Is EOR Useful? (Split from OftM Opening thread)

teliot,

DJTB mentions a link on your blog to the discussion: sorry for the inconvenience if the HE/EoR is the subject of that link. HERE is the permalink to the start of this thread if you need to update your blog. Thanks again for the insight on the topic; a very important one for me.

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I can't comment on whether the EoR has any mathematical value, it isn't my area of expertise.

But from a player's perspective, telling a player they are playing a game with an HE of X% is translated (by most players) to mean that if you multiply that percent by the sum of every dollar they wager on the game gives them the expected -EV.

That isn't correct and to me that is the reason that EoR has a very practical application to casino players and is a fair way to compare games with multiple wager decisions. It tells players what the house edge is expressed as a percentage that is applied towards every dollar they wager when they play the game correctly.

That has value in analyzing a game.....I don't know if it has mathematical value, but it has value in a practical sense and that is important IMHO.

Quote: Paradigm

But from a player's perspective, telling a player they are playing a game with an HE of X% is translated (by most players) to mean that if you multiply that percent by the sum of every dollar they wager on the game gives them the expected -EV

Most players don't want that. They have no idea what HE means. They don't even understand the concept of percent, having barely made it through 8-th grade math. But, they do want to have some sense of how long their money will last at the game. In that sense, N_0 = (sd/ev)^2 is the perfect number, if you have to give a number at all. It is the very definition of what "the long run" means for the game.

Quote: Paradigm

But from a player's perspective, telling a player they are playing a game with an HE of X% is translated (by most players) to mean that if you multiply that percent by the sum of every dollar they wager on the game gives them the expected -EV.

I suspect that that isn't true. Most players do not understand the terms that you just used. Out of the ones who do, I'd suspect that most of them know the correct definition of house edge.

Should we equate a craps game with double odds as the same game for the player as a craps game with 100X odds? The HE on the pass line only bet is 1.41% so under your argument, the two games are the same.

I disagree......and I think the average craps player knows that a double odds game is not as good for them in the long run as a 3/4/5 odds game or a 10X odds game or 100X odds game. Telling them there is no difference for them in the long run playing a 2X game vs. a 100X game is incorrect. I grant you that very few players make a 100X bet, but double odds vs. 3/4/5 is a very real difference that is implemented by many dice players.

Quote: Paradigm

Should we equate a craps game with double odds as the same game for the player as a craps game with 100X odds? The HE on the pass line only bet is 1.41% so under your argument, the two games are the same.

What argument? Who ever said that games with the same house edge are the same?

The two games you described have the same house edge. They are not the same game. A game is fully described by a function that maps possible outcomes to probabilities (ie, a random variable).

House edge is just one measure. It is extremely useful for some things -- particularly, it makes calculating your expected loss trivial if your initial bet does not change. But it is just one measure. It does not fully describe the game. Attempting to describe an entire random variable with a single number is a waste of time.

Quote:

I disagree......and I think the average craps player knows that a double odds game is not as good for them in the long run as a 3/4/5 odds game or a 10X odds game or 100X odds game.

They may "know" that, but, if they don't change their pass line bet, they are wrong. They will lose the same amount.

Do most players make smaller pass line bets on games that offer higher odds? That has not been my experience. I think that most players bet table minimum on the pass line regardless.

Quote: beachbumbabs

teliot,

DJTB mentions a link on your blog to the discussion: sorry for the inconvenience if the HE/EoR is the subject of that link.

Actually, Eliot's blog entry was about OFTM, and a possible advantage using hole carding.
http://apheat.net/2014/06/11/one-for-the-money-hole-card-play/

Quote: AxiomOfChoice

The two games you described have the same house edge. They are not the same game. A game is fully described by a function that maps possible outcomes to probabilities (ie, a random variable).

And to me EoR helps in explaining the differences between the two games where the HE doesn't. I am disengaging from the discussion but appreciate the exchange :-)

Quote: AxiomOfChoice

A game is fully described by a function that maps possible outcomes to probabilities (ie, a random variable).

I don't believe you can determine EoR from the game's RV. In that sense, the RV doesn't fully describe the game. For example, in 3CP you can lose 1 unit in two different ways (fold or have a straight that loses). These correspond to different total wagers (1 unit vs. 2 units), and hence contribute differently to the EoR. The fact that EoR can't be described by the distribution is reason enough to disregard it.

Quote: teliot

I don't believe you can determine EoR from the game's RV. In that sense, the RV doesn't fully describe the game. For example, in 3CP you can lose 1 unit in two different ways (fold or have a straight that loses). These correspond to different total wagers (1 unit vs. 2 units), and hence contribute differently to the EoR. The fact that EoR can't be described by the distribution is reason enough to disregard it.

