Profitability of No Zero Roulette?
What would happen if the house ran a game with no house edge?
I see that Betfair has done this with No Zero Roulette.
Assuming they don't pay any comps, I would think they would still make money for the simple fact that players would go broke before the house did...
Also assume the table limits aren't super high...
Is this the sort of thing that could only work online (where overheads are low) or do you think it could theoretically work in a land casino (eg. a coin toss game paying even money)...
Thoughts?
Gamblers are just plain STUPID . With rare exceptions. For years back in 50's and early 60's horse racing was the only legalized gambling. Could not even buy a lottery ticket legally. I know, because in high school I hustled Irish Sweepstakes tickets. The only exotic bet was the Daily Double, 1st and 2nd race only, to get the chumps there early.
Heard guys bitching for years about 14% take. Then along came quinella exacta trifecta etc. Take went to 18 % on exotics and nobody said nothing. Churchill Downs just went to 17.5 on WPS and 23.5 on exactas.
When 6/5 BJ came out, even the Motley Fool screamed foul. BJ sites promised to boycott such games. Anybody seen how that has worked out ?
Penny slots increased the HE and now most have 30 or 50 cent minimums to be eligible for the bonus.
Poker rooms drag 10% on first $50 in some places, plus $2 for Bad beat jackpots. Is there a worse bet in the house than the Bad Beat. And it's mandatory Welcome To Fruita.
All you need is a requirement that outside bets cannot exceed inside bets.
Naturally fair-pay means no comp.
No you have to pay a dealer to run it.Quote: 13sTotally get that it would be a foolish move... But do you think theoretically that such a table would still make money?
Do tell.Quote: BuzzardSomebody would lose their job, pure and simple. I have no way of knowing, but have always thought a certain member of this forum may have lost his job as a proponent of 3/2 BJ.
.
That said, a private club in a casino with tables that have either tiny or no HA could work. Charge a fee somewhere between noticeable and substantial for admission, and serve up games such as blackjack or carnival games that have zero HA (with perfect play, of course, and enough hassle to discourage counters.) The downside would be that food and alcohol would have to be bought, although more reasonably than at the bars and restaurants; the ideas is to make the highest profit off memberships.
Quote: 13sThis is something that I've wondered from time to time while working in casinos...
What would happen if the house ran a game with no house edge?
I see that Betfair has done this with No Zero Roulette.
Assuming they don't pay any comps, I would think they would still make money for the simple fact that players would go broke before the house did...
This doesn't happen.
For every player losing their bankroll, another player makes the same amount. Overall. There is no advantage to the house by having a bigger bank roll in a zero sum game. Not over the entire population. People here have claimed it before, but you can either do the sums or run a simulation.... it makes no difference, no house edge per spin = no profit overall.
Quick thought experiment:
if a casino with a 0 edge wheel made $200,000 on $10 million worth of bets due to 'bankrupting' players, then they've got an edge of 2%. But we just said it was a 0 edge game. So... where did that 2% come from?
Quote: thecesspitThis doesn't happen.
For every player losing their bankroll, another player makes the same amount. Overall. There is no advantage to the house by having a bigger bank roll in a zero sum game. Not over the entire population. People here have claimed it before, but you can either do the sums or run a simulation.... it makes no difference, no house edge per spin = no profit overall.
Quick thought experiment:
if a casino with a 0 edge wheel made $200,000 on $10 million worth of bets due to 'bankrupting' players, then they've got an edge of 2%. But we just said it was a 0 edge game. So... where did that 2% come from?
Variance?
Quote: Lemieux66Variance?
Assume for the sake of argument, we are well beyond 3 standard deviations of variance on the $200,000.
And the variance can go the other way, of course.
According to some of the gr8players(not necessarily him) Variance can be used to beat casinos in the long run because they play short run sessions.Quote: thecesspitAssume for the sake of argument, we are well beyond 3 standard deviations of variance on the $200,000.
And the variance can go the other way, of course.
I still can't understand how seemingly well educated people, even at math, can't grasp something so obvious.
However this theorem assumes all the players keep playing infinitely. We know that eventually they will stop so even if player A loses a million dollars on a million spins of roulette there are a million other players who won a single dollar on a single spin. The house would be losing money by virtue of having to keep the lights on and pay someone to take bets.
Quote: 13sAssuming they don't pay any comps, I would think they would still make money for the simple fact that players would go broke before the house did...
