Does large number gambling real put you at an advantage?

[Mia Chloe]

So lately I've been thinking about how much probability and variance affects betting basically overtime. For instance let's consider a game with a 55% probability of winning which  actually gives us a 45% probability of losing which basically means after 1000 independent bets the expected number of wins should be something like;

Code:

E(X) = np = 1000 × 0.55 = 550

However, the standard deviation is gonna  give us;

Code:

σ = √(npq) = √(1000 × 0.55 × 0.45) ≈ 15.7

Which basically means the results between roughly 534 and 566 wins (550 ± 15.7) are statistically normal despite having a positive edge now what if we consider games with way smaller winning probability which obviously makes our variance smaller too. Now what do with do with the fact that there is a probability I still could lose 700 games worse case scenario? Because it looks like overtime you'll still run into net loss.

[Findingnemo]

That is not how probability works in math, the probability of each bet is the same for every bet but it is irrelevant to every other bet so even with 55% probability of winning one can still end up with 0 wins at the end of 500 or 700 bets or the number can be anything. People just assumes that they will win 55 bets if they bet on a game with 55% probability of winning after 100 bets and think that is strategy to have an edge over the casino, while in reality it is not.

[BALIK]

what if we consider games with way smaller winning probability which obviously makes our variance smaller too.

This is not always true, mate. In binomial distribution, variance = np(1-p), so variance is highest around p=0.5. And variance decrease as p approaches 0 or 1. So better you could say if winning probability moves away from 0.5 and toward 0 or 1 then the variance decrease.

And even with 55% edge, we could lose 700 game, yeah it doesn't seem mathematically impossible, but it's not a realistic expectation, right? With 55% win rate on 1000 bets, 300 wins/700 losses means about 250 wins less than the expectation, which is more than 16 standard deviation away. The probability of such an outcome is practically close to zero with independent bet.

[Alphakilo]

I doubt your trial at using large numbers during gambling gives you the gambler any real advantage because to me it depends on how long you play. A short period of play could even get you the luck of a win as compared to a longer duration of play with large sample size when the house edge is present and active.
Scaling up with large numbers or amounts is never a mathematical advantage and that's why I always make it a habit to gamble with a free mind to manage my capital and avoid the illusion of control or gamblers fallacy taking hold of my account.

[Mia Chloe]

That is not how probability works in math, the probability of each bet is the same for every bet but it is irrelevant to every other bet so even with 55% probability of winning one can still end up with 0 wins at the end of 500 or 700 bets or the number can be anything. People just assumes that they will win 55 bets if they bet on a game with 55% probability of winning after 100 bets and think that is strategy to have an edge over the casino, while in reality it is not.

Well that's the point. Mathematically based on just the variance values and the probability distribution you actually ought to be at an advantage over time then again the problem is the existence of no win in that same distribution. Basically there's still a chance you could lose all 100 games but the only difference is it's smaller.

And even with 55% edge, we could lose 700 game, yeah it doesn't seem mathematically impossible, but it's not a realistic expectation, right? With 55% win rate on 1000 bets, 300 wins/700 losses means about 250 wins less than the expectation, which is more than 16 standard deviation away. The probability of such an outcome is practically close to zero with independent bet.

I like your analysis. I tried a quick calculation and it's way smaller than I thought it would be if you approximate to the nearest two decimal you'll still have zero but sadly it doesn't make it impossible lol..

[tiCeR]

Statistically the only scenario where you end up with guaranteed profit is when p>0.5 and an infinite number of bets. That is when mathematically you can describe an experiment as guaranteeing profit, but it is only theoretical because there is no such thing as an infinite number of bets. In any other case you can never end up with a mathematically definitive answer.

