Built in house edge

Alright so I wasn't really sure where to put this, it probably would have done better under "questions" but I would have felt weird asking two consecutive questions in that category but...

I'm wondering if there is an established name or thought process when it comes to the house having basically an infinite amount of money as compared to the players. Let's say that I walk into a casino and play a game with absolutely 0% house edge. Not .1, not .01, absolutely nothing. Every other game (1:1) I should theoretically win. Let's take an extreme case: I'm playing $50 per hand of this game with a $200 bankroll. In thousands of simulations, the variance will get to me and I should lose a good portion of my bankroll pretty quickly. On the other hand, there would be a lot of simulations where I win a lot of money as well. Now comes my main question: There would be a handful of simulations where I might get up by $300-400, then come back down to $200 or even lose it all. This compares to (if I could go into a negative bankroll) where I might go down $300-400 and come back up to break even or maybe even turn a profit. Because of my bankroll limitations, I would end out losing money on AVERAGE in this 0% edge game. In the end, simply put, is there a term or idea for the aspect that the casino can handle infinite variance compared to the players?

I agree with you. I think a casino would win money on a zero house edge games because the casino doesn't face risk of ruin. More players would be greedy and lose their bankroll than would walk away.

Hundreds of people walking into a casino with limited bankrolls is different than one person with the same size bankroll as the casino.

I don't know any terms other than risk of ruin. I don't think it would be a good business strategy since the casino would also face wide variance, but mathematically I think they would still win.

Yeah I'm curious how much casino revenue comes from risk of ruin. I would think a very high amount, I mean a lot of newbie gamblers don't have risk of ruin planned out at all... which can cause a lot of problems. When I first went to Vegas I had a gambling budget of $300 for three days... now I bring $1500 for a single day.

Quote: ahiromu

Yeah I'm curious how much casino revenue comes from risk of ruin.

There's an old thread where the Wizard weighed in to dismiss the idea of Gambler's Ruin. Now, true, we are calling it Risk of Ruin here, which is real of course. But posters are concluding that Risk of Ruin is a way to make money for the Casinos, and that is what is in dispute.

From what I know about it, the times you go bust are supposed to be balanced by when you win, and not a way for casinos to make money. Note that the Wizard has an interesting spin [see link].

The idea that forcing Ruin is a correct strategy for a player in a poker tournament, where elimination is a goal and a player cannot return, still makes sense to me BTW.

/https://wizardofvegas.com/forum/questions-and-answers/gambling/332-question-for-the-wizard-gamblers-ruin

There is at least one aspect of this that I don't have my head totally wrapped around. ahiromu's initial description considers a large number of "simulations" of a single gaming experience, and the risk of ruin in even a game with zero house advantage. For actually playing in casinos, most of us are instead expecting to have multiple gaming experiences (sessions, visits, whatever) with only one actual "simulation" of each.

Consider the scenario of the player who supposedly loses his entire bankroll but some time later (hours or months) comes back for another session. Did he really experience "ruin", or did he just take a break from his game? This obviously assumes that his declared bankroll didn't represent all of the funds that could be made available. How does that aspect affect the concept of risk of ruin, if at all?

In contrast, consider a player who wins, reaches his win goal, and walks away. If he really expects to play again some day, has he avoided ruin? It seems to me, it's all a matter of what temporary status we have at each moment we walk away from a table, unless there is true ruin that drives the desperate never to be able to return.

When I get to Vegas tomorrow, I will have some amount of cash with me. I plan to gamble in multiple casinos in Las Vegas, Mesquite, Primm, California, Laughlin, and maybe even in Searchlight before returning home a little over a week later. Whether I come out ahead, lose every cent I brought with me and more, or stop somewhere in between, I am quite confident that if I survive, I will be back in a casino again some day, almost certainly in the next few months. If I am sure that I will be willing and able to play the games again in the future, does that mean I have no risk of ruin on my trip?

Id also have to imagine for this to work youd have to have a 'spending' limit for the players- or you could have a whale want to take advantage of the even odds and if his variance gets high enouhg with as many as they can bet- the casino would be in trouble. even at $500,000 a hand (which if the game had even odds I coudl definatly see a whale making) with the variance involved the casino could be hurting quickly.

