No House Edge -- How Will It End?

[deisik]

As this topic has shown, there are many people who erroneously assume that on a 50-50 win chance and no house edge in a game of chance, there'll be no clear winner on an infinite timescale, i.e. until someone busts with no time limits imposed (a kind of "a zero-sum game"). In fact, I was rather surprised with this view because it is pretty simple to prove the opposite, which I'm going to do below

For simplicity's sake, let's consider a simple game of coin tossing. Two players are staking 1 dollar at each toss of a coin. It should be obvious without any further explanation that if they have only 1 dollar, one of them is going to bust straight away. If they have 10 dollars each, it will take a little bit longer but one player will still bust in the end, and it was estimated that it is going to happen under just 200 tosses on average

It doesn't take a lot of brain power to see the overall dynamic, and draw a reasonable conclusion that it doesn't really matter what fraction of the bankroll the two players start off with since on a long enough timescale one of them is still set to bust. It could be further generalized that on an infinite timeframe gambling on a 50% win chance with a finite bankroll inevitably ends in a bust of one of the players. This is what I would call a statistical certainty

And this is in stark contrast to what I've seen people claim. So what is your opinion?


To avoid ambiguity and misunderstanding, I changed the part "it doesn't really matter what fraction of the bankroll the two players stake at each toss" to "it doesn't really matter what fraction of the bankroll the two players start off with"

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[DarkDays]

When playing on a 50/50 odds PvP, the player with the most potential attempts will be least likely to bust.

For example, a player with $10,000 going up against somebody with $10 on a 50/50 odds table, the latter is most likely to first to bust—simply because he only gets 10 attempts vs 10,000 for the other guy.

If you scale this to infinity, both players will eventually bust.

[tyKiwanuka]

It doesn't take a lot of brain power to see the overall dynamic, and draw a reasonable conclusion that it doesn't really matter what fraction of the bankroll the two players stake at each toss since on a long enough timescale one of them is still set to bust. It could be further generalized that on an infinite timeframe gambling on a 50% win chance with a finite bankroll inevitably ends in a bust of one of the players. This is what I would call a statistical certainty

Ok, so I have a finite bankroll of 100,000,000,000,000 USD and I stake 0.00000000000000000000000000000000000000000001% of it with every bet. My Stake is divisible into any imagineable amount - it can get as low as I want or as I need it to be, if I get very unlucky and lose 100000000000000000000000000000000 bets in a row. How can I bust ? 

Even if I have only 0.01 USD left and I always stake 50%, the next bet would be 0.005, next bet 0.0025 etc.. I can't go broke, it's not possible.

[deisik]

For example, a player with $10,000 going up against somebody with $10 on a 50/50 odds table, the latter is most likely to first to bust—simply because he only gets 10 attempts vs 10,000 for the other guy

That's an extension for the case of different bankrolls

And that's also the reason why an extremely wealthy casino (or way wealthier than all its players combined) doesn't need a house edge at all to stay profitable. But that's a point of discussion in this thread. The present topic is a sort of spin-off of that thread to deal with a certain misconception that was revealed there

Ok, so I have a finite bankroll of 100,000,000,000,000 USD and I stake 0.00000000000000000000000000000000000000000001% of it with every bet. My Stake is divisible into any imagineable amount - it can get as low as I want or as I need it to be, if I get very unlucky and lose 100000000000000000000000000000000 bets in a row. How can I bust ?

As long as your bankroll is finite, the staked amount is not zero, and remains the same (e.g. 1 dollar), on an infinitely long timeframe you will either bust or win provided the same terms are honored by your opponent too

Even if I have only 0.01 USD left and I always stake 50%, the next bet would be 0.005, next bet 0.0025 etc.. I can't go broke, it's not possible

This is a separate case which needs to be dealt with independently (read, it is a different case)

[tyKiwanuka]

Ok, so I have a finite bankroll of 100,000,000,000,000 USD and I stake 0.00000000000000000000000000000000000000000001% of it with every bet. My Stake is divisible into any imagineable amount - it can get as low as I want or as I need it to be, if I get very unlucky and lose 100000000000000000000000000000000 bets in a row. How can I bust ?

As long as your bankroll is finite, the staked amount is not zero, and remains the same (e.g. 1 dollar), on an infinitely long timeframe you will either bust or win provided the same terms are honored by your opponent too

Yes, this is a correct statement. And now ?

It's against proper money management though, since when you are down to 1 USD, you shouldn't stake that 1 USD on one bet/toss And if the (finite) bankrolls are big enough, assuming 1USD stakes, this will take like forever - at least longer than this world will exist

And with "my" case I can't go broke, which is more realistic imo - the staking with % of your bankroll that is. Always staking the same amount regardless of your bankroll is not what any gambler should do.

