Is the Element of Risk a useful concept?

(Sorry if this is not the appropriate forum; if not, could an Admin relocate the post?)

Players are using the House Edge in order to compare games. Simply put, the higher the HE, the best for the casino, so these players would want to choose games with the lowest HE.

Now, HE is actually the Expected Value (EV) per unit bet. This ratio makes sense when you have only one opportunity for betting an amount, and just wait for the bet resolution. In games like Blackjack or Caribbean Poker, this is not the case. Hence, the Wizard proposed another measure, that He calls "element of risk", where you divide the EV by the average amount you are expecting to wager. At first sight, this seems reasonable; but I quickly frowned because, as every student of statistics knows, the expectation of a ratio is NOT the ratio of expectations. So what does this formula measure exactly?

Let us take a concrete example to clear the point. You play Caribbean Poker: ante 10, then according to your cards you either fold or enter play by betting 20. (In some versions, you can even raise this by 'buying' a replacement card. Let us stick to the simplest for now.) Say we calculated the EV (whatever it is). Using HE, you would divide it by 10, the ante. Using ER, you would compute the average fraction of time that you enter play, hence calculating an average wager, and dividing the EV by it.

But consider that game from another point of view. You can never win anything if you don't enter play. Any CP player knows it is useless to participate if you don't have 30 in your roll. So the actual 'price' of the game is 30. You can describe it as a game where you wager 30, and according to cards and actions you can lose the 30 or 'win' back 20 (when folding) or win some other amount. Then both HE and ER would mean you must divide the EV by that initial wager of 30 (instead of 10 or an average of 10 and 30). Before someone argues that getting back your wager is not standard play, please see that is exactly what happens in, say, roulette, if you bet 10 on Red and 20 on a column and then the ball hits a Red outside your column: you wagered 30 and 'won' 10. The House Edge is still calculated on your 30.

Yet another point of view is to say: either you dont play, your wager is 10 and you lose 10, or you play, wager is 30 and you get a conditional EV that is higher than the overall EV since you wouldn't have played on a bad hand. If you are using this to compute the average "ratio of earnings to wager", you get a result that is even better than the three previous approaches.

So... What is the appropriate concept to use for comparing games, for example between roulette, BJ and Caribbean?


My answer would be that it is preposterous to wish a single measure, as the comparison of systems relies on several parametres. The reliable criterion is EV, and its relationship to wager size should be incorporated in some variance measure.

But how? Any ideas?

Haven't read this yet, it's kind of long, but I can tell you the Wizard will 'have the knives out' if you are concluding it is *not* 'a useful concept'

Quote: kubikulann

My answer would be that it is preposterous to wish a single measure, as the comparison of systems relies on several parametres. The reliable criterion is EV, and its relationship to wager size should be incorporated in some variance measure.

But how? Any ideas?

By examining the bottom line: what is your expected loss per hour in dollars? Example: $10 blackjack vs. $10 roulette vs. $10 CStud. In roulette, the wager is always $10 but in BJ or CStud the average wager is higher than $10. But that's just part of the game. The question is how much does it cost you to play? EV doesn't take time into consideration, so the idea that you have a 0.7% edge in BJ vs. 1.4% edge in craps could lead to the mistaken conclusion that BJ is a better bet. But with 100 hands/hour on BJ and 35 pass decisions/hour, your expected loss per hour is lower at a $10 craps table than a $10 blackjack table.

So rather than EV, I recommend Expected Loss Per Hour (ELPH), stated in number of bets. For example, the ELPH of $5 American roulette is about 2 bets ($10/hour), while the ELPH of blackjack is around one and the ELPH of the craps passline is about 0.5. You obviously need to state the assumptions (35 pass bets/hour, 100 bj hands/hour, 40 roulette spins/hour, etc.) but once you do that, I submit that ELPH is a solid basis for objective comparison. It leads to interesting observations, such as this one: playing single-zero roulette is about as expensive over time as playing blackjack.

Edit: I'll take credit in a footnote when the Wiz puts up the comparative ELPH chart on his website. :)

Quote: MathExtremist

Edit: I'll take credit in a footnote when the Wiz puts up the comparative ELPH chart on his website. :)

This is typically what I personally do. People weigh the percentages too much, if you gain similar enjoyment from a slower paced game, you can withstand a higher house edge.

" Expected Loss Per Hour " leaves out the other E Entertainment. If I expect to lose, I should chose the game I can both afford and like. Why would I leave a nice BJ game to join the loudmouth losers at CRAPS? There is a reason it is called CRAPS !

