The odd of winning... when computers are involved

[Malintent]

Just for fun, I decided to work out the probabilities.

From what I've found online, $1 slots have a house advantage of about 10%, with a single wager payout standard deviation of about $5.

That means that, for the 90% payout slots, after 100,000 spins you should expect to lose $10,000 with standard deviation of around $1581.

To be honest, I was a little surprised at how high the standard deviation is, but, on second thought, high volatility makes the games more fun for the player and the casino can afford to wait and let the law of large numbers do its thing.

40 million people visit Vegas each year, and I'd guess that on average it's $100 in slot pulls each? More?

That would mean the casinos should expect to make $400,000,000 in profit on slots in a year with standard deviation of only $300,000. That's crazy.

When the Treasury Casino opened in Brisbane, I went to have a look around with a mate. He said "I have a system for playing roulette; I can't lose". I said "Take a look around. Plush deep carpets; crystal chandeliers; expensive paintings on the walls; Cheap food and drink; loads of staff everywhere; all of this costs a LOT of money. Do you think that this place would look like this, if there was a system where the punter 'can't lose'?".

The only casino that I would patronise as a gambler would be one where they were about to shut down due to bankruptcy. That's at the minimum indicator that the house doesn't have an edge. Even then, I would suspect that their problems didn't arise because the odds were against them.

While casinos are glitzy, it is clear that Mr Burns had the business model all worked out

Well, I've discovered the perfect business: people swarm in, empty their pockets, and scuttle off.

I know that 'trick' to 'never losing' at roulette. The 'trick' relies on vey high (or non-existent) house betting limits.. .which, is precisely how the casinos avoid bankruptcy... So they set table limits very carefully to prevent this trick from working.

This is the method:

always bet the minimum table bet on a color (black or red).
if you win, do it again.
If you lose, make your next bet DOUBLE your last bet, plus the table minimum
repeat that until you win
once you win, go back to the minimum bet

Let's say the minimum bet on a particular roulette table is $10. That table would then have a MAXIMUM bet of $1,000.

Choose a color (black or red).. let's just say we choose black.

on your first bet, put $10 on black.
If you win, you will profit $10, and you bet $10 again.

If you lost your first bet, put $30 on black for your second bet (double your last bet + minimum)
if you win, you will have profited $20 ($30 win - $10 loss)

If you keep doing this, you will earn $10 per spin of the wheel, no matter if you win or lose...

UNLESSS!!!!!!!!!!!!------

the wrong color comes up 6 times in a row. Then you are fucked.

loss 1: $10
loss 2: $30
loss 3: $70
loss 4: $150
loss 5: $310
loss 6: $630

You cannot make your 7th bet, as it would exceed the house limit. At this point, you have lost $1,200, and cannot make an appropriate bet to recover it.

So, this tick relies on answering the following question for yourself....

will the same color appear on the wheel 6 times in a row before you have played 120 times... by your 120th spin, you will have profited enough to cover a 6-in-a-row-defeat.

 

[beero1000]

When the Treasury Casino opened in Brisbane, I went to have a look around with a mate. He said "I have a system for playing roulette; I can't lose". I said "Take a look around. Plush deep carpets; crystal chandeliers; expensive paintings on the walls; Cheap food and drink; loads of staff everywhere; all of this costs a LOT of money. Do you think that this place would look like this, if there was a system where the punter 'can't lose'?".

The only casino that I would patronise as a gambler would be one where they were about to shut down due to bankruptcy. That's at the minimum indicator that the house doesn't have an edge. Even then, I would suspect that their problems didn't arise because the odds were against them.

While casinos are glitzy, it is clear that Mr Burns had the business model all worked out

Well, I've discovered the perfect business: people swarm in, empty their pockets, and scuttle off.

I know that 'trick' to 'never losing' at roulette. The 'trick' relies on vey high (or non-existent) house betting limits.. .which, is precisely how the casinos avoid bankruptcy... So they set table limits very carefully to prevent this trick from working.

This is the method:

always bet the minimum table bet on a color (black or red).
if you win, do it again.
If you lose, make your next bet DOUBLE your last bet, plus the table minimum
repeat that until you win
once you win, go back to the minimum bet

Let's say the minimum bet on a particular roulette table is $10. That table would then have a MAXIMUM bet of $1,000.