I know; I pointed that out in a previous post :) (Edit: Here)

I came to the same conclusion that you did.

Suppose I walk up to a table that says minimum bet $5, the questions I want to know (assuming I'm betting minimum):-

(i) What is my expected loss per hand when playing the game (i.e. HE) - this gives me an understanding of the expected cost of playing the game per hour and whether I'll get value for money - a high HE means it costs more to play this game than others;

(ii) How much money am I usually having to wager (e.g. BJ sometimes you have to split and double, 3CP usually you'll need a raise, some games have two compulsory bets then others) - this affects the required bank roll given one might have thought the typical bet was only $5 (the assumption is you need to ensure you have the available money to handle most situations; or if you're down to your last $x, can you afford to play this game - with 3CP you need two bets' worth to make the Ante bet);

(iii) What is the typical pattern of wins - mathematically what is the variance - am I just needing the occasional big win (typical in poker-style games where you need a good hand every now and then to keep you going) or is it regular win-some lose-some game (like BJ).

The one thing I dislike is saying a $5 game has x% EoR when I have no idea how many bets one typically makes. So saying OFTM has x% EOR doesn't really answer the question "How much does it cost on average to make the initial $5 bet?".

I have pondered the question (is EoR useful) and came to the conclusion that -

A. It has the same default as HE: it is based on an original wager, which is arbitrarily depending on the presentation of the game.
As an example let us use Caribbean Stud, where the ante is 1 unit but it would be silly to play if you don't have 3, because that's the only way to win anything. If you have only 1 unit left in your bankroll, the only thing you can do is fold, with certainty of losing it.
So, in an alternative presentation, one might say that the original wager is actually 3, and the player may get something back when they fold (similar to surrender in blackjack).

Should H.E. be based on 1 unit or 3 units?
The exact same question arises for EoR: should you consider that you sometimes wager 1 and sometimes 3, or is it always 3?

This is one example, but you may build a similar alternative description for any game.

B. I have shown an example here of a simple roulette martingale, which had the same EoR as another but was undisputably a better bet (better prob of winning the same amount in a simple two-results setting).

C. A problem I have with the definition of EoR is mathematical: it computes the expectation of gain divided by an expectation of wager. Any statistician would tell you that the correct computation is the expected ratio of gain on wager. And they do not lead to the same result. (Axiom of Choice, we had a discussion on that one about Expected Count in blackjack.)

Why you would want to compute the expectation of the ratio is beyond me. So is the question of why you'd project this desire onto statisticians.

The expectation of (loss / total bet) is truly a useless measure. It doesn't allow you to calculate anything useful. Why do you care about this number? What does it represent to you?

Come on, guy !!!

I showed you an example where the expected number of 10's in a deck, divided by the excpected number of cards, was different from the prior ratio of 10's in the deck. You did all you could to present it as folly and stupidity and how it was "obvious" that the expected ratio would remain the same.

Now you take the exact opposite stance !!!

Are you trying to make me lose my temper ?

Quote: kubikulann

Come on, guy !!!

I showed you an example where the expected number of 10's in a deck, divided by the excpected number of cards, was different from the prior ratio of 10's in the deck. You did all you could to present it as folly and stupidity and how it was "obvious" that the expected ratio would remain the same.

Now you take the exact opposite stance !!!

Are you trying to make me lose my temper ?

The situations are completely different.

In the case of blackjack, the true count is linearly correlated with the edge. You care about the expeted count if you care about the expected edge. Expected number of 10s / expected number of cards is beyond useless. It doesn't tell you anything.

In this case, we are concerned with determining how much someone will win or lose. The expectation of the ratio does not tell you that. Therefore, it's completely useless.

Do you just like coming up with useless measures of things? Are you intentionally looking for things that you can calculate that give you absolutely no useful information whatsoever?

Quote: AxiomOfChoice

The expectation of (loss / total bet) is truly a useless measure. It doesn't allow you to calculate anything useful.

If that is true (and I do not pretend otherwise, I just dont know - or care), then the EoR is even more useless, for the exact same reasons.

Quote: AxiomOfChoice

Do you just like coming up with useless measures of things? Are you intentionally looking for things that you can calculate that give you absolutely no useful information whatsoever?

Why do you need to make it a personal insulting matter ? Do you have an ego problem? Is a mathematical debate not enough for your ridiculous little pampered-up ego-challenged person ?

EDIT: as I'll be suspended, let me take the opportunity to add "fucking moron".

Quote: kubikulann

If that is true (and I do not pretend otherwise, I just dont know - or care), then the EoR is even more useless, for the exact same reasons.

I actually said earlier in the thread that I thought that EoR was useless as well. However, is is not quite as useless as this measure. At least if you multiply it by the average total bet amount, you get a useful number (total expected loss per hand). So, perhaps, it is not quite useless.