Large number gambling puts you at an advantage as soon as p>0.5, otherwise it never does. In gambling you usually benefit from variance being in your favor on a lucky day. If your p was 0.99, and you don't play an infinite number of rounds, you can't ever reach p=0 for ending up losing. Mathematically never possible as there will always be a p like p=0.00000000000000000........1 for purely theoretically losing. An analogy to this example stems from the so called measure zero event. If you are asked to pick a real number between 0 and 1, the chance of choosing exactly 0.5000000000..... is zero beause there are infinitely many possible numbers and one number is an infinitely tiny fraction of them. But that doesn't mean the number 0.5 exists and therefore, theoretically, the number 0.5 could be selected, but the chance to exactly select it is zero. There is indeed a difference between saying the chance for failure is zero and failure is logically impossible. Logically, it is possible, but the chance is zero.

I know it sounds crazy, but this stuff goes back to gambling, too. If you have a winning probability of 99% in a game, theoretically the craziest of the craziest losing streaks could still happen to you. The chance might be extremely small, but if your budget is limited and the number of rounds you can play is limited accordingly, the impossible could still happen to you.

And there are examples for unbelievable streaks in roulette or other games. You can search in Google for it and you will find some very interesting info there about "impossible" streaks.

[BRINIRHA]

It might look a little better but I feel that probability doesn't make that a certainty in terms of the end result.

For the beginning indeed we will have a probability that can be used as a benchmark like the example you give but the final result is not a sure thing in gambling because when the probability of 55% or even more than that even in terms of percentage can make our bet will end without a win.

So, for me the calculation will still feel like a rough picture but the results become speculative because it could be true or even be a big mistake because the results are not in accordance with what is expected. Uncertainty in the final result because there is a luck factor makes this calculation to be speculative if applied in gambling.

[JeromeTash]

I think you have noticed that even with large numbers, in most cases millions of bets, the RTP value, for example, is usually referred to as "theoretical", which means that in a game of chance (probability), there is no guarantee that it will always be close to the stated percentage. Sometimes you could get "too lucky", and other times you could hit a very bad losing streak even after those 1000 bets.

[lionheart78]

So lately I've been thinking about how much probability and variance affects betting basically overtime. For instance let's consider a game with a 55% probability of winning which  actually gives us a 45% probability of losing which basically means after 1000 independent bets the expected number of wins should be something like;

Code:

E(X) = np = 1000 × 0.55 = 550

However, the standard deviation is gonna  give us;

Code:

σ = √(npq) = √(1000 × 0.55 × 0.45) ≈ 15.7

Which basically means the results between roughly 534 and 566 wins (550 ± 15.7) are statistically normal despite having a positive edge now what if we consider games with way smaller winning probability which obviously makes our variance smaller too. Now what do with do with the fact that there is a probability I still could lose 700 games worse case scenario? Because it looks like overtime you'll still run into net loss.

This actually looks good, and yes, the higher the probability the higher our chance of winning but this will only work on  games that gives a linear pay out like 1 dollar will win 1 dollar but casino does not work like this.

If we make the probability of winning increase, their system will make the reward to decrease, thus, with house edge and all, we are still bound to lose.  One good example is the dice game. Setting the possibility of winning to 98% it will reward us with this calculation : Payout = (1 − House Edge) / Win Probability.  So, no matter how many times we win in this setup, we will lose these winning with just 1 losing roll.  And as we observe, rolling dice in longer time always yield increasing losing streak.  Thus, at the end, the gambler will eventually lose thier bankroll.

[DPHOR]

No matter how close you could be still the possibility and probability still remains 0/1 meaning one is not that sure of the outcome, and when gamble do not think that your accuracy could or would easily lands you into winning based on your fact that your accuracy is that next to your precision level.
And in all precision the tendencies of winning is still unseen or unfactorized, permits me if there is any words like this, as the more you try to narrow your mind into that positive thinking to make you draws your winning ratios closely or around the said value could be false because gambling sites usually encodes their algorithm to be not less than 1/0 or 0/1.