Choose a color (black or red).. let's just say we choose black.

on your first bet, put $10 on black.
If you win, you will profit $10, and you bet $10 again.

If you lost your first bet, put $30 on black for your second bet (double your last bet + minimum)
if you win, you will have profited $20 ($30 win - $10 loss)

If you keep doing this, you will earn $10 per spin of the wheel, no matter if you win or lose...

UNLESSS!!!!!!!!!!!!------

the wrong color comes up 6 times in a row. Then you are fucked.

loss 1: $10
loss 2: $30
loss 3: $70
loss 4: $150
loss 5: $310
loss 6: $630

You cannot make your 7th bet, as it would exceed the house limit. At this point, you have lost $1,200, and cannot make an appropriate bet to recover it.

So, this tick relies on answering the following question for yourself....

will the same color appear on the wheel 6 times in a row before you have played 120 times... by your 120th spin, you will have profited enough to cover a 6-in-a-row-defeat.

Yeah, casinos LOVE people who think a martingale strategy is a good idea. Even without maximum bet limits, since the house has access to significantly more money than the gambler, the doubling strategy is basically guaranteed to bankrupt the player, not the casino.

The reason for maximum bets is not because you'd win all the money. It's a variance minimization technique casinos use to make sure people make more, smaller, bets, and to avoid significant losses to advantage playing (card counting, roulette bias, etc).

 

[skepticalbip]

When the Treasury Casino opened in Brisbane, I went to have a look around with a mate. He said "I have a system for playing roulette; I can't lose". I said "Take a look around. Plush deep carpets; crystal chandeliers; expensive paintings on the walls; Cheap food and drink; loads of staff everywhere; all of this costs a LOT of money. Do you think that this place would look like this, if there was a system where the punter 'can't lose'?".

The only casino that I would patronise as a gambler would be one where they were about to shut down due to bankruptcy. That's at the minimum indicator that the house doesn't have an edge. Even then, I would suspect that their problems didn't arise because the odds were against them.

While casinos are glitzy, it is clear that Mr Burns had the business model all worked out

Well, I've discovered the perfect business: people swarm in, empty their pockets, and scuttle off.

I know that 'trick' to 'never losing' at roulette. The 'trick' relies on vey high (or non-existent) house betting limits.. .which, is precisely how the casinos avoid bankruptcy... So they set table limits very carefully to prevent this trick from working.

This is the method:

always bet the minimum table bet on a color (black or red).
if you win, do it again.
If you lose, make your next bet DOUBLE your last bet, plus the table minimum
repeat that until you win
once you win, go back to the minimum bet

Let's say the minimum bet on a particular roulette table is $10. That table would then have a MAXIMUM bet of $1,000.

Choose a color (black or red).. let's just say we choose black.

on your first bet, put $10 on black.
If you win, you will profit $10, and you bet $10 again.

If you lost your first bet, put $30 on black for your second bet (double your last bet + minimum)
if you win, you will have profited $20 ($30 win - $10 loss)

There is a few problems with this. It combines a few errors in thinking.
... It includes the gambler's fallacy that you need to keep betting on black (or red) consistently thinking that four or five hits on red means that black is now more probable. Past hits are irrelevant. Each spin is independent and either red or black for each spin has a little less than a 50/50 chance but (0 and 00) give the house a little better chance of you guessing wrong. There are 18 slots the ball could fall into for you to win and 20 slots for the ball to fall into for you to loose.
... The house has no fear of this scheme bankrupting them because the money you are trying to recover is the money you lost on the last few spins so still at the table and not money they will need to go to their vaults to cover your bet, no matter if it is in the hundreds of thousands or even millions.

The problem, even if there is no limit, is how much you are willing or able to bet on less than a 50/50 chance trying to recover the money you have already lost.

 

[Barbarian]

I don't have a clue how Vegas does the video card games but the gaming commission likely requires and checks that the cards are dealt randomly. I don't know how the casino guarantees themselves an edge in poker but in blackjack the odds are with the house unless the player is a card counter. But then a shuffle between each deal will make card counting useless.