Quote: Buzzard

" There is a reason it is called CRAPS !

yes.. but thats not the reason why. :D

The "Element of Risk" concept is useful when there are actions that increase the base wager. Common examples include 21 (Doubles and Splits), Carribean Stud raises, and Ultimate Texas Hold'em where there are 3 opportunities at raises 4x-2x-1x. For these games among others it is very useful to know the House Advantage per average bet, as opposed to the initial bet. However, one MUST keep in mind the amount of money this figure represents. If the initial bet is $5 a UTH game causes a Blind Bet of $5 and an average raise of about $11. In this simplified example, the House collects 2.2% on the total average wager of $21 (about 46c): not the original $5 (11c).

The Element of Risk quantifies the 2.2% total average wager, and divides by average units wagered (about 4.2) to achieve the answer of about 0.52% per unit wagered.

Quote: 98Clubs

The "Element of Risk" concept is useful when there are actions that increase the base wager. Common examples include 21 (Doubles and Splits), Carribean Stud raises, and Ultimate Texas Hold'em where there are 3 opportunities at raises 4x-2x-1x. For these games among others it is very useful to know the House Advantage per average bet, as opposed to the initial bet. However, one MUST keep in mind the amount of money this figure represents. If the initial bet is $5 a UTH game causes a Blind Bet of $5 and an average raise of about $11. In this simplified example, the House collects 2.2% on the total average wager of $21 (about 46c): not the original $5 (11c).

The Element of Risk quantifies the 2.2% total average wager, and divides by average units wagered (about 4.2) to achieve the answer of about 0.52% per unit wagered.

For UTH, you have it flipped. The house edge = expected loss/initial bet (aka ante in UTH), which for UTH is about 2.185% or about (0.02185)*$5 = $0.109 for a $5 ante game. The "element of risk", which is expected loss/average total bet. For UTH this is about 2.185%/4.15 = 0.526%. Using the element of risk the expected loss is also: (0.00526)*(4.15 antes/hand)*$5 = $0.109

Trin,

I think uth is deceptive as a basis for your calculation because there is no such thing as a five dollar game. The blind bet is required before the cards are even dealt. So it's a ten dollar game. I saw half a dozen new ones today that are using the same mechanism. So HE is outdated or too confining. I think EOR is very useful because it takes into account things like that. And I'm liking ELPH too, nice one.


I have played pgp at better than 40Hph, and at less than 20. I'm not sure a rate factor that's so variable fits as an accurate equivalency to HE, though. One is math, the other is optimized expectation. EOR better evauates the exposure from the player's point of view than any, while elph may be more useful to the house in terms of drop estimates. The casino can better determine profitability perhaps, or performance metrics or retraining needs wi the latter.

Quote: beachbumbabs

Trin,

I think uth is deceptive as a basis for your calculation because there is no such thing as a five dollar game. The blind bet is required before the cards are even dealt. So it's a ten dollar game. I saw half a dozen new ones today that are using the same mechanism. So HE is outdated or too confining. I think EOR is very useful because it takes into account things like that. And I'm liking ELPH too, nice one.


I have played pgp at better than 40Hph, and at less than 20. I'm not sure a rate factor that's so variable fits as an accurate equivalency to HE, though. One is math, the other is optimized expectation. EOR better evauates the exposure from the player's point of view than any, while elph may be more useful to the house in terms of drop estimates. The casino can better determine profitability perhaps, or performance metrics or retraining needs wi the latter.

Yes, you're right, it is deceiving, so when I talk about the house edge of this game, I never say just 2.185%. I will say things like you will lose 2.185% of an ante per hand on average. Unfortunately, the house edge definition is a holdover from older games where there was just a single bet to consider, and is now generally considered as house edge = house win / single bet size.

Quote: MathExtremist

I'll take credit in a footnote when the Wiz puts up the comparative ELPH chart on his website. :)

Ahem: https://easy.vegas/games/crash

Quote: MichaelBluejay

Ahem: https://easy.vegas/games/crash

I'm a big fan of your site. I especially like the Casino Births and Deaths list. Thank you for keeping it current. (sorry off topic, I know)

Quote: JimRockford

I'm a big fan of your site. I especially like the Casino Births and Deaths list. Thank you for keeping it current. (sorry off topic, I know)

Needs to be updated. I don't see the Klondike on the
list, which closed in 2006. The only casino I've ever
been thrown out of.

Quote: MichaelBluejay

Ahem: https://easy.vegas/games/crash

very nice MB

also for 16 hours here:
https://easy.vegas/gambling/average-loss

and a cool little 'how the house edge works' simulator here:
https://easy.vegas/gambling/house-edge
"The longer you play, the closer your losses will approach the house edge."
Thumbs Up!

also
"The casinos don't beat the players because they get lucky,
they beat the players because the odds are stacked in their favor."

