House Edge vs. Luck - the Last Stand

[deisik]

It is not a secret that the longer you gamble, the less impact luck will have on the net outcome of your bets in games of chance. On the other hand, the house edge is what makes you lose in the long run by and large. Thus we have two forces which are fighting with each other -- the force representing randomness in the form of luck, and the force representing determinacy in the form of house edge

So how are they going to score against each other in the games of chance such as dice? Read on and find out

As said above, the house edge is set to win the longer you roll (read, you are going to lose). But this abstract knowledge doesn't tell us anything when exactly the house edge is going to dominate luck, i.e. how many rolls we will have to make until luck and its impact become insignificant and can thus be safely discarded for almost all practical intents and purposes. This is what I tested for myself and share with my fellow gamblers in this topic

At first, I ran a series of 10k rolls to see if this was enough for the house edge to beat luck. The short answer is no, as the snapshot below proves (with 9995 rolls):



After making so many rolls, I was still in profit. What does it tell us? Basically, that the impact of chance is still important at 10k bets with the given house edge (1%). Below is the table of all 10k tests that I ran:

Result	Snapshot link
+0.00000042	link
+0.00000098	link
-0.00000142	link
-0.00000122	link

However, with 100k rolls, the house edge leaves no chance to chance (pardon the pun):

Result	Snapshot link
-0.00000846	link
-0.00000867	link
-0.00001115	link
-0.00001386	link

And here's the last test with 200k rolls:



As you can see, the house edge becomes overwhelming, and there is no reason to believe that it won't be even more devastating as the number of bets increases further

So the conclusion is that the house edge turns into a dominating force somewhere after 10k, while luck stops being a factor right there. It doesn't mean that we can't be in profit after 100k rolls, but it will be a statistical outlier, i.e. an extremely rare event

[alani123]

Your image host is down at the moment!
Nice post, but still it doesn't JUST have to do with the total number of rolls. The odds tend to even out in the long run, but long unlucky streaks can have the exact opposite effect of good luck even in the short run. That's why strategies like martingale always fail and can be especially catastrophic in a short run too.

[deisik]

Here we go again!

Now I ran 7 tests with 50k bets each. Long story short, luck received heavy beating by the house edge. The best it could get is -0.00000068, which is still a loss. But a loss is a loss under any name:



The worst result is -0.00000920, which is not as bad as the baddest of 100k rolls (or even the second worst) but still more than enough to kill you and wipe out your balance in the process:



The table of all 50k tests:

Result	Snapshot link
-0.00000405	link
-0.00000555	link
-0.00000688	link
-0.00000233	link
-0.00000068	link
-0.00000920	link
-0.00000593	link

The bottom line is that with 50k rolls, there's not much you can hope for in terms of luck, which gets massively run over and trampled on by the house edge (1% in all these cases)

Your image host is down at the moment!

Tested under Opera VPN, everything should be fine

[tyKiwanuka]

I will put this discussion from the other thread here, hope you don't mind @deisik

I think many people misunderstand how the house edge works(or it is I who misunderstands it, but, anyways, I think differently). The house edge is not working against you in particular, because you simply can't, you physically can't, not only play a quadrillion times in a row, like in your example, but you can't play a billion times during your lifetime. And, as you rightly put it, only with the enormous amounts of bets, we can predict with high probability what is going to happen.

In short, one particular player can either win because of good luck, or lose because of bad luck, but the house edge, especially as small as just 1%, has little to do with it.

I can't argue against that. There might be players, that only played dice very few times and they could be overall winning dice players. There are also people, that won millions in a lottery having played only once. But I am just looking at the theory/statistics/math behind it. The majority of people don't poker, play dice or do sportsbets only once, but they always come back and they are probably victims of the math then.

Change your point of view and think of the gambling site operator as a (single) player. They are easily able to play dice gazillion of times. And they will win 1% (if that is the house edge) with every play on average.

