Gambling method?

There is a chapter in the book How Not to Be Wrong where the expected value of a lottery game was more than the bet, and one was guaranteed to make money AND the casino made money too, but those are rare.

Once you understand Expected Value, and Bayesian probability, you have covered most ways to optimize risk. There are some ways to optimize choice when you want to cover variations in the bet without waste that use combinatorial design, but usually the bookie knows all these and sets the game up to cover both his share and the integrity of the game.

The morale of the story is to use probability to eliminate risk first, then to manage risk second, but never to actually risk.
That leaves games of chance for the suckers.

>There is a chapter in the book How Not to Be Wrong where the expected value of a lottery game was more than the bet, and one was guaranteed to make money AND the casino made money too, but those are rare.
No, that's impossible. It's a zero sum game. The expected value of the casino is the negative of your expected value. Unless there's something stupid going on with infinite amounts of money, or infinite amounts of games.

>doesn't actually explain whats wrong with it though.
The wiki page, which I had already linked before him, does.

Did you suggest there is a game that generates new money out of thin air? Or are you talking about a case in which you may basically rob less knowledgeable players without affecting the Casino's profit?

It was a lottery game in Mass where, when the lottery exceeded $2M, the payoff for non-jackpot winners would "Roll Down" so that every once and a while, the down game would change the expected value of the whole game so that a sufficiently large random (or better combinatorially chosen selection) would guarantee to payout more than the cost of the tickets. The State would have already gotten its percentage, due to winning more than they projected, and so used the rest to sweeten the game. At these times, savvy betters (a bunch of students from like MIT or something) would buy up tens of thousands of tickets, and, on average, would increase their investment by the percentage difference of the E(x) to the ticket cost.

That doesn't mean the expected value is positive on both sides. Overall it's towards the state. If you split the games up the expected value can only be positive for the players or the state, not both at the same time.

I've seen that. That's not gambling, that's redistribution of wealth.

The state implemented a system to give away money from the gamblers on other days in order to increase their own cut purely based on tickets sold.

State didn't care if others took a cut of their scam lottery as long as it didn't impact them, until the story got too big.

(cont) So in one game in the book, the 4out of 5 and 3 out of 5 and 2 out of 5 payouts made a E(x) = payout/ chance = $50k/39k + $2385/800 +$60/47 = $5.53 return on a two dollar ticket.

Since this is for the whole game, you just had to compute the size of the sample needed to guarantee the return, so $20K investment brought @$60K return.

However, if he divides it into three parties, two of them can have positive expected value. He's just failing to be clear about that requirement.

State doesn't care. The more tickets bought, the higher their return. They make more off a game lots of people participate in regardless of how the payout is distributed.
Remember, this is for roll over only. They have already made more money off a smaller set of players, and so to increase the total money coming in, the increase the payout. They make their money on a percentage of every ticket, not on the luck of not paying out. More tickets bring more money than not paying out.

>You can't just ignore gigantic losses just because there's a small chance of it happening.
You can because it's a game theory problem, not a probability problem. Say that casinos did allow the betting described, they had infinite money, and everyone played. almost every person would be expected to win. In fact you can make the probability of no one losing arbitrarily close to 1 by making the max bet bigger. So it'd be any single person's interest to be part of the game even if as a group it's neutral.

>You can because it's a game theory problem, not a probability problem.
LOL this is meaningless.

>Say that casinos did allow the betting described, they had infinite money, and everyone played.
>So it'd be any single person's interest to be part of the game even if as a group it's neutral.
>infinite money
DURRRRRRRRRRRRRRR

Blackjack is the only game in a casino where you can tip the odds in your favor - and even then, properly counting cards (without getting caught) is a skill you have to train really hard for.

You can be skilled and tip the odds in your favor at poker too, but that's not playing against the house.

You are right it is a Game Theory problem in that the expected value changes with each bet, because the payout changes. But the expected value also changes sides, and that is the key.

It depends on who stops the game, and at what point in the iteration. Since the most anyone can ever win back is what they have lost, the game devolves into deciding when the game stops.
If the casino decides when the game stops, the casino will always win.

Presuming infinite money and infinite time is pointless. This was already addressed in the second fucking response:
>It doesn't take much analysis to realize that this strategy only works if you have infinite money and there is no bet limit.