The house edge in Roulette simply comes from paying the winning bets off
at less than true odds.
(most casino bets use this method of short pays on a win
so the odds are stacked in their favor)

a 0% HE for any even money bet for example
(00 wheel, would make for a nice promotion bet)
would be bets of 9 pays 10 (10:9)
instead of the 1:1 current payoffs

back to work
thanks for sharing!

Quote: EvenBob

Needs to be updated. I don't see the Klondike on the
list, which closed in 2006. The only casino I've ever
been thrown out of.

Thanks for the tip. I added it.

Also, thanks JimRockford and 7craps for the kind words!

OK, I got it bassacwards. Its ~2.2% on the $5, divided by the ~4.2 units or about 0.52+% for the average bet made.

Quote: MichaelBluejay

Thanks for the tip. I added it.

You're funny. It's been gone for 7 years and nobody
noticed. The had the famous 99 cent breakfast buffet
in the 60's, as much eggs and bacon and sausage and
pancakes as you could eat for a buck.

Quote: tringlomane

Yes, you're right, it is deceiving, so when I talk about the house edge of this game, I never say just 2.185%. I will say things like you will lose 2.185% of an ante per hand on average. Unfortunately, the house edge definition is a holdover from older games where there was just a single bet to consider, and is now generally considered as house edge = house win / single bet size.

I knew you knew that. I phrased it badly as I was stating my opinion. Sorry about that.

Quote: 98Clubs

The "Element of Risk" concept is useful when there are actions that increase the base wager. Common examples include 21 (Doubles and Splits), Carribean Stud raises, and Ultimate Texas Hold'em (...)

The Element of Risk quantifies the 2.2% total average wager, and divides by average units wagered (about 4.2) to achieve the answer of about 0.52% per unit wagered.

Thank you 98, I know what the ER is. If you had read my post, you'd know your post does not answer it.

What I say is, it is not good practice to divide by the average wager.

Quote: kubikulann

Thank you 98, I know what the ER is. If you had read my post, you'd know your post does not answer it.

What I say is, it is not good practice to divide by the average wager.

kubikulann,

I would be extremely interested in more detail from you about why you think it's not a legitimate tool for evaluation. To me, as a non-mathematician, it's a very valid measurement for certain dynamics, as I mentioned before. Is it that you think the tool is valid but mis-applied, the measurement is incorrectly done, or the concept itself has no validity, and if so, why?

Thanks in advance!

Quote: beachbumbabs

kubikulann, I would be extremely interested in more detail from you about why you think it's not a legitimate tool for evaluation. (...) Is it that you think the tool is valid but mis-applied, the measurement is incorrectly done, or the concept itself has no validity, and if so, why?

A little of the three... :-)

House edge is a weird concept even in the simple cases (roulette, baccarat, videopoker, lottery), because one does not see why you should be interested in the ratio of your expected gain/loss on your initial wager. What you are interested in is the expected gain/loss.

For example, say you decide to play 100$ on roulette. Your expected loss is 5.26$ if you play it all on one bet and quit the table after that bet. But expectation is of small interest in the short term: either you'll win an amount, or lose your 100$. To make expectation more meaningful, you may imagine betting the 100$ in rounds of 5$. But again, your EV is -5.26$ only if you refrain from putting on the table whatever you won on previous trials. Most players, if winning, will try their hand at a new bet. This means that, though they joined the table with 100$, they will actually bet more than 100$, and their Expected Loss will consequently be more than 5.26$. Ultimately, for a player who continues playing as long as he has chips left, the loss will be 100$, meaning that this kind of player betted an average 100/0.0526 = 1901$. Yet in his mind, he got in with 100 and out with zero. Would you say his ratio of earnings on wager is -100%?

House edge is a concept for the casino manager. Something similar, I guess, to Benefit/Turnover ratio. Think of a lottery, with a typical HE of 50%. What this means is they gather an amount M of bets, and after paying the winners they get to keep 50% of it. This works for simple betting games, but not for Blackjack, CStud, etc. The equivalent concept may then be the "Element of Risk", which is the amount the casino gets to keep, compared to the total amount that transited in the dealers' stack.

But who cares? A casino is not a state lottery. They don't actually collect the bets in money form and then, at a separate moment, pay out winnings. One chip is used for several bets. Some chips are not even betted. Why should the casino take notice of these amounts that pass & go in the hands of dealers? For practical management, they are more interested in computing the necessary size of an opening table's stack.

What about the player's viewpoint?

We definitely do not care about the total amount collected by the casino. So the validity of both HE and EoR are questioned, when applied to the player.