I don't see any way to manipulate E(loss/total bet) and get something that anyone cares about. Do people really care if they lose $5 more on one hand and $5 less on another? In the end they just care how much they are up or down.

Quote: kubikulann

Why do you need to make it a personal insulting matter ? Do you have an ego problem? Is a mathematical debate not enough for your ridiculous little pampered-up ego-challenged person ?

EDIT: as I'll be suspended, let me take the opportunity to add "fucking moron".

Well, I have to admit I was going to call it a draw with warnings in both directions, but the edit forces my hand. See you soon.

B^3, this is a situation where you definitely *should* let AoC correct the other party. Saying that mathematically useless ideas are useless is important, especially when those opinions come from experts.

Quote: teliot

B^3, this is a situation where you definitely *should* let AoC correct the other party. Saying that mathematically useless ideas are useless is important, especially when those opinions come from experts.

Thanks, teliot. AoC comes off as provocative and condescending sometimes; he has not said anything suspense-worthy, and I was going to ask him to dial down the tone a notch, while giving kubi a little latitude for temper, short of suspension. It is important for people to be heard in opposition, I agree, and it's definitely in the spirit and intent of the board. OTOH, other people would rightfully be upset if I did not apply some semblance of continuity, and the edit made it mandatory. Hopefully they can resume debate on topic in 3 days.

Back on the first few pages of the split-off thread there is the discussion of HE vs EoR (for OftM). The ideas/concepts are being modified to a non-simplistic symantic hocus-pocus language to separate the knowledge from the new knowledge. Changes have and are being made to the base-bet of many games. I'd like to look at a few examples to illustrate the minefield of symantical traps.

The first game is Craps. Most everyone knows you put a one-unit pass-line wager out on the Come-Out. Then you are given OPTION to add a further Free-Odds wager. The way this works is that the free odds are an additional sum placed AS a pass-line bet. So instead of say $5, you have $25 at risk. The original bet has a HE of 1.414%, the COMPLETE bet is 0.283%. Such wagering is treated as ONE wager. Note that the INITIAL wager is upon the first roll of the dice and the "Odds" are for SUBSEQUENT rolls pertaining to the same event, and that all rolls are independent of the previous roll.

Next up is Three Card Poker. Here one makes an Ante wager before privately exposing the hand so dealt. Upon inspection, one decides to Raise or Fold requiring an additional wager, or tossing out the hand- losing the Ante. This is not a Completion of a wager, it is strictly a wager made knowing the value of the poker hand so dealt. Therefore the offered gambit has a risk of one or two units in a particular fraction. The Customer has both a HE and an EoR. For the sake of discussion lets say the HE is based on 1 unit Ante and a 1 2/3 unit EoR. In this case we have a "Before and After" event, and there are no further gaming actions outside of a Customer decision.

Third is UTH. This game is unusual in that TWO MANDATORY SEPARATE wagers are made, an Ante bet and a Blind bet. This does muddy the view of HE and EoR. The risk of the Blind bet is ignored as an "INITIAL" wager. Yet it it is forced, and the Ante wager is not valid should one not place such a Blind wager. So when EoR is attempted one counts this unit with any Raise wager as part of the determination. Yet one cannot place any wager legally without the Blind bet. The semantic element missing is "FORCED initial wager". In a $5 UTH game, one MUST risk TWO $5 wagers. The Raise portion of the gambit involves a Customer decision based upon the Ante portion of the Forced initial wager. So the Customer has outomes involving 6, 4, or 3 units of total risk in various fractions. Note here that further actions involve the dealing of the remainder of a standard deck of 52 cards, and is thus not independent.

More to follow when I get a better grasp of OthM.

Quote: 98Clubs

BThe first game is Craps. Most everyone knows you put a one-unit pass-line wager out on the Come-Out. Then you are given OPTION to add a further Free-Odds wager. The way this works is that the free odds are an additional sum placed AS a pass-line bet. So instead of say $5, you have $25 at risk. The original bet has a HE of 1.414%, the COMPLETE bet is 0.283%. Such wagering is treated as ONE wager. Note that the INITIAL wager is upon the first roll of the dice and the "Odds" are for SUBSEQUENT rolls pertaining to the same event, and that all rolls are independent of the previous roll.

I've never thought of craps in this way. I've always thought of the odds as a separate wager. It's paid at different odds, and you you raise or lower it as you please until it wins or loses.

It's certainly tied to the pass line bet, in that it wins when the pass line bet wins, and loses when the pass line bet loses, and the max bet is (usually) a multiple of the pass line bet, but it's still its own wager.