Nope. A lot of people think this. They also think that if APs aren't properly bankrolled they can't hurt the casino because even though they are playing with an edge, they will eventually go broke. This is the same fallacy that leads people to think that you can beat a -EV game with a negative betting progression.
Quote: geoffPlaying long enough the casino will beat any player at a 0% HE game. There is a mathematical proof that any finite bankroll will eventually run out given infinite time and while both the casino and the player have finite bankrolls in theory the casino has so much more it might as well be infinite.
No, this is wrong. The fact that all the money on the player's side is broken up among many people, while all the money on the casino's side is in one coffer, is irrelevant.
No finite number "might as well be infinite". This is fallacy.
Quote:However this theorem assumes all the players keep playing infinitely. We know that eventually they will stop
Not relevant. There is always someone to take their place. Unless the general population stops gambling, as a whole, which doesn't see likely.
Quote: AxiomOfChoiceNo, this is wrong. The fact that all the money on the player's side is broken up among many people, while all the money on the casino's side is in one coffer, is irrelevant.
No finite number "might as well be infinite". This is fallacy.
Not relevant. There is always someone to take their place. Unless the general population stops gambling, as a whole, which doesn't see likely.
It is irrelevant when talking of the overall + or - expectation. However when it comes to the individual player it matters a great deal.
P_1={N2}/{N1+N2}
P_2= {N1}/{N1+N2}
This is the probability formula for the odds of going broke in a coin flipping contest (even money bet for roulette) where N2 is P_2's bankroll and N1 is P_1's bankroll.
Because of the larger resources the casino against the average bettor it will more than likely prevail. However the problem with this formula and what I expressed rather poorly before was that it assumes both sides go until one is bankrupt.
Sure, lots of people would go broke, but some people would win far more than they brought to the casino. In a game with 0 house edge, it breaks even.
As Axiom pointed out, it doesn't make sense to "separate" the pool of player money into individual segments. It's all one big pool of player money bet against the house at 0 expectation.
Don't assume the house has a bigger bankroll, just because they out match each individual player. In this 0% game (and the one's where they have the edge), they have less than all the other players who come in put together.
Quote: Lemieux66I chalk up a zero HE game winning or losing anything as just one of those things.
Indeed, but the people who tell you busting players out is where the casino makes money don't get that... they think the house will make money, but can't point to where the edge is.
I could say they could offer zero edge, but the player wouldn't know the rules until the bet is ....forget it.
Quote: geoffIt is irrelevant when talking of the overall + or - expectation. However when it comes to the individual player it matters a great deal.
The question was whether the casino would make money, not whether a particular pre-chosen player would.
Quote: onenickelmiracleI don't think it's an easy answer just because people aren't rational. You have people who just won't stop until they lose and some who will stop when they win a little. In the real world, the casino would offer 0 edge but steal it back.
I could say they could offer zero edge, but the player wouldn't know the rules until the bet is ....forget it.
All the people who win a little would add up to the one who went broke.
Tough one because not everyone has the same amount of money to lose and so many people would gamble until they lost everything just like real casinos. There isn't an edge with the game but the human nature edge isn't counted in the math.Quote: Lemieux66All the people who win a little would add up to the one who went broke.
Let me stress that this is just a theoretical musing and I appreciate everybody's quantitative and qualitative analysis!
It would be you bought chips on a Tuesday and have to cash it on Friday after you're dead and stupid rules like that to not pay.
Quote: 13sI think that this is what I was getting at... Would people stop at all if they were winning? Do people ever stop if they win a little? Or even if they win a lot they may stop but will ultimately return at some point...
Let me stress that this is just a theoretical musing and I appreciate everybody's quantitative and qualitative analysis!
Doesn't matter. There expected bankroll after playing for a while is exactly the same as what they started with. If they win 'a lot' and keep playing, they are likely to stay up 'a lot' still.
Human nature doesn't come into to it. There is no profit on each spin of the wheel, so extra spins can not magic it up.
Human nature includes ripping people off like the unpaid chips and internet sites that just make cases up and don't pay. The profit would be in things not counted in edge like ripping people off with arbitrary rules. The Ohio Lottery kept 269 million in unclaimed winnings over ten years none of which would be counted as edge.Quote: thecesspitDoesn't matter. There expected bankroll after playing for a while is exactly the same as what they started with. If they win 'a lot' and keep playing, they are likely to stay up 'a lot' still.