Common technique for advanced slots players... observe the players around you. When someone is on a loosing streak and leaves a machine that has wiped them out, that machine is 'hot' and is likely due to payout (it has to, eventually, by law).

I think there's a bit of confusion here. The hotness of a slots machine is a preprogrammed feature: if the machine senses that some time has passed since its last use, it will assume that a new player is trying his luck, and this new player should be hooked by some easy early wins. It does look like winning was overdue after a sequence of losses, but that's because the sequence of losses heralds the departure of the previous player. Simply fulfilling a payout quota would not require this feature.

 

[Kharakov]

There are no shills for the gambling industry here. Seriously- you guys trying to pick off low hanging fruit or something? You should be lined up and shot.

 

[beero1000]

There are no shills for the gambling industry here. Seriously- you guys trying to pick off low hanging fruit or something? You should be lined up and shot.

They have a surprisingly prevalent false belief. As I suspected, Vegas slot machine outcomes are serially independent and identically distributed. In addition to being sensible, it is also required by law:

14.040 Minimum standards for gaming devices. All gaming devices submitted for approval:1. Must theoretically pay out a mathematically demonstrable percentage of all amounts
wagered, which must not be less than 75 percent for each wager available for play on the device.
(a) Gaming devices that may be affected by player skill must meet this standard when using a
method of play that will provide the greatest return to the player over a period of continuous play.
(b) The chairman may waive the 75 percent standard if the manufacturer can show to the
chairman’s satisfaction that this requirement inhibits design of the device or is inappropriate under
the circumstances, the device theoretically pays out at least 75 percent of all wagers made when all
wagers are played equally, and the device otherwise meets the standards of subsections 2 through
6. A waiver will be effective when the manufacturer receives written notification from the chairman
that this standard will be waived pursuant to this paragraph. A waiver of this standard pursuant to
this paragraph is not an approval of the device.
2. Must use a random selection process to determine the game outcome of each play of a
game. The random selection process must meet 95 percent confidence limits using a standard chisquared
test for goodness of fit.
(a) Each possible permutation or combination of game elements which produce winning or
losing game outcomes must be available for random selection at the initiation of each play.
(b) For gaming devices that are representative of live gambling games, the mathematical
probability of a symbol or other element appearing in a game outcome must be equal to the
mathematical probability of that symbol or element occurring in the live gambling game. For other
gaming devices, the mathematical probability of a symbol appearing in a position in any game
outcome must be constant.
(c) The selection process must not produce detectable patterns of game elements or
detectable dependency upon any previous game outcome, the amount wagered, or upon the style or
method of play.
3. Must display an accurate representation of the game outcome. After selection of the game
outcome, the gaming device must not make a variable secondary decision which affects the result
shown to the player.

ETA: I find it hilarious that the casinos are REQUIRED to make their games patternless and independent, and people insist on seeing patterns and dependencies regardless.

 

[skepticalbip]

Essentially, if you are playing a one dollar slot that has the payout at 90% and after 100,000 spins you haven't lost $10,000 +/- $2,000 or so then you should really complain to the management.

Just for fun, I decided to work out the probabilities.

From what I've found online, $1 slots have a house advantage of about 10%, with a single wager payout standard deviation of about $5.

That means that, for the 90% payout slots, after 100,000 spins you should expect to lose $10,000 with standard deviation of around $1581.

To be honest, I was a little surprised at how high the standard deviation is, but, on second thought, high volatility makes the games more fun for the player and the casino can afford to wait and let the law of large numbers do its thing.

40 million people visit Vegas each year, and I'd guess that on average it's $100 in slot pulls each? More?

That would mean the casinos should expect to make $400,000,000 in profit on slots in a year with standard deviation of only $300,000. That's crazy.

You don't have to calculate probabilities here, just look at human nature. If someone goes to Vegas and has budgeted $100 to play the slots then they will likely keep playing until they lose that $100. Few will stop while they still have some of the budgeted money and will just cycle any winnings back into the slot. I don't think many would stop with $10 left of their originally budgeted $100. So if 40 million show up with $100 each to play the slots then Vegas can expect something closer to $4,000,000,000 profit from the slots.

