can report that 2020 turns out to be a bad year, so I'll be skipping the rest of it.
$:o)
Take care out there. Spare a thought for the newly poor who were happy in their world just a few days ago, but whose whole way of life just collapsed..

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