Again, it is not that simple. The "longterm" can mean a thousand years. Within a year or two anything can happen with the best poker player, or sports bettor. Look at the Tom Dwan's performance during the year 2009, for example:

Yes, there are lots of graphs like this to be found from a lot of very good poker players. Quite a few of them were broke at least once during their career. Variance can hit very bad in poker - and for a long time. But Tom Dwan is a multi-millionaire nowadays. Is he a poker millionaire just because he was lucky ? No, he is a poker millionaire, because he mastered the game and played the odds/probabilities (while having the same starting hands - again on average - as everyone else). He surely played millions of hands in his career and the luck factor is negligible for him.

[deisik]

Change your point of view and think of the gambling site operator as a (single) player. They are easily able to play dice gazillion of times. And they will win 1% (if that is the house edge) with every play on average

I had already tried this approach in the past

Like 1 billion people playing 1000 times can be re-framed as a single player betting a trillion times, and she will lose exactly the house edge, whatever it might be. But we still shouldn't discard a key difference between 1 player versus 1 billion players, and it is variance. Variance can't do anything with 1 billion gamblers as it gets instantly averaged out among so many players with only 1000 bets to make each -- too few bets for too many people. However, it will most certainly kill a lonely player, and I would say it won't take anywhere close to 1 trillion bets. Just like it will probably kill some of the players in their first, and only, 1000 bets, but not en masse

[Lakai01]

First of all thank you very much for this interesting data.

We have often had discussions here about why Martingale works (or doesn't work). Most of the time it was argued that longer loss streaks are very unlikely. I would like to take up this again on the basis of your screenshots. Here you can see a loss-streak of 14 rolls:



To put it short if someone doesn't know what Martingale is:

The strategy had the gambler double the bet after every loss, so that the first win would recover all previous losses plus win a profit equal to the original stake. The martingale strategy has been applied to roulette as well, as the probability of hitting either red or black is close to 50%.

Source

Let's imagine that you had bet on Martingale here at your Rolls and started with 0.0002 BTC (= $1.6). With a loss streak of 14 Rolls you would already have to bet 1.6384 BTC on your 15th attempt. That this is not unrealistic is shown by your screenshots where the loss-streaks vary between 12 and 18 attempts.

[Tipstar]

There's no wining if you go with same strategy for a long time as house edge keeps on working. If you want to have a luck favor, you need to keep changing your strategy and pause gambling if you thing you are in a bad streak. Martingale is a good strategy but don't use it plain and straight. Do it manually and change target to avoid long streak.

[deisik]

First of all thank you very much for this interesting data

You're welcome, bro

We have often had discussions here about why Martingale works (or doesn't work). Most of the time it was argued that longer loss streaks are very unlikely

The longer losing streaks are called statistical outliers (or variance)

They are rare but they are far from being unlikely. In fact, they are a given in any martingale setup for the simple reason martingale is about making a very large number of rolls, so you are inevitably going to see very long losing or winning streaks eventually. Moreover, the only way to stay in the game while using martingale is to exploit the power of these outliers against the casino, and thus beat the house edge

The strategy had the gambler double the bet after every loss, so that the first win would recover all previous losses plus win a profit equal to the original stake. The martingale strategy has been applied to roulette as well, as the probability of hitting either red or black is close to 50%

The approach described in Wikipedia is an illustrative example of how things should not be done in practice. If followed precisely, that is recovering all previous losses plus winning a profit equal to the original stake, it becomes an utterly useless strategy. With each successful bet you should not only recover what you have lost in previous rolls but also earn as much or even more

Let's imagine that you had bet on Martingale here at your Rolls and started with 0.0002 BTC (= $1.6). With a loss streak of 14 Rolls you would already have to bet 1.6384 BTC on your 15th attempt. That this is not unrealistic is shown by your screenshots where the loss-streaks vary between 12 and 18 attempts

That's why you must stick with cryptocurrencies like Dogecoin and with casinos that allow the lowest possible denomination as a base bet

[DarkDays]

Randomness and the house edge are actually working with each other, not against each other.