There may be a few that hit it big with a couple thousand in winnings and stop but that wouldn't cut very deeply into the four billion.

 

[beero1000]

Just for fun, I decided to work out the probabilities.

From what I've found online, $1 slots have a house advantage of about 10%, with a single wager payout standard deviation of about $5.

That means that, for the 90% payout slots, after 100,000 spins you should expect to lose $10,000 with standard deviation of around $1581.

To be honest, I was a little surprised at how high the standard deviation is, but, on second thought, high volatility makes the games more fun for the player and the casino can afford to wait and let the law of large numbers do its thing.

40 million people visit Vegas each year, and I'd guess that on average it's $100 in slot pulls each? More?

That would mean the casinos should expect to make $400,000,000 in profit on slots in a year with standard deviation of only $300,000. That's crazy.

You don't have to calculate probabilities here, just look at human nature. If someone goes to Vegas and has budgeted $100 to play the slots then they will likely keep playing until they lose that $100. Few will stop while they still have some of the budgeted money and will just cycle any winnings back into the slot. I don't think many would stop with $10 left of their originally budgeted $100. So if 40 million show up with $100 each to play the slots then Vegas can expect something closer to $4,000,000,000 profit from the slots.

There may be a few that hit it big with a couple thousand in winnings and stop but that wouldn't cut very deeply into the four billion.

Given the payout and standard deviation statistics, the casinos will win a huge amount of money, but certainly not every dollar bet, or even every dollar budgeted. Sure, people who keep betting will eventually lose everything, but they are betting more cumulatively.

The standard deviation is high enough that it is not that rare to win in Vegas. That is how casinos keep people coming back, they give back a large portion of the money bet. One of my parents' friends won a 5 million dollar progressive jackpot in Atlantic City. He lost it all, plus most of his life savings, trying to chase that win. The fact that people do actually win makes it that much more insidious.

 

[Bomb#20]

(b) For gaming devices that are representative of live gambling games, the mathematical
probability of a symbol or other element appearing in a game outcome must be equal to the
mathematical probability of that symbol or element occurring in the live gambling game. For other
gaming devices, the mathematical probability of a symbol appearing in a position in any game
outcome must be constant.
(c) The selection process must not produce detectable patterns of game elements or
detectable dependency upon any previous game outcome, the amount wagered, or upon the style or
method of play.

Interesting. On its face, that would appear to make blackjack slot machines illegal; but they're all over the place.

 

[beero1000]

(b) For gaming devices that are representative of live gambling games, the mathematical
probability of a symbol or other element appearing in a game outcome must be equal to the
mathematical probability of that symbol or element occurring in the live gambling game. For other
gaming devices, the mathematical probability of a symbol appearing in a position in any game
outcome must be constant.
(c) The selection process must not produce detectable patterns of game elements or
detectable dependency upon any previous game outcome, the amount wagered, or upon the style or
method of play.

Interesting. On its face, that would appear to make blackjack slot machines illegal; but they're all over the place.

Why would that make blackjack slots illegal?

 

[Bomb#20]

Interesting. On its face, that would appear to make blackjack slot machines illegal; but they're all over the place.

Why would that make blackjack slots illegal?

The probability of blackjack elements appearing in the live game has a detectable dependency upon previous game outcomes. So rule (c) implies a blackjack slot machine is illegal if it duplicates live blackjack probabilities. But blackjack slots are representative of a live gambling game, which means rule (b) applies to it; and rule (b) says a blackjack slot machine is illegal if it doesn't duplicate live blackjack probabilities.

 

[beero1000]

Why would that make blackjack slots illegal?

The probability of blackjack elements appearing in the live game has a detectable dependency upon previous game outcomes. So rule (c) implies a blackjack slot machine is illegal if it duplicates live blackjack probabilities. But blackjack slots are representative of a live gambling game, which means rule (b) applies to it; and rule (b) says a blackjack slot machine is illegal if it doesn't duplicate live blackjack probabilities.

I don't think you're interpreting that correctly. Every game (deal) would incorporate a new shuffle, so no game element is dependent on previous games' outcomes.