Human nature doesn't come into to it. There is no profit on each spin of the wheel, so extra spins can not magic it up.
The aslo offer HE 0% BJ, which of course applies only to perfect basic (I think composition dependent perefct basic) again with low maximums but on that one they make money becuase most people do not the perfect basic for those rules and ven if they knew it they would still not follow it.
It does not cost much to betfair to maintain a HE 0% game (no dealers, no rent) but obviously they do have some costs.
On the other hand there are charges when you cash out, so that probably covers the costs for a zero profit game just for marketing purposes.
Not with a probability of 1Quote: geoffBecause of the larger resources the casino against the average bettor it will more than likely prevail.
against any player bankroll
example
casino has 100 trillion dollars (I doubt any casino has this available without extending credit, which would be suicide offering a 0% HE game)
100,000,000,000,000
a player has $10,000
the casinos chances of winning all the players 10,000 before losing all of it's 100 trillion is less than 1
0.99999999000000009999999900000001 = S
meaning it WILL lose, on average, all $100 trillion to a $10k player with probability >0 = 1-S or 1/1-S = 1 in 10,000,000,001
Ah ha! a casino should never fear a $10k bankrolled player.
How about one with $1 million, there would be many many players with even higher.
the casinos chances of winning all the players $1,000,000 before losing all of it's $100 trillion is less than 1
0.999999999900000000009999999999 = S
meaning it WILL lose, on average, all 100 trillion to a $1 million player with probability >0 = 1-S or 1/1-S = 1 in 100,000,001
100 million
the casino should never take that chance
many different people hit the lottery with higher odds against multiple times each year.
the casino can never have enough money to have their risk of ruin at 0Quote: geoffHowever the problem with this formula and what I expressed rather poorly before was that it assumes both sides go until one is bankrupt.
someone would take them for everything they have.
Those that think the way the casino makes it's money
is by players playing until they are busted
really do not at all understand why a casino offers it games with a house edge.
they short pay the player when the player wins and
take too much when the player does lose
all the casino needs is many many bets and a house edge
Sally
Quote: mustangsallyThose that think the way the casino makes it's money
is by players playing until they are busted
really do not at all understand why a casino offers it games with a house edge.
Yes, exactly, this.
How many times do you read (on this forum!!) that casinos do not need to fear counters because most of them are not properly bankrolled so they will bust out anyway? What nonsense.
While it is true that most under-bankrolled players will bust out, if the casino will lose money in aggregate over all the +EV bets that they let the player make.
Just like you can't beat a -EV game with a betting system, the casino can't make money from a +EV game by distributing the money in a certain way between the players. It's the same fallacy.
Also there are some carnival games, which have a small HE, but don't really make money as it costs more to put the dealer on than the table makes (due to nearly everyone betting minimum). Buy I think they're worth having as it makes that casino have something the other one in town/nearby doesn't, and some of them every catch on.
I would love to see the REAL accounting for that game.Quote: AceTwoI think Betfair has the zero game roullette basically as a gimmick (marketing) with low maximums.
The aslo offer HE 0% BJ, which of course applies only to perfect basic (I think composition dependent perefct basic) again with low maximums but on that one they make money becuase most people do not the perfect basic for those rules and ven if they knew it they would still not follow it.
It does not cost much to betfair to maintain a HE 0% game (no dealers, no rent) but obviously they do have some costs.
On the other hand there are charges when you cash out, so that probably covers the costs for a zero profit game just for marketing purposes.
Ultimately even the House has a finite bankroll.
Lets call it whip-out your wallet in the meantime.
If anyone (player our house) engages in a zero edge game playing forever, they are going bankrupt with probability of 100%.
This is not a question of EV (which is zero in this game), but of fluctuations. The thing about fluctuations regarding your bankroll is: You can still play after any huge win, but you can't play after any huge loss. In a zero edge game (which is almost a random walk), you will cross any set barrier from any starting point with probability of 100%. The only thing different from a random walk to the zero EV game is: Once you cross the bankrupt barrier, you stay there (bankrupt). Most people can imagine that this is true for the player, but rarely anyone can imagine this scenario for the casino.
Another view on the problem is: for a zero edge game, player and house sides are symmetric. Any long term result for player and house must be identical. (which it is: bankrupt by 100%).