Casinos hope that you wager more and more, that way they increase the odds that your results will fall within the normal distribution.

A lot of people play into their hands by wagering extremely small amounts with a high frequency, meaning they're moving closer and closer to the expected distribution very quickly.

However, the really smart gamblers are the ones that bet big, but infrequently. That's why I pay more attention to the higher rollers than the small fish, and probably why the high rollers tend to come out on top more often than the auto-bettors.

[STT]

The overwhelming appeal to martingale is its simplicity, thats it and why its a strategy repeated and remembered by punters for ages.   To employ more complex statistical techniques and analysis would involve more time, effort and education to gain any advantage if there was one to have.
   I heard about martingale sitting in a casino bar 20 years ago, I wont be surprised if it goes back decades before that and its just like an urban myth that lights peoples imaginations.   No discernible benefit clearly where as the OP points out house advantage is ongoing in in its importance and is something worth noting every bet placed.

[deisik]

Randomness and the house edge are actually working with each other, not against each other

Without randomness there would be no luck

But without luck there would be no winners (other than the casino, obviously). Pretty simple logic, isn't it? In that way, I'm not sure if randomness and the house edge could ever be living peacefully together. Let me guess, you are mistaking uniform distribution for random. If this is the case, then I agree with you. In a uniform distribution there is no place for variance (it simply makes no sense), and thus no place for luck either as the house edge becomes a dominating force from the very first roll. That's essentially why any casino would go for a uniform distribution instead of a truly random one, with its potentially devastating statistical outliers (aka lucky streaks)

Casinos hope that you wager more and more, that way they increase the odds that your results will fall within the normal distribution

Random distribution is very different from normal distribution. Again, you are likely confusing random distribution with uniform. But uniform is not normal either (was there a pun there?)

A lot of people play into their hands by wagering extremely small amounts with a high frequency, meaning they're moving closer and closer to the expected distribution very quickly

And?

However, the really smart gamblers are the ones that bet big, but infrequently. That's why I pay more attention to the higher rollers than the small fish, and probably why the high rollers tend to come out on top more often than the auto-bettors

Could you specify what you mean by "high rollers coming out on top more often than the auto-bettors"? What metric do you refer to here that the high-rollers are defeating auto-bettors in?

[Ryker1]

[snip]
Without randomness there would be no luck

But without luck there would be no winners ..

Well, you are right. Gambling is always a game of luck though, there are strategies that can be used to recover losses like the martingale strategy. It will be best if you double your bet if you lose once and if you win when you double your bet then you already be able to recover easily but think of it what if you lose again on your next bet then automatically that makes you lose thrice. Sadly with a house edge, it only secures the profit of the gambling sites you may get eager to win back what you have lost but luck is your only hope, perhaps before playing you must be aware and ready that there is a chance of winning and a chance of losing and that will make you not to be emotionally distracted when the game doesn't on your side.
Indeed, I am sure if you will accept the fact that you may either win or lose then you will always have control and think to stop playing since you don't need to be eager in winning back your losses to the point of betting all you have and in the end lose everything.

[Saint-loup]

It is not a secret that the longer you gamble, the less impact luck will have on the net outcome of your bets in games of chance. On the other hand, the house edge is what makes you lose in the long run by and large. Thus we have two forces which are fighting with each other -- the force representing randomness in the form of luck, and the force representing determinacy in the form of house edge

So how are they going to score against each other in the games of chance such as dice? Read on and find out

As said above, the house edge is set to win the longer you roll (read, you are going to lose). But this abstract knowledge doesn't tell us anything when exactly the house edge is going to dominate luck, i.e. how many rolls we will have to make until luck and its impact become insignificant and can thus be safely discarded for almost all practical intents and purposes. This is what I tested for myself and share with my fellow gamblers in this topic

At first, I ran a series of 10k rolls to see if this was enough for the house edge to beat luck. The short answer is no, as the snapshot below proves (with 9995 rolls):