 

[skepticalbip]

You don't have to calculate probabilities here, just look at human nature. If someone goes to Vegas and has budgeted $100 to play the slots then they will likely keep playing until they lose that $100. Few will stop while they still have some of the budgeted money and will just cycle any winnings back into the slot. I don't think many would stop with $10 left of their originally budgeted $100. So if 40 million show up with $100 each to play the slots then Vegas can expect something closer to $4,000,000,000 profit from the slots.

There may be a few that hit it big with a couple thousand in winnings and stop but that wouldn't cut very deeply into the four billion.

Given the payout and standard deviation statistics, the casinos will win a huge amount of money, but certainly not every dollar bet, or even every dollar budgeted. Sure, people who keep betting will eventually lose everything, but they are betting more cumulatively.

The standard deviation is high enough that it is not that rare to win in Vegas. That is how casinos keep people coming back, they give back a large portion of the money bet. One of my parents' friends won a 5 million dollar progressive jackpot in Atlantic City. He lost it all, plus most of his life savings, trying to chase that win. The fact that people do actually win makes it that much more insidious.

If we stick to the $1 slot at 90% payout. Your numbers mean that you are assuming that someone arriving with $100 will only make 100 spins of the slot, pocketing any winnings. I'm saying that the more typical Vegas visitor will take their $100 and make 1000 spins of the slot, feeding the winnings back into the slot. Of course there will be some who come out ahead but most will lose most if not all of what they brought with them to lose. The 90% payout means that the house keeps 10% of the bets made not that it keeps 10% of the money someone arrives with. And if those 90% payouts are used to make more spins of the slot than the original $100 would allow then the house will take a bigger bite of the funds brought to Vegas than the 10% you assumed.

 

[beero1000]

Given the payout and standard deviation statistics, the casinos will win a huge amount of money, but certainly not every dollar bet, or even every dollar budgeted. Sure, people who keep betting will eventually lose everything, but they are betting more cumulatively.

The standard deviation is high enough that it is not that rare to win in Vegas. That is how casinos keep people coming back, they give back a large portion of the money bet. One of my parents' friends won a 5 million dollar progressive jackpot in Atlantic City. He lost it all, plus most of his life savings, trying to chase that win. The fact that people do actually win makes it that much more insidious.

If we stick to the $1 slot at 90% payout. Your numbers mean that you are assuming that someone arriving with $100 will only make 100 spins of the slot, pocketing any winnings. I'm saying that the more typical Vegas visitor will take their $100 and make 1000 spins of the slot, feeding the winnings back into the slot. Of course there will be some who come out ahead but most will lose most if not all of what they brought with them to lose. The 90% payout means that the house keeps 10% of each bet not that it keeps 10% of the money someone arrives with.

You misunderstood what I said. I'm saying some people don't play slots at all, some people make 20 bets, and some people make tens of thousands. On average, my guesstimate was $100 in slot bets per person, not $100 in incoming dollars per person. I have no idea how close that is to being correct, but that was the number I picked.

 

[fromderinside]

But they can audit the slots if there is a record kept of plays, wins, and payouts. Just check the records over a month or year to see that they are close to those randomness would indicate. To check (and "correct") hourly or daily would mean that they had no understanding of probability. I assume that the regulators have some understanding but then since they are government agents, who the hell knows.

One of the easiest ways to detect mechanical or electronic malfunction is to track payout. We do the same in A/C maintenance and operability. A sequence of test rivet holes provides sure evidence whether the drilling process is sustaining reliable, within tolerance, drilling performance. By taking samples of holes and running variance tests variance numbers out of range tell us which component of the drilling assembly needs replacement. there is an entire domain of manufacturing statistics built on constancy with random number behavior and expectation. Important because stopping processes to manually set up and test rivet hole samples brings the entire operation to a stop. With multiple drilling devises on large fuselage and wing assemblies this reduces up time of machines to less than 40%. With intermittent non invasive hole measurement out of tolerance conditions can be quickly spotted without need to stop and change elements bringing up times for 200 million dollar drilling machines up to over 80%.

Yeah, off topic, but consistent with the truths bilby has already presented.