Quote: 98Clubs

Third is UTH. This game is unusual in that TWO MANDATORY SEPARATE wagers are made, an Ante bet and a Blind bet. This does muddy the view of HE and EoR. The risk of the Blind bet is ignored as an "INITIAL" wager. Yet it it is forced, and the Ante wager is not valid should one not place such a Blind wager. So when EoR is attempted one counts this unit with any Raise wager as part of the determination. Yet one cannot place any wager legally without the Blind bet. The semantic element missing is "FORCED initial wager". In a $5 UTH game, one MUST risk TWO $5 wagers. The Raise portion of the gambit involves a Customer decision based upon the Ante portion of the Forced initial wager. So the Customer has outomes involving 6, 4, or 3 units of total risk in various fractions. Note here that further actions involve the dealing of the remainder of a standard deck of 52 cards, and is thus not independent.

At this point, I consider "house edge" = house win divided by the game's base unit. So when discussing UTH, I will say things like the "house edge" is 2.185% of an ante, so there is zero confusion.

Suppose you can get dead chips or some type of promo chip for your action, what would the casino base your average bet to be? Same goes for craps and the odds bets.

Quote: AxiomOfChoice

I've never thought of craps in this way. I've always thought of the odds as a separate wager. It's paid at different odds, and you you raise or lower it as you please until it wins or loses.

It's certainly tied to the pass line bet, in that it wins when the pass line bet wins, and loses when the pass line bet loses, and the max bet is (usually) a multiple of the pass line bet, but it's still its own wager.

Of course its not a separate wager....just try and make this "separate wager" without making the pass line bet.

Quote: Paradigm

Of course its not a separate wager....just try and make this "separate wager" without making the pass line bet.

So do you also consider the ante and blind bets to be the same wager in UTH? Just try making the ante without the blind. For that matter, just try making the play bet without the ante and/or the blind.

The fact that one is a prerequisite for the 2nd does not mean that they are the same. It just means that one is a prerequisite for the 2nd.

I guess what is confusing for we non-mathematicians is the assertion that the extra money bet has no usefulness to consider. IF it is true that craps is an example of how EOR comes into play with the lower HE obtained by betting free odds[yes?no?], and this is useless to consider, or a canard, then I'm mystified for sure. The free odds are everything to a bettor like me, it affects how my session is likely to go as far as possible swings up and down, affects how much bankroll I think I need, the chances for a positive session, on and on. The casino too frets over this; you get the feeling offering 10x odds keeps somebody up at night with insomnia when they offer that [clearly they prefer not to]. Given half an excuse, they'll limit it to 2x.

I can accept that EOR has no role in statistical math, but that it has no validity to the house or the players is harder to swallow.

Quote: AxiomOfChoice

So do you also consider the ante and blind bets to be the same wager in UTH? Just try making the ante without the blind. For that matter, just try making the play bet without the ante and/or the blind.

The fact that one is a prerequisite for the 2nd does not mean that they are the same. It just means that one is a prerequisite for the 2nd.

They aren't the same bet, but when you play the game the effect of both bets should be considered when expressing the players disadvantage vs the house. Since you can't make one without the other, why would you combine the net loss of the game and state it as a percent of only the first bet?

Quote: Paradigm

Of course its not a separate wager

Now another opinion, it is a separate wager

math experts (if there are any)
get wrong answers and at first say they are correct answers but then correct their first answer. Are they correct in doing so?.
Is the new answer correct?
Happens to all of them.

Quote: Paradigm

just try and make this "separate wager" without making the pass line bet.

I myself have done this many, many, many times and know of others that do the same. Even on the don't pass/don't come bets.

What have you to say about that.

Did I cheat the game and the casino?
answer
no one cared that I did (and continue) this madness
hehehe

But I have found that the craps players that make the odds bet know it is a good bet.
The house or player has no edge on the bet is what many tell me.
but still most do not know why it is a good bet and do not even care to know why.

Sally

Fully disclosing my severe limitations in the field of higher mathematics, I think the question (Is 'element of risk' a useful measure?) is an interesting one. I have my own thoughts about it, but will reserve expressing them until we hear from EOR's creator. I hope the Wiz will enter the conversation and explain the "what and why" of its usefulness and application, especially distinguishing it from the universally accepted variance and standard deviation statistics.

Quote: Paradigm

They aren't the same bet, but when you play the game the effect of both bets should be considered when expressing the players disadvantage vs the house. Since you can't make one without the other, why would you combine the net loss of the game and state it as a percent of only the first bet?

Because that's how "house edge" is defined. It's just semantics, of course, but that's the definition of the term. If you want to calculate something else then you should use a different term, to avoid confusion (which is why the Wizard talks about "element of risk" rather than using a non-standard definition of "house edge")