No one disagreed that it works with infinite money and infinite time.

>No one disagreed that it works with infinite money and infinite time.
No one addressed this because it's not a realistic condition.

But since you asked...
For any finite number of bets (even trillions) there's a small chance you will lose a large sum of money.
As the number of bets approaches infinity, the chance of losing approaches zero, but the amount of total loss approaches infinity.
The *average* expected return is still always zero.
And if you have infinite money, why are you gambling?

I'm not asking. I'm telling someone who is arguing that it works with infinite money that no one said it didn't. Requires infinite time for the reason you said - you will still have zero expected value, but hurr I could set any arbitrarily high goal of profit and go until I reach it with infinite time and infinite money.

Yes, why are you gambling. That's why I agree it's a stupid thing to discuss.

yea i said something like that here >The real problem is that a house will always limit your bets
You don't need infinite money money though. You don't even need an unusually large amount of money depending on how much you're trying to win.
>No one disagreed that it works with infinite money and infinite time.
and no one disagreed that it doesn't work in any practical formulation. But OP's question is seemingly like asking why wouldn't any single person want to do this, which is like a game theory problem. In a game theory perspective, the vast majority would win so you seemingly should do it even though the win value is incredibly disproportional to the lose value. It's why pascal's wager doesn't work.
The practical explanation for why no single person should attempt this is because of house limits.

Are you saying house limits and house cut the only reasons why it's impractical? Yes, you do need infinite money and time. Please tell me I'm misreading.

Also, my impression is that OP was asking for a "fair" casino and otherwise practical conditions. Especially due to
>Anf if so, do people do this?

>I could set any arbitrarily high goal of profit and go until I reach it
You really don't get it.
No matter how low you set the goal, even a single win, there's a small chance you'll never reach it.
en.wikipedia.org/wiki/Random_walk

>Are you saying house limits and house cut the only reasons why it's impractical?
i'm saying that's the only practical way of convincing someone not to do it. Obviously people already know there's a very small chance of losing everything but if they're considering this system obviously they don't care. Explaining that the expected value is 0 isn't going to convince them because the probability that they'll be the ones to lose everything is incredibly small. But explaining the casino constraints shows that any single is more likely to lose than win so no one should do it.

Again, infinite time. I don't think you know what infinite means. Why am I still debating this, I came in this thread to say that seriously discussing the infinite time & money case is most likely irrelevant to OP and most other people because the practical answer is that it's a shit strategy even in a "fair" casino.

This is actually a system of betting known as the Martingale System. It involves doubling bets on every sequential loss and reverting to the original on a win.

In theory, it will always work out, but a losing streak can really cut into your bankroll. If You start with $100 and bet $5 on the first flip, after 4 consecutive losses (which is very possible) you will be unable to bet according to the system again. It gets expensive very quickly.

>Explaining that the expected value is 0 isn't going to convince them because the probability that they'll be the ones to lose everything is incredibly small.
Well I would have been less lost if I realized you were suggesting that mathematical truth would be ignored in favor of naivety. Sure, the other details are probably easier for the average person who asks this. Think we're otherwise in agreement.

>In theory, it will always work out,
No it won't.
It's just biasing you towards frequent small wins and rare large losses. There's no change in the actual expected value.

>In a game theory perspective, the vast majority would win so you seemingly should do it even though the win value is incredibly disproportional to the lose value.
No.
The expected return is still zero.
If a billion people used the system, their average winnings would be zero dollars.

>I don't think you know what infinite means.
see:
>As the number of bets approaches infinity, the chance of losing approaches zero, but the amount of total loss approaches infinity.
>The *average* expected return is still always zero.

All you've said is that if you "exhaust" your allotted infinite time, your expected value is still zero. A more useful analysis is:

>hurr I could set any arbitrarily high goal of profit and go until I reach it with infinite time and infinite money.

fuck off. you're not adding anything new to the thread. Everyone knows the expected value is zero. you're only adding wrong shit
>It follows that N is finite with probability 1; therefore with probability 1, the coin will eventually show heads and the bettor will realize a net gain of 1 unit.This property of the idealized version of the martingale accounts for the attraction of the idea.
try reading the thread and making sure anything you're saying hasn't already been brought up. no one cares that you googled and answer.