[famososMuertos]

I understand what you're saying and where you're coming from. The interesting thing about these concepts (and/or the formulas you're using) is that you truly understand them empirically only after making hundreds of thousands, or even millions, of bets. In other words, those numbers you mention, which anyone can calculate, are a good statistical reference, but there's something that's often overlooked: the long term in betting is a much broader concept than we usually imagine.

Your formulas perfectly describe the expected behavior of a sample of 1,000 bets, but they don't guarantee that the actual results will match those expectations. Variance means that, even with a mathematical edge, you may follow a very different path before the expected value ultimately prevails. That's why I like to call variance "the dictator"; it's definitely not democratic.

So, rather than focusing solely on the expected number of wins, I'm always concerned with how the losses are distributed within those 1,000 bets. You can experience losing streaks that are long enough to jeopardize your bankroll if it isn't properly managed. That's where bankroll management comes into play.

In traditional casino games, everything ultimately comes down to variance. It's variance that dictates how your betting journey unfolds (you know, the "dictator"). In other words, it's what can make you feel incredibly lucky or incredibly unlucky along the way, even if the mathematical expectation remains in your favor.

In conclusion, these calculations are crucial for estimating your expected gains or losses and, consequently, determining how much bankroll you'll need to fight variance.

One more^imo thing:
I think this is one of the most overlooked aspects of betting. Most people have no idea how much risk they're actually exposing their bankroll to. If more bettors took the time to run these calculations, many of them would either reduce their stakes or think twice before placing a bet  

[o48o]

So lately I've been thinking about how much probability and variance affects betting basically overtime. For instance let's consider a game with a 55% probability of winning which  actually gives us a 45% probability of losing which basically means after 1000 independent bets the expected number of wins should be something like;

Code:

E(X) = np = 1000 × 0.55 = 550

However, the standard deviation is gonna  give us;

Code:

σ = √(npq) = √(1000 × 0.55 × 0.45) ≈ 15.7

Which basically means the results between roughly 534 and 566 wins (550 ± 15.7) are statistically normal despite having a positive edge now what if we consider games with way smaller winning probability which obviously makes our variance smaller too. Now what do with do with the fact that there is a probability I still could lose 700 games worse case scenario? Because it looks like overtime you'll still run into net loss.

55% winning rate doesn't mean anything if multipliers for those wins aren't worth it. And if they are worth it, casino itself wouldn't be sustainable business.

Not sure how anyone would think that very basic math that acts as fundamental to casino revenue could be overwritten with some other speculative math.

[GxSTxV]

I believe that not how it always works because each spin or bet is independent from the previous one on any game or slot. So basically having a 55% edge doesn’t mean you will automatically end up close to 550 wins every time on 1000 total. There is a chance you can still go through a very long losing streak before the results start reflecting that edge.

That is why I always say having an edge is only one part of the equation. If your bankroll isn’t big enough or you let emotions take over after a bad run, you will probably never reach the point where the math starts working in your favor. In gambling, variance can be much stronger than most people expect especially over what many of us would consider a big sample.

[AmoreJaz]

I doubt your trial at using large numbers during gambling gives you the gambler any real advantage because to me it depends on how long you play. A short period of play could even get you the luck of a win as compared to a longer duration of play with large sample size when the house edge is present and active.
Scaling up with large numbers or amounts is never a mathematical advantage and that's why I always make it a habit to gamble with a free mind to manage my capital and avoid the illusion of control or gamblers fallacy taking hold of my account.

Let us put it this way, whatever mathematical calculation you will apply here, I don't think you have the advantage as this is gambling. The advantage for me is that when you gamble with your extra funds. That for me won't give you financial problem.

[uneng]

Problem is that with 55% winning chance, the profit made on each bet won't be 100%. Therefore, you are risking 100 units to win 78 units, let's say.

At some point, the 55% chance won't be enough to afford losses at the rate of 100 base bet, because in winning case you are profiting only 78. You have an advantage in terms of winning chance, but this advantage is overcame by inferior odds provided by the casino.

You can't avoid this in gambling. It's the house edge system ensuring the house profits on long run.