The notion that the bankruptcy of one side is to a benefit of the opposing side, is simply not true.
Quote: MangoJNobody wrote the obvious answer to the original question. So here it is:
If anyone (player our house) engages in a zero edge game playing forever, they are going bankrupt with probability of 100%.
This is not a question of EV (which is zero in this game), but of fluctuations. The thing about fluctuations regarding your bankroll is: You can still play after any huge win, but you can't play after any huge loss. In a zero edge game (which is almost a random walk), you will cross any set barrier from any starting point with probability of 100%. The only thing different from a random walk to the zero EV game is: Once you cross the bankrupt barrier, you stay there (bankrupt). Most people can imagine that this is true for the player, but rarely anyone can imagine this scenario for the casino.
Another view on the problem is: for a zero edge game, player and house sides are symmetric. Any long term result for player and house must be identical. (which it is: bankrupt by 100%).
The notion that the bankruptcy of one side is to a benefit of the opposing side, is simply not true.
Unless a billionaire begins playing right? I assume it just depends who has more money if he flat bets every time.
Quote: MangoJIn a zero edge game (which is almost a random walk), you will cross any set barrier from any starting point with probability of 100%. The only thing different from a random walk to the zero EV game is: Once you cross the bankrupt barrier, you stay there (bankrupt). Most people can imagine that this is true for the player, but rarely anyone can imagine this scenario for the casino.
You might be right about the probability of 100% bankruptcy for infinite play with a set bankroll (however high).
The fulctuations are reduced % wise as the trials increase BUT increase in absolute terms.
So with a fixed bankroll, the probability of bankruptcy will be incease as these fluctuations incerase in absolute terms.
Infinity calculations are of course an impossibility using 'mormal' math.
So the answer is like, as the the trials approach infinity, probability of bankruptcy approaches 100% (never quite reaching it)
But for real world situations (say real world Betfair) the scenario is not like that.
The bankroll might be increasing over time.
Say Betfair allocates 1% of its $100m bankroll to this game, ie $1m and has low maximus etc, so the level of action in a year cannot exceed a certain amount.
Year 2, its bankroll has grown to $105m and it allocates 1%, ie $1.05m to the game and do forth in the future.
That, provided is controlled gives a 0% bankruptcy probability.
sorry.Quote: MangoJNobody wrote the obvious answer to the original question. So here it is:
If anyone (player our house) engages in a zero edge game playing forever, they are going bankrupt with probability of 100%.
public perception says the casino makes it's money because players play until they are broke and the casino has way more money than one player.
The OP obviously believes this that the house makes it's money by players losing and going broke instead of the truth from a house edge.
The public perception is "what is a house edge?"
They really are clueless at how a house edge even works.
here is an example
16Red they win, The casino pays them $18. they are happy.
so is the casino.
The casino should have paid the player $20 to have a fair game.
That is because there are 20 numbers to lose and only 18 to win
odds against winning is 20:18 and that should be the winning payoff
They short paid the player on a win of $18 by $2
Now a player bets $20 on Red and 0 spins
They lose.
The casino had odds against them of winning (and so their fair payout) at 18:20
so they should have only taken from a $20 loss... $18
(9/10 * 20 = 180/10 = 18)
another $2 taken but this time it was too much taken.
for the casino, it is just a numbers game.
they love lots of bets
bets
bets and more bets
keep them coming
The proof is in the Gambler's Ruin formula
for Becoming infinitely rich or getting ruined can be found in any Gambler's Ruin paper or book
like this one
http://www.columbia.edu/~ks20/stochastic-I/stochastic-I-GRP.pdf
after simple math that will not be repeated here
"Thus, unless the gambles are strictly better than fair (p > 0.5), ruin is certain."
That is why casinos do not gamble.
They have the edge.
Their gamble is getting in enough players to make enough bets.
Public perception easily takes hundreds of years to change at a minimum.
Blackjack as an example, the vast majority of all players that have ever played BJ believe that the Dealer's down card is a 10.
That is how to play the game they say.
Figure the dealer always has a 10 and play
Sally
Quote: AceTwo
So the answer is like, as the the trials approach infinity, probability of bankruptcy approaches 100% (never quite reaching it)
But for real world situations (say real world Betfair) the scenario is not like that.
Well, the thing about "approaching infinity": it is meant as the limiting value - and the limiting value is indeed 100%.