"Ruin" solely means for that bankroll, not for life and not even for that trip.

Its the same way with Winners and Losers. Winners DO pay for those fancy casinos. So do losers. Most will come back another day with an additional bankroll ... and that term Winner or Loser changes.

Its possible that you have a particular bankroll in mind at each of those casinos ... well I hope you don't face ruin in any of them, but if it happens... you know you'll be back next year. And so do they! That is why the casino considers comps to be an investment. Its your future loyalty and future bankroll they are thinking about.

If we simulated players making flat bets, then I don't think the house would gain anything from wiping out the players in a 0-sum game. I think the house hold would be 0. This would also assume the players have stop win point.

If, however, players increased their bets after winning, or chased losses, then they would increase their risk of ruin, and the hold would increase. I think, at least.

It'd be interesting to simulate, especially if you put in a mix of playing styles... you could probably simulate quite well.. and I bet someone, somewhere has done this commercially.

casinos would have swings with the players while slowly being ground down by expenses until inevitably broke.

Quote: thecesspit

This would also assume the players have stop win point.

Do I really need to say it?




Players tend to have stop TIMES, but not win dollar points.

Quote: DJTeddyBear

Quote: thecesspit

This would also assume the players have stop win point.

Do I really need to say it?




Players tend to have stop TIMES, but not win dollar points.

I think they have both, to be fair.

There are certainly people that have win dollar amounts. But most people stop for three reasons. There bankroll is gone, they have run out of time because they have to go somewhere, or they have had a bad run that stopped a long winning streak.

Slot machines favor awards of roughly 100 times the unit bet, because it is enough to get people excited, but not enough for them to gather their winnings and go home. The majority of slot player quit when their bankroll runs out.

It is hard not to think that risk of ruin is part of the ways that a casino makes a profit. Greed will always win over prudence.

To answer the question initially posed, if the casino offered a game with exactly zero house edge, then it still have zero advantage over the general public, regardless of what kind of betting strategy the players followed. The argument that the casino would still make a profit is that players would run out of money sometimes, and the casino never would. That is true. However, that is offset by the fact that players who went bust might have lost even more money if that hadn't. That is why casinos would prefer players didn't run out of money. They would like to keep them playing as much as possible. It isn't just for the players benefit there are lots of ATM machines in the casino.

A similar question is what country would have a higher percentage of female babies:

Country A) Each woman has exactly one child.
Country B) Each woman keeps having children until she has one boy, and then stops.

Very clear answer. Thanks Wizard!

So country A with four women named alpha, bravo, charlie, delta has 2 boys and 2 girls.

So country B with four women name alpha-b, bravo-b, charlie-b, delta-b has
2 boys and 2 girls in first generation
1 boys and 1 girls in second generation
possibility of 1 boy or 1 girl in third generation
possibility of 1 boy or 1 girl in fourth generation

So country A and country B has the same percentage of female babies. Their birthing strategy did not change the underlying 50/50 odds.

Quote: Wizard

A similar question is what country would have a higher percentage of female babies:

Country A) Each woman has exactly one child.
Country B) Each woman keeps having children until she has one boy, and then stops.

theyre both equal

i forget how to do sums of limits but you can visualize it here.

GB = 1/4 GGB = 1/8 GGGB = 1/16 GGGGB = 1/32...

i put the values into excel

0.25
0.125
0.0625
0.03125
0.015625
0.0078125
0.00390625
0.001953125
0.000976563
0.000488281
0.000244141
0.00012207
6.10352E-05
3.05176E-05
1.52588E-05
7.62939E-06
3.8147E-06
1.90735E-06
9.53674E-07
4.76837E-07

and the sum of these values are .49999953

To do sums of infinite series define the variable S
eqn 1) S = 1/4 + 1/8 + 1/16 + ...
eqn 2) 2*S = 1/2 + 1/4 + 1/8 + 1/16 + ...
eqn 2 minus eqn 1) S = 1/2