[Rgram]

That is not how probability works in math, the probability of each bet is the same for every bet but it is irrelevant to every other bet so even with 55% probability of winning one can still end up with 0 wins at the end of 500 or 700 bets or the number can be anything. People just assumes that they will win 55 bets if they bet on a game with 55% probability of winning after 100 bets and think that is strategy to have an edge over the casino, while in reality it is not.

You have the right kind of ideal about gambling, though we might see an accumulated bet as wholesome, they are indeed independent and once one goes rogue, all the accumulated bets is lost. That’s how it works in this industry when you use a multiple bet pattern. That means, even the most probable bets can be made irrelevant by any rogued bet, rendering all our efforts out of place.

Despite what our probability might tell us, all bets in an accumulation series are independent and has the ability of affecting every selected and placed bets.

[davis196]

So lately I've been thinking about how much probability and variance affects betting basically overtime. For instance let's consider a game with a 55% probability of winning which  actually gives us a 45% probability of losing which basically means after 1000 independent bets the expected number of wins should be something like;

Are you trying to solve gambling by using math? This ain't gonna work. What game with 55% probability are you talking about? Consistently gambling in the long run is a way to lose money, not to win money. Just pick any gambling game that has an auto-bet feature, like dice, crash, plinko, etc. Deposit a big amount of crypto, set up the auto-bet at place small bets. Do you really think that you will end up winning more money than what you have deposited? The "large number gambling" does not dive you any advantage whatsoever. The house edge would always kick in. The best approach in gambling is to wait for your "lucky moment", place a big bet, get that big win and quit before you waste everything.

[Royal Cap]

A 55% chance of winning means you have a mathematical advantage but when that terrible losing streak (like 20% losses) comes along, most people's capital is wiped out. Actually the reality is that, the paper calculation is not the same as the real world. And where the odds of winning are low, the odds may seem small, but in the long run the house edge wins. The biggest risk here is not mathematical, but psychological. People get emotional and increase their bets to recover losses. If you don't risk more than 1- 2% of your total fund on each bet, even such bad streaks won't completely knock you out of the game.

[pawanjain]

So lately I've been thinking about how much probability and variance affects betting basically overtime. For instance let's consider a game with a 55% probability of winning which  actually gives us a 45% probability of losing which basically means after 1000 independent bets the expected number of wins should be something like;

Code:

E(X) = np = 1000 × 0.55 = 550

However, the standard deviation is gonna  give us;

Code:

σ = √(npq) = √(1000 × 0.55 × 0.45) ≈ 15.7

Which basically means the results between roughly 534 and 566 wins (550 ± 15.7) are statistically normal despite having a positive edge now what if we consider games with way smaller winning probability which obviously makes our variance smaller too. Now what do with do with the fact that there is a probability I still could lose 700 games worse case scenario? Because it looks like overtime you'll still run into net loss.

I had been thinking the same until few years ago but then I got to know that it's not how probability works.
The number of bets won't affect the outcome because every bet we place is individual and will have it's own probability.
So for a given bet, you will have 55% probability of winning and it will repeat the same for every bet.

[Oasisman]

I believe that not how it always works because each spin or bet is independent from the previous one on any game or slot. So basically having a 55% edge doesn’t mean you will automatically end up close to 550 wins every time on 1000 total. There is a chance you can still go through a very long losing streak before the results start reflecting that edge.

Exactly. This is where some people get lost with their expectations, because they think a 55% winning rate automatically translates into the total number of bets. So, the expectations should be around 550 wins (a little more or less). What they fail to realize is that there is still a possibility of incurring more losses than wins, as the winning rate always apply independently in every roll. So, that means when you flip a coin, there is a possibility that it will result to a 10 straight heads, even though the chances for both sides is 50%.

Now, if a particular game really has a 55% probability of winning, this could be a lot more noticeable in the long term. A thousand bets maybe a perfect example. But on a short period, a bad start can ruin it.