Gambler's Fallacy BUT...

[BellagioOwner]

Before we get started on a wrong basis. I would like to make clear that I know what Gambler's Fallacy states and I agree. I also agree that "wheel has no memory", each spin is independent and random and that 10 blacks in a row won't make red more likely to be hit next spin. Furthermore  progressions are all the same  susceptible and exposed to the same HE with just different amount staked every spin etc etc. They make sense and I agree.

BUT...  Imagine this scenario.

2 people are playing at the same table good old martingale. Table limits are very big. They can bet from 1$ to 2000$+ on EC. (It may be more convenient to imagine an online casino like BetVoyager that indeed allows such depth speaking about Units).

The one starts straight away and the other waits for any EC to repeat 12 times in a row. This scenario happens sometime and the guy started straight away busted 2000$ while the other guy had just started betting risking now his first 1$ Finally after a VERY RARE EVENT the streak stops after 20!!! in a row and the player that waited wins at spin 21 having risked 256 (and 511$ in total rounds) and made his 1$ back. With his strategy he survived 20 misses in a row. Yes I count and the ones he waited. Why? Because if he had started from spin 1 as the other player he would have been busted as well. So what would he have earned if he had started playing from spin 1? Since his plan was from the beginning to be able to survive 20 misses+ in a row the only thing he would have earned is risking a ton more money starting betting from spin 1

I'm not saying that his EC was more likely to be hit after the 12 misses in a row. What I'm saying is that he wasn't playing against the EC. He was playing against the odds and the rare event. With waiting 12 misses and 12 step progression he can survive 24 misses in a row! That happens 1 in 9,000,000 spins! 9 millions spins is huge. He will never in his lifetime play so many spins to see such an event.

YES! His bankroll would eventually bust but maybe in 18,000,000+ spins when an event of 25 misses COULD HAPPEN. Why should he care if his strategy is going to fail once in 18,000,000 spins when all he would play in his entire lifetime is not even 500,000 spins?

YES! He is not going to become Warren Buffett betting and winning in so rare conditions/triggers but he will probably never lose his bankroll either.

My conclusion? I believe there is no point saying that past spins are not affecting the future result in a statistical way.
If sometime we have reached a rare event that an EC strikes 20 in a row, I have much better chances to win in THESE spins if my strategy was to wait for 12 in a row and then bet than if it was to start betting right away.

It's not lucrative way of playing but surely it gives me a head start in runs from hell so how it is not affecting if I win or lose within a normal bankroll if I start betting after an already rare event? It won't go much more rare than this(for the length of spins that will ever witness. Not theoretical forever)

What do you guys think? Thinking in this way I think Gambler's Fallacy and betting after for example 10-12 in a row has a meaning and improves you odds of winning within a normal bankroll within the normal amount of spins you will ever play.

[ignatus]

Even the best triggers will lose sooner or later, (due to random), ie waiting for a trigger of 5-6 spins before starting to bet with a 10 step martingale "seems to be safe" (is not), you need a minimum of 1000u, (playing with 1u bets) and even with that you must be prepared to lose now and then, and problem is you must win more that 10 games in a row for each 1 loss (of 1000u to be in profit). But then you think OK! no problem i can win 10 games in a row! But what do you know? What if this extreme event happened on the 3rd game? Then you still be in loss, (nothing will say that you are guaranteed to win 10 games in a row!)....that's the problem...

[falkor2k15]

All those spins are independent... same probability for EC regardless of how many come in a row or not. The longer you wait is equivalent to how much you can win/lose. You could bet 20 units on the next spin and boost your BR to 40 - or you could wait for 20 reds in a row and only win 1 unit then wait years for the next rare event only to win another 1 unit. By the time you won 20 units you might still be alive to witness 30 reds in a row and then lose everything over a longer period that you could have lost in the same, equivalent, short term.

So the first thing you need to look for is dependency...
131... = 2 dozens in 3 spins = more chance for this combination (U2) to repeat. The repeat is dependent on what uniques come before it. That's the first step.

[BellagioOwner]

you might still be alive to witness 30 reds in a row

I understand what you mean but 30 reds in a row is once in 482 million spins. I doubt that I will see it in my lifetime (in a non-rigged wheel or fair RNG) That was my point. Some rare events that will bust you are TOO RARE to count them in real life scenarios

[falkor2k15]

Meaning you won't win any profit playing for rare events other than enough for a bowl of soup that won't sustain enough energy to supply your games anyway...

[BellagioOwner]

Did you read my initial post? Yes. i said it myself. That such approach and play won't be lucrative. Maybe a bot could capitalize it to wait for 2000-3000 spins before any bet. But still my argument stands. Some rare events are indeed too rare to be considered as a loss irl. Gambler's Fallacy is true in real life scenarios but not in general as in theory. You will never see 50 or 100 or 150 blacks in a row even if you wait universe to freeze

I have a much better example to post but I will do tomorrow after work. It's late now here 

[falkor2k15]

the more millions or billions of spins you do the more and more rare events you will see. Most rare events that you are talking about you won't see in our lifetime anyway. You need to understand how it's equivalent/comparable: the longer you wait the less profit you can make only to eventually lose it all and only ever handle a couple of units through your entire life; or play quicker and win bigger or lose bigger. At the end of the day it's 2.x% for the house - unless you can bring enough concepts together to overcome it.