As well you need an exact 50/50 split. Casinos first step against this strategy was to put the 00 spot into roulette games.

you don't. you can just triple the money instead, etc. please think before posting.

having different odds doesn't change anything. what you might mean is having a lower than 1to1 payoff, in which case

I'm not entirely sure what point your trying to make here. Are you trying to say there are circumstances where Martingale system isn't unreasonable?

read the posts will you?
infinite money and infinite time means arbitrarily high yield

>infinite money and infinite time means arbitrarily high yield
That's true of absolutely every system ever that allows a player to win >0% of the time. So fucking what?

i was making the point that you should fuck off if you're not adding anything to the thread.

So fucking what indeed. Read the fucking thread maybe? It may be useless, but it is mathematically true, and so is the fact that in ALL OTHER CIRCUMSTANCES it is a garbage strategy.

In other words, the discussion in this thread has been thoroughly finished for a goddamn while now. Which is why multiple posters are telling everyone to shut the fuck up. Waah infinity is meaningless. Never said it wasn't. Just shut the fuck up. Thank you.

If you're fine with a betting strategy with the expected value of 99.878%*$1000000-(1-99.878%)*$1000000000 = -221220, I'd assume you didn't earn your billion with reasonable investments.

>thinking a casino will run a game that the house only wins 50% of the time.

Want to buy some Kansas beach front property?

en.wikipedia.org/wiki/Law_of_large_numbers

As the game goes on, there is a small but increasing chance that you'll loose an almost infinite number of times in a row.

>loose

kill
your
self

Are you fucking retarded? The house takes a cut of every bet that's how they make their money jfc

By the second law of thermodynamics, the universe can be thought of as a giant casino with molecular movements playing the role of coins.

Therefore given infinite time everyone in this thread will eventually be reassembled into cute animu girls.

((un)fortunately the universe is probably a supermartingale so we'll probably end up as some kind of primordial soup instead. Thanks, Doob.)

Games in casinos have betting minimums and betting caps for this system to never be beneficial to you. If you do manage to find a loophole, Las Vegas casinos know about it, and if they see you using a system you bet your ass a pit boss will be telling you to get the fuck out ASAP.

You never outsmart Vegas.

That said, I was doing this at a Pai Gow table last time I was in Vegas. Usual bet 20$, lose, bet 40$, lose, bet 80$, then win. But nothing was escalating to 5000 dollar bets and I believe the table I was at had a 200 max bet.

>infinite money and infinite time means arbitrarily high yield

no it doesn't fucktard

Yes it does. If it's possible to win at all, and you're willing and able to play for long enough, eventually you'll end up with a arbitrarily large net balance. You can just keep rolling the dice until you end up with the outcome you want.

In practice, of course, it would take more money than has ever existed and more time than the age of the universe.

Thanks for reading the whole thread before making a response that has already been dealt with. Oh, wait...

>infinite money and infinite time means arbitrarily high yield
Infinity * zero still = zero

>The house takes a cut of every bet that's how they make their money jfc
You're thinking of something like horse tracks,
In roulette, blackjack, slots, etc. the house loses sometimes, but wins enough to make up for it.

I dont know how to calculate it but ive heard its 52/48 house favor.

Yes people do this. They're called 'addicts'. Enjoy your oxygen tank and free watered down drinks.

no cuz u still lose whatever u lost aside from ur bet if u win

>Thanks for reading the whole thread before making a response that has already been dealt with. Oh, wait...
Also, though it's irrelevant, inf * zero is an indeterminate form you fucking idiot.

>inf * zero is an indeterminate form you fucking idiot
While it technically is, this is a discussion about probability, which is a special case of measure theory, where inf * zero is indeed taken to be zero.

See e.g. en.wikipedia.org/wiki/Extended_real_number_line and note in particular the line

>However, in the context of probability or measure theory, [math]0 \times \pm\infty[/math] is often defined as 0.

Not to say you can't come up with your own Wildbergerian system of probability where inf * zero is undefined, but you would have to forgo lots of things (the monotone convergence theorem, for example) and it would probably have too few theorems left to be of any practical use.