After making so many rolls, I was still in profit. What does it tell us? Basically, that the impact of chance is still important at 10k bets with the given house edge (1%). Below is the table of all 10k tests that I ran:

Result	Snapshot link
+0.00000042	link
+0.00000098	link
-0.00000142	link
-0.00000122	link

However, with 100k rolls, the house edge leaves no chance to chance (pardon the pun):

Result	Snapshot link
-0.00000846	link
-0.00000867	link
-0.00001115	link
-0.00001386	link

And here's the last test with 200k rolls:



As you can see, the house edge becomes overwhelming, and there is no reason to believe that it won't be even more devastating as the number of bets increases further

So the conclusion is that the house edge turns into a dominating force somewhere after 10k, while luck stops being a factor right there. It doesn't mean that we can't be in profit after 100k rolls, but it will be a statistical outlier, i.e. an extremely rare event

Thank you for this thread. It clearly shows that dice rolls aren't as independent as people think. Results aren't random at all here, they respect the rule of the probability. So your luck isn't independent from your previous results.

[20kevin20]

Now that is a possible explanation why all my overnight auto-betting bots turned into losses. IIRC, the casino at the time could handle ~1 second per bet which means 10k bets would be reached within 3 hours.

So does that mean that the strat should be changed every 5k bets in order to avoid the house edge losses?

~
there are strategies that can be used to recover losses like the martingale strategy. It will be best
~

I think martingale is the quickest way to lose. It always made me lose everything within minutes. I had streaks of +20 losses with it. Start with 0.00000001BTC on martingale and after 20 losses you'll need to bet 0.02097152BTC already. Starting from one satoshi! That is equal to starting with $1 and having to bet a whopping $2,097,152 after 20 losses.

[deisik]

It will be best if you double your bet if you lose once and if you win when you double your bet then you already be able to recover easily but think of it what if you lose again on your next bet then automatically that makes you lose thrice

I'm not sure I fully understand what you mean by the above

Regardless, I double at each loss, so when I score a win I do not only recover what I have lost until now but also win as much. In fact, I win even more than that for the simple reason I typically use multipliers a little higher than a regular x2. The whole idea consists in using variance against the house edge and waiting for an outlier that is long enough to produce juice but not long enough to take me out

Thank you for this thread. It clearly shows that dice rolls aren't as independent as people think. Results aren't random at all here, they respect the rule of the probability. So your luck isn't independent from your previous results

Well, what you see is the house edge taking on luck (i.e. randomness) and then decisively taking it down. As such, this has little to do with whether rolls are independent of each other or not. Simply put, you are making an interpretation error, i.e. the results are valid but your interpretation of them is not

[deisik]

~
I remember we have already discussed this matter, and recently you have been forwarded to my topic where I actually show real-life stats proving that after 100k bets luck, as the only force opposing the house edge, becomes utterly irrelevant and inconsequential. Simply put, 1 billion bets, whether made by a single player or by a crowd of countless players, is a massive overkill in this regard

Then how would you explain that some people are in overall profit after making millions of bets on dice sites? Do you think all of them are using some kind of sophisticated betting strategy, something like that "Martingale-DOGE" one of yours? Or how else could they beat the house edge, if not by pure luck?

Let's keep it simple

You show me these people who "are in overall profit after making millions of bets" while not using "some kind of sophisticated betting strategy" (like "Martingale-DOGE" by my invention), i.e. by pure luck alone, and I will agree that there is however small a chance that you can still be in the game after so many rolls betting randomly (as we are talking about luck here) and risking your entire balance at each roll of a die (don't miss this part)

It would be an extreme outlier, most likely caused by a glitch in a casino RNG expertly exploited by a smart gambler, even though in that very case it makes no sense to place so many bets when you could just bet high once or twice and then run with the spoil. Unless, of course, you mean successfully betting high a few times and betting 1 satoshi 1 million times afterwards. Then you would likely remain in profit indeed

[batang_bitcoin]

there are strategies that can be used to recover losses like the martingale strategy.