I admit, that I have trouble to understand what you are trying to achieve with this and the other thread. This is so far from reality, that it's just theoretical discussion, which is of course fine and interesting too. But it seems to me, that you are trying to prove something, what will have no added value to you, since it's not realistic to happen in real world.

[deisik]

Ok, so I have a finite bankroll of 100,000,000,000,000 USD and I stake 0.00000000000000000000000000000000000000000001% of it with every bet. My Stake is divisible into any imagineable amount - it can get as low as I want or as I need it to be, if I get very unlucky and lose 100000000000000000000000000000000 bets in a row. How can I bust ?

As long as your bankroll is finite, the staked amount is not zero, and remains the same (e.g. 1 dollar), on an infinitely long timeframe you will either bust or win provided the same terms are honored by your opponent too

Yes, this is a correct statement. And now ?

Now let's wait for other folks to come to terms with this

It's against proper money management though, since when you are down to 1 USD, you shouldn't stake that 1 USD on one bet/toss. And with "my" case I can't go broke, which is more realistic imo - the staking with % of your bankroll that is. Always staking the same amount regardless of your bankroll is not what any gambler should do

If we thoroughly follow this logic through, then you shouldn't be tossing coins in the first place

How come? Cause if you assume proper money management, you should assume it for both sides, right? Then the whole endeavor becomes an exercise in futility whether your goal is to win or not to bust as there are only two outcomes possible, a total win or a complete loss. In practice, though, you typically can't stake less than the base amount previously agreed upon, and you can't leave when in profit either (street gambling rules). So someone has to lose and accept it

I admit, that I have trouble to understand what you are trying to achieve with this and the other thread. This is so far from reality, that it's just theoretical discussion, which is of course fine and interesting too. But it seems to me, that you are trying to prove something, what will have no added value to you, since it's not realistic to happen in real world

Ever gambled on the street? This topic has everything to do with how things are going to pan out there. And you are in for a big surprise if you expect "a zero-sum game" there. It is also called "learning it the hard way". Can anything be more practical and realistic?

[crwth]

It's merely a reliable way to test your different tactics and strategies in a game. For the house, it wouldn't be so ideal, though, because if you have no edge, there's no additional chance for the house to win, no profit for them. For players, it's ideal, but there wouldn't be anything good coming out of it for the house, so that isn't happening. It will end only in the player in profit and the house losing the "chance" or vice versa.

There's not infinite gameplay, there would be a time where one side is having more "winning" than the other, so whichever comes first, that's the game-ender. It's bound to luck, I guess.

[tyKiwanuka]

Yes, this is a correct statement. And now ?

I think everyone will agree. And then ? What is your conclusion for real world ?

Ever gambled on the street? This topic has everything to do with how things are going to pan out there. And you are in for a big surprise if you expect "a zero-sum game" there. It is also called "learning it the hard way". Can anything be more practical and realistic?

I never gambled on the street, no, sorry And while I agree this is being "practical and realistic", it's unrealistic again then. You are comparing a realistic scenario with unrealistic assumptions and rules.

Please give an example how such a "street game" would look for you with all the parameters and what you would expect the result to be.

Lets say you have 1,000 USD bank roll and there are 200 players with 1 USD bankroll each. Now you toss a coin with each one of them, stake 1 USD. What do you expect your profit to be ? In first round you would eliminate 100 players. 100 players remain with bankroll of 2 USD each; your bankroll is still 1,000. Then in second round, third round etc. you would keep eliminating players, until there is only one player left with bankroll of 200 and you still have your 1,000 bankrolll. You will eliminate that player too sooner or later. And then we are here again:

As long as your bankroll is finite, the staked amount is not zero, and remains the same (e.g. 1 dollar), on an infinitely long timeframe you will either bust or win provided the same terms are honored by your opponent too.

Is all this a realistic scenario ? No. Players that are in profit will leave the game before it ends. Now you will say: but, street rules. Yes, street rules, but no sane person will play against you.

[deisik]

Yes, this is a correct statement. And now ?

I think everyone will agree

Well, you can't speak for everyone. Moreover, you can't even assume that everyone is going to agree with this statement in the first place

Ever gambled on the street? This topic has everything to do with how things are going to pan out there. And you are in for a big surprise if you expect "a zero-sum game" there. It is also called "learning it the hard way". Can anything be more practical and realistic?

I never gambled on the street, no, sorry

I gambled, like a lot. Lost as much, due to a failure to see and understand how things work in practice and for trusting other people a way too much. Remember that climax moment from Interstellar (probably worth watching the whole movie)?