[BellagioOwner]

Let me give a MUCH more interesting example. Based on a trend topic I saw here couple days ago. The chance of not hitting 8 numbers. I have reached 6 million spins and the highest so far not to hit 8 numbers is 68 spins.

Let's say now that a guy keeps playing the numbers 2, 6, 14, 15, 23, 28, 32, 36. He keeps on betting them and keeps on missing all of them until he finally gets a hit at spin 68. (already a rare enough event based on what I first talked about)
Next to him another guy keeps tracking the numbers that come until there are left 8 numbers that has not been hit. After tracking 62 spins there are finally the last 8 numbers not being hit which as it turns out there are indeed the 2, 6, 14, 15, 23, 28, 32, 36. So now he starts betting them and after just 8 spins on spin 68 he also got the hit.

What benefit would the 2nd guy had if he had started betting right from spin 1? He got on board an already rare event at spin 62. Ηis progression was good enough to keep him going for 20+ spins. He started at spin 62 and he could go until spin 82. What are the chances that he would keep missing them for all 82? Once in some billions? (since we already explored that 68 missed times is already once in 5 millions)

The point? Why bet any numbers from start that could have turned out to be the very last to be hit? Why not use the already 62 spins passed and then start betting these last 8? He already has a 62 spins head start starting betting now. You mean the chance to be finally hit until spin 68 is the same as to be finally hit in spin 82? I don;t think so. I'm not speaking for individual spin by spin. In this example we speak about the same numbers form start to finish so you jump into the event. The odds are already behind it.

I doubt to believe that after 62 missed spins there is still the same chance for these 8 numbers to reach 68 more misses because I just started now betting on them and past doesn't count (a total of 130 misses!!)

[ozon]

Only theoretically, in william hill we have about 10 Roulett tables, if the wait for the same 14 EC and start betting 8 step marty we have chance win.
A long time ago I saw a simulation of 10 million spins, and the highest number was 22, other EC was 18-19.
My theory is that it is followed delicate mitigation of probability, if that was different, line of 20 repetitions was by breaking down very smoothly.
Virtual limits are higher than 22, but if we got time and patience, we can try to play this way.

[GarciasMuffin]

Hi BellagioOwner,

Firstly, I have the same way of thinking about Roulette as you. I don't care that in a million spins this or that scenario will happen. I only care about what is likely/unlikely to happen within the lifetime that I play in and what I see with my own eyes happening in the real world on a table, regardless of maths.

In a theoretical casino with infinite table limits (or even just huge table limits), Bill Gates would walk into the casino using a Martingale progression and wipe them out. I also agree that if he was simply betting on for example, red to come in at some point, even if he spent 24 hours a day for a year at one table he would never have to get anywhere near the 50th spin to win his progression. It is possible obviously as all things are but a) we never see it happen in our real betting lifes b) You'd then have to factor what the chances would be of him sitting at the one table from all the tables on earth that suddenly produces this world record event. So yes, in real life it's not going to happen regardless of maths/theory or whatever, the casino would end up closing down.

However, I believe I can explain why what you are thinking is not true or workable from how we will bet in our lives, without the need for maths.

The critical bit of the following explanation is the 'each spin is independent' rule which fortunately you have already acknowledged and understood, which makes this all a lot easier

Giving an example like yours, let's say players A and B have decided to bet on red with a Martingale that for ease of example can only be sustained for 5 progressions. As you've said, player A busts early but player B only starts betting after he sees 25 blacks as he's never ever seen 30 blacks in a row reached in all the time he's played in his life. Now the mind of humans naturally think 'well, considering I know its highly unlikely 30 blacks in a row will hit he must stand a better chance of winning in the next 5 spins than the guy who started at spin 1'. However, this isn't true. As we have already acknowledged (correctly) that all spins are independent what player B is actually betting on is the chances of a red coming in within the next 5 spins that his bankroll can last for, exactly as player A had done in the very beginning and his chances of winning are exactly the same as player A's were.

To think of it another way that might make some sense, the table has already completed the incredibly hard and highly unlikely work of spinning black 25 times in a row at the point player B starts to bet and now only has left the relatively common and easily achievable task of spinning just 5 blacks on the bounce to accomplish the incredible feat of 30 blacks in a row and wiping out player B, which you can acknowledge you see all the time.

Yes, absolutely, the table will eventually spin red as happens in real life, but it's no more likely in the next 5 spins as the very first 5 because of that independence of spin.

The casinos deliberately set the table limits so as to only need common amounts of repetitive results to wipe out a Martingale or bring your progression to the table limit quickly (the cheating bastards

I hope this makes some kind of sense