I can't prove this that it's a good strategy to recover. I do agree with 20kevin that it's a way to lose even quicker. But if you can prove it on your own and you have recovered much with this strategy, you are one of those few that's really using this strategy for your own good.
As for the luck, IMO there's really no point to determine when it is effective for those ton of bets you've made because it will come unexpectedly but there's one sure thing for us, the house edge remains no matter what.

[swogerino]

I have been playing slots during all April and lost always except the first day where I won a big amount and I thought the longer I play the longer I have a chance to hit that maximum payout or the 5000x your bet.I was proven wrong during all other days but I don’t think i played 200.000 spins.

If you can show the same graphs in slot machine playing with minimal bet that would be a great help in convincing myself to stop playing as I am still actively playing and losing.

When someone else show you results you tend to believe him more that is why I would love to see the same image regarding slots.

[deisik]

there are strategies that can be used to recover losses like the martingale strategy.

I can't prove this that it's a good strategy to recover. I do agree with 20kevin that it's a way to lose even quicker. But if you can prove it on your own and you have recovered much with this strategy, you are one of those few that's really using this strategy for your own good

It is a matter of understanding variance, and how you can profit off it

As for the luck, IMO there's really no point to determine when it is effective for those ton of bets you've made because it will come unexpectedly but there's one sure thing for us, the house edge remains no matter what.

Luck gets completely averaged out over thousands of bets (in fact, more like millions of bets), and that is exactly the point of running so many tests to determine when it will happen, or rather start out to, for 999 players out of 1000. There can be extreme outliers, but in real life before you hit one you will have lost your balance many times unless you bet small. However, in the latter case your winnings will be as small compared to the balance, so your only reward will be witnessing such an outlier for real eventually (like in a decade of nonstop rolling or so)

[Betwrong]

~
Change your point of view and think of the gambling site operator as a (single) player. They are easily able to play dice gazillion of times. And they will win 1% (if that is the house edge) with every play on average.

I absolutely agree with you, and this is my point: a gambling site will win/earn around their house edge after billions and billions bets made on it. However, one particular player will not necessarily lose that amount, let alone all his/her bankroll(as it is alleged by many), after making several millions of bets.

~
I remember we have already discussed this matter, and recently you have been forwarded to my topic where I actually show real-life stats proving that after 100k bets luck, as the only force opposing the house edge, becomes utterly irrelevant and inconsequential. Simply put, 1 billion bets, whether made by a single player or by a crowd of countless players, is a massive overkill in this regard

Then how would you explain that some people are in overall profit after making millions of bets on dice sites? Do you think all of them are using some kind of sophisticated betting strategy, something like that "Martingale-DOGE" one of yours? Or how else could they beat the house edge, if not by pure luck?

Let's keep it simple

You show me these people who "are in overall profit after making millions of bets" while not using "some kind of sophisticated betting strategy" (like "Martingale-DOGE" by my invention), i.e. by pure luck alone, and I will agree that there is however small a chance that you can still be in the game after so many rolls betting randomly (as we are talking about luck here) and risking your entire balance at each roll of a die (don't miss this part)

It would be an extreme outlier, most likely caused by a glitch in a casino RNG expertly exploited by a smart gambler, even though in that very case it makes no sense to place so many bets when you could just bet high once or twice and then run with the spoil. Unless, of course, you mean successfully betting high a few times and betting 1 satoshi 1 million times afterwards. Then you would likely remain in profit indeed

I can’t say anything definite in this regard because since recently many gamblers choose to hide their stats. But when it was open I remember seeing several of such examples. ... Oh, well, luckily I've managed to find one(but only one, unfortunately):



As you can see, this player made over 1 million dice bets, and his total profit is 0.31624212 BTC. And looking at his total wagered amount, over 845 BTC, I don't think this guy was betting 1 satoshi ever.