The thing about betfair offering the zero EV roulette game: There must be some politics about this game.
Math-wise, there is no reason to offer the game alone at all. As math tells you: unless there are countermeasures, they will always reach their loss stop limit with probability of 100%. So there is some kind of other countermeasure - one could be a stop win limit, a limited number of rounds per year, or a limited number of rounds per customer. No serious business would want the exposure to a significant amount of their capital to the fluctuations. As a serious business they will have an insurance against these fluctuations (and insurance companies are quite eager to sell, as the risk can be calculated quite precisely). This all costs moneys to betfair.
The only benefit for betfair would be to get some free advertisement about peoples talk (which is happing, as like now). That game might seriously cost them less than any other campain. But the benefit from the game alone will always be negative.
Quote: MangoJWell, the thing about "approaching infinity": it is meant as the limiting value - and the limiting value is indeed 100%.
The thing about betfair offering the zero EV roulette game: There must be some politics about this game.
Math-wise, there is no reason to offer the game alone at all. As math tells you: unless there are countermeasures, they will always reach their loss stop limit with probability of 100%. So there is some kind of other countermeasure - one could be a stop win limit, a limited number of rounds per year, or a limited number of rounds per customer. No serious business would want the exposure to a significant amount of their capital to the fluctuations. As a serious business they will have an insurance against these fluctuations (and insurance companies are quite eager to sell, as the risk can be calculated quite precisely). This all costs moneys to betfair.
The only benefit for betfair would be to get some free advertisement about peoples talk (which is happing, as like now). That game might seriously cost them less than any other campain. But the benefit from the game alone will always be negative.
Betfair charges to cash out so the 0% roulette works as an advertising piece and they get to take a cut from people who win so it's not really 0%.
Quote: MangoJIf anyone (player our house) engages in a zero edge game playing forever, they are going bankrupt with probability of 100%.
That assumes a fixed bankroll. It probably doesn't apply to either the casino or the player.
Quote: rudeboyoiA zero edge roulette table would only function as a loss leader to try to get players into the casino.
This. Much like poker rooms they would have to situate the game far away inside the casino, so you'd have to walk through the slots, video poker, electronic roulette, electronic craps, and the table games to leave.
Maybe they can figure out a way to turn the winnings they give out into comp dollars or gift shop certificates, to profit from retail gouging and breakage.
I was fairly surprised to hear that the game is coming to a town fairly near me next week - I might have incorrectly wrote it down as "Party Dice" known as Shoot Dice, but it's the same game. The maximums are fairly low (e.g. £25 on 4 at 2/1). Note the excessive use of the word "fair"!Quote: charliepatrick..."fair" games....Dice Magic....
Assume you have a totally informed gambler base and table limits that would prevent too-high swings in casino win/loss (even though neither player nor house would win or lose in the long run). No zeros, bets straight to the number pay 35 to 1, odd/even and red/black pay even money, first/second/third pay 2 to 1, etc. What do you think would be the consequences?
Would the casino attract roulette players who would in turn also play other games at negative EVs, spend money at shops and restaurants, pay for parking (at least if they're in AC), etc.?
Would players just crowd the roulette tables knowing that they have neither a player nor house advantage and not patronize any of the hotel/casino/spa/etc's other businesses, including -EV games?
Would the limited number of roulette tables get so crowded that patrons would effectively be forced to go somewhere else to entertain themselves?
Or is spreading -EV roulette more optimal? Because most folks wouldn't be totally aware of the house edge, know about it on some level or another but not care and chalk it up to entertainment money, e.g.? Would the casino be sacrificing the lost roulette business and not offsetting it elsewhere?
Or are there any other places where the casino could tantalize folks by offering zero-EV bets to draw folks in, and then meantime they'd play other games, eat, stay overnight, etc.?
Is this viable or is it just not justifiable? Would be interested to hear your thoughts.
Quote: mustangsally"Thus, unless the gambles are strictly better than fair (p > 0.5), ruin is certain."
Would it be technically more accurate to revise this to "unless the gambles are strictly fair or better (p less than or equal to 0.5 with bets payed and taken at even money), ruin is certain?"
Might be splitting hairs but I'm basically asking, "if I'm making bets with zero EV, is ruin still certain?"
Cheers thanks
It's an interesting topic whether casinos should have 0HE offers, same as whether supermarkets should sell cans of baked beans at -2p.