Please give an example how such a "street game" would look for you with all the parameters and what you would expect the result to be

Does coin tossing count?

If it counts, then you can start out with the example presented in the OP. A simple setup, known for literally millennia. You have 100 dollars and I have 100 dollars, the base bet is 1 dollar. Someone has to bust and relatively fast at that. Pretty much a "street game" if you ask me, and nowhere near a "zero-sum game" (as you mean it), Certainly worth trying it out with your friends, to feel it with your skin in the game, so to speak

As long as your bankroll is finite, the staked amount is not zero, and remains the same (e.g. 1 dollar), on an infinitely long timeframe you will either bust or win provided the same terms are honored by your opponent too.

Is all this a realistic scenario? No. Players that are in profit will leave the game before it ends. Now you will say: but, street rules. Yes, street rules, but no sane person will play against you

To begin with, no sane person will gamble on the street. Yes, I was basically insane back in the day to gamble on the street if this is what you want to hear. But I was young, stupid and stubborn as youths can sometimes be. You can't leave while in profit unless the other side agrees or you have agreed beforehand upon the time when it is allowed to take dough and run. Indeed, if you could force your way out you would, but no one would be playing with you again

[mu_enrico]

A player that has sufficient bankroll cannot go bust mate, because the RTP will always return to the theoretical RTP of 100%. Yes, there will be variance; however, it will return to the theoretical after xxx bets. Meaning if a player wagers $1 he will get $1 back.

Anyways, sure one can get bust if the bankroll is not sufficient. *I use the term "sufficient" because I believe we don't need to have an infinite bankroll in order to see the "stability."

[Mauser]

A player that has sufficient bankroll cannot go bust mate, because the RTP will always return to the theoretical RTP of 100%. Yes, there will be variance; however, it will return to the theoretical after xxx bets. Meaning if a player wagers $1 he will get $1 back.

Anyways, sure one can get bust if the bankroll is not sufficient. *I use the term "sufficient" because I believe we don't need to have an infinite bankroll in order to see the "stability."

The variance can be quite large, but if the number of games is fairly large and the bankroll is big enough, both players should just end up with their starting balance.

So why would someone play a PvP game with 50% winning chance?

Also, who is running the site? No expenses, or is just a simulation?

I think PvP only becomes interesting if people believe they have an edge over the opponent, but if its clear from the start everyone has a 50% chance, there would be no fun involved.

[deisik]

A player that has sufficient bankroll cannot go bust mate, because the RTP will always return to the theoretical RTP of 100%. Yes, there will be variance; however, it will return to the theoretical after xxx bets. Meaning if a player wagers $1 he will get $1 back

So we have two conflicting and mutually exclusive ideas

And that's actually a good thing because it allows us to work out a constructive approach that will lead to a correct conclusion, whatever it might be. If what you say is true and we know that with small bankrolls (relative to bet amount) someone is going to bust, there should necessarily be a tipping point, a cusp, where the function (its derivative) changes the sign. In more mundane terms, there should be an exact bankroll to bet amount ratio above which it statistically becomes a "zero-sum game", no matter how long you are going to play. That's highly suspicious if you ask me

So why would someone play a PvP game with 50% winning chance?

To find out who is luckier?

[bbc.reporter]

I reckon that there might be a misunderstanding.

The infinite toss theory assumes that you also have infinte bankroll for the very long timescale to occur and for the wins and losses to always become 50-50.

Place a 1% house edge to the infinite bankroll, infinte toss game, what result do you have?

[swogerino]

The infinite theory is correct but I don’t see any point as why should we know how it will end when in fact nowadays no one like to play PvP as we prefer more to play against a casino.I think that when two players start with the same bankroll in a no house edge game like PvP there will be equal chances for both of them to go bust.What I mean is that the chances for them to go bust first is 50 percent.

[el kaka22]

Why too much of concerns about house edge? Will you ask for no-fee trading on exchanges or tax free transactions from your government? Basically, I am not seeing house edge will be having any big impact on gambler's experiences but if you remove, it will get big impacts on house's profit levels.

Moreover house edge is a concern for profit seeking gamblers but as per I have seen most gamblers here are playing only to entertain themselves and for them paying house edge is not a big thing.

People had already tried this by having a dedicated token: Edgeless.

I guess no-house-edge concept may not end now but it may open doors for many other innovations because some houses may plan up based on this so that they want to stand tall to attract gamblers.

[deisik]

The infinite toss theory assumes that you also have infinte bankroll for the very long timescale to occur and for the wins and losses to always become 50-50

That's not the case here

It is indeed about a very finite and, moreover, equal bankrolls. So the question is that whether one of the players is going to bust or it will be a "zero-sum game", i.e. no one winning or losing anything (give or take) provided the player's bankrolls are big enough to allow for a very large number of tosses

We have two polar opposite outcomes which exclude each other, and I'm utterly curious to find out which one is actually going to play out in real life (as it may have very important and practical implications in other domains). So far it looks more like one of the gamblers will invariably bust eventually

[Lakai01]

-snip-
Lets say you have 1,000 USD bank roll and there are 200 players with 1 USD bankroll each. Now you toss a coin with each one of them, stake 1 USD. What do you expect your profit to be ? In first round you would eliminate 100 players. 100 players remain with bankroll of 2 USD each; your bankroll is still 1,000. Then in second round, third round etc. you would keep eliminating players, until there is only one player left with bankroll of 200 and you still have your 1,000 bankrolll. You will eliminate that player too sooner or later.
-snip-

The risk scenario is based purely on PvP, which will hardly ever happen in the "real world". This scenario here which tyKiwanuka posted reflects the world of online casino very well: 1 casino vs. an undefined number of players.

Let's think the scenario described here further, so the casino at the end of the day again has 1000 USD. But in reality it is much less:

• During the time of the casino operation employees, servers and infrastructure must be paid.
• There were ev. advertising campaigns like here in the forum by signature. So you have to pay the campaign participants.
• It was developed further on new games to keep the players happy in the future.
• ...

So you have not lost any money by just playing, but if you include the additional costs of a casino, you will see that at the end of the day you'll be left with less money than when you started and will eventually go bankrupt in no time if you don't generate any income (e.g. by getting a house edge in place).

[deisik]

Lets say you have 1,000 USD bank roll and there are 200 players with 1 USD bankroll each. Now you toss a coin with each one of them, stake 1 USD. What do you expect your profit to be ? In first round you would eliminate 100 players. 100 players remain with bankroll of 2 USD each; your bankroll is still 1,000. Then in second round, third round etc. you would keep eliminating players, until there is only one player left with bankroll of 200 and you still have your 1,000 bankrolll. You will eliminate that player too sooner or later

Why all the fuss with 200 players?

The whole task can be reduced to just one player with 200 dollars. Then it is a bankroll of 1000 USD versus a bankroll of 200 USD, the point of discussion in this thread (of which you are certainly aware). But that's all side issues as the main issue here is still not settled decidedly, i.e. whether it is a bust and a win or a definite no-win for either player if the bankrolls are the same as well as large enough in a PVP game like heads or tails (with square odds in mind). And yes, it is important to know the answer to this dilemma (especially if it is a "zero-sum game", after all), and it is not like everyone agrees with the conclusion drawn in the OP

[tyKiwanuka]

Sorry, if my comments offend you, that is not my intention, don't take it personal

Why all the fuss with 200 players?

That was in reference to your previous thread, which you referenced in the first post here. In the end it boils down to 2 players going against each other for the win of all the money in the game - no matter how many players joined the game initially.

The whole task can be reduced to just one player with 200 dollars. Then it is a bankroll of 1000 USD versus a bankroll of 200 USD, the point of discussion in this thread (of which you are certainly aware). But that's all side issues as the main issue here is still not settled decidedly, i.e. whether it is a bust and a win or a definite no-win for either player if the bankrolls are the same as well as large enough in a PVP game like heads or tails (with square odds in mind). And yes, it is important to know the answer to this dilemma, and it is not like everyone agrees with the conclusion set forth in the OP.

From a theoretical point of view, one player will bust in the end. This could be the player with the 200 USD, but also the player with the 1000 USD. It's more likely to be the player with the 200 USD though, because to put it very simple: It's more likely to occur a 200-winning-streak with 50/50, than to occur a 1000-winning streak with 50/50. But both are possible.

From a practical point of view......well.....I guess you know what I would write here

[arallmuus]

and it is not like everyone agrees with the conclusion drawn in the OP

Everyone doesnt have to agree with the conclusion but it is one of the conclusion that would happen. In the OP however you are insisting this

It could be further generalized that on an infinite timeframe gambling on a 50% win chance with a finite bankroll inevitably ends in a bust of one of the players. This is what I would call a statistical certainty

So let me draw these conclusions . Assuming that there is no house edge or in the case of two people tossing coin game with exactly 50% chance for each player, Also finite bankroll and infinite time to play

There would be several conclusion after X number of game
1. Each player's bankroll would remain the same
2. One player will have higher bankroll and another with lower bankroll than what they started with
3. One would be the winner while one bust


It isnt 100% certainty that one will bust while one win because at exactly 50% chance to win with no edge, no one could tell how things will be after several number of games