As for the measurement, one way to look at my criticism is to reflect that a concept should yield the same measure, whatever the particular dressing you give to the description of the same game. That is not the case with the EoR, as I showed in my original post. Consider a roulette where you must place 20$, you get 10$ back on a losing result and 30$ on a winning one (simple chances). EV is -0.526$, HE is 2.63%. Yet this is exactly the game of classical roulette with a 10$ wager. Why is the HE different if it is the same game? Because, for a few minutes, you had to put a chip on another space on the table? (This made me think of the Kahnemann-Tversky experiment, where people acted differently according to whether they were presented a game as "You receive 1000 and have 50% risk of losing 500" or "You have a 50% chance of winning 500".)

The other criticism (probabilistic) is that we are not living at the quantic level* :-) Only one outcome results from the card dealing or dice rolling. In each of these outcomes, there was ONE total wager and ONE gain/loss. You must compare these, and then only average out over all outcomes. What the EoR does is first averaging, separately, the wager sizes and the gains/losses, then comparing. Bad math. I was taught in first grade that A/B + C/D is not equal to (A+C)/(B+D).

* where all possible outcomes 'exist' together


But as I said, I think that even with the correct measurement, the concept still lacks validity, from the players' point of view.

Yet I'm not sure. Why I posted this. To get other people's views.


Kubikulann

The element of risk is a statistic to measure the overall value of a game. It is simply the ratio of the expected loss to average units bet by the end of the hand. I created the statistic to measure the value of one game against another.

For example, the house edge in double-zero roulette and Caribbean Stud Poker are about the same at 5.26% and 5.22% respectively. However, I consider Caribbean Stud to be a better gambling value, because the player makes a lot of raise bets. Comparing the element of risk in the two games it is 5.26% for roulette and 2.56% for Caribbean.

If anyone has a better suggestion on how to measure one game against another, I'm all ears. Variance was mentioned in the OP. However, some gamblers are risk-prone and others risk-averse. Depending on what the gambler wants to accomplish, variance can be good or bad.

Quote: Wizard

The element of risk is a statistic to measure the overall value of a game. It is simply the ratio of the expected loss to average units bet by the end of the hand. I created the statistic to measure the value of one game against another.

For example, the house edge in double-zero roulette and Caribbean Stud Poker are about the same at 5.26% and 5.22% respectively. However, I consider Caribbean Stud to be a better gambling value, because the player makes a lot of raise bets. Comparing the element of risk in the two games it is 5.26% for roulette and 2.56% for Caribbean.

If anyone has a better suggestion on how to measure one game against another, I'm all ears. Variance was mentioned in the OP. However, some gamblers are risk-prone and others risk-averse. Depending on what the gambler wants to accomplish, variance can be good or bad.

Like I said before, I think the most relevant comparison is expected loss per hour. Neither the house nor the typical gambler care about the ratio of that loss to the average wager. The bottom line is the only thing that matters to either party to a wager, and based on that analysis, a craps game at 1.4% (passline only, no other bets) is actually a better bet than a blackjack game at 0.7% (main bet only, no side bets).

Additionally, virtually nobody -- and I'm betting that includes you -- plays for either a predetermined number of bets or a predetermined amount of handle. Bettors are much more likely to play for a fixed period of time, or at least a time-based session ("a few hours", etc.) As a result, using an hourly rate of loss seems most appropriate. That is, after all, how casinos evaluate comps for players: one of the factors is how fast the game is moving.

And in your example above, your figures could be used to conclude that Caribbean Stud players expect to lose at half the rate of roulette players, but in reality a $10 Caribbean Stud player expects to lose about $5 *more* per hour than a $10 roulette player. Given that, I don't think it's fair to consider Stud a better value.

True, we are trying to find something that does not depend on risk-aversion and/or subjective utility.

I fear that this quest is an impossible one, though.

Maybe the "average ratio" instead of the "ratio of averages" can serve a purpose? It should be tested.

Quote: MathExtremist

Like I said before, I think the most relevant comparison is expected loss per hour.

Problems with that:

1. Speed of play is not built-in, undisputable. Always a part of estimation.
2. Measure is dependent on the wager size, which is precisely what HE or EoR were trying to avoid.

Quote: kubikulann

Problems with that:

1. Speed of play is not built-in, undisputable. Always a part of estimation.
2. Measure is dependent on the wager size, which is precisely what HE or EoR were trying to avoid.

Game speed is always going to be variable, but not infinitely so. Hands per hour has a physical maximum and a practical minimum, and casino operators know this. It's entirely proper to provide an estimation based on an average rate of play. As to wager size, I don't propose strictly using a dollar amount but a per-unit amount. The ELPH of the passline is about 0.5 bets (or lower), so a $10 bettor expects a $5/hour loss while a $50 bettor expects a $25/hour loss. ELPH is simply EV * hands/hour. 1.41% * 35 = 0.4935.

I believe the goal should be to create a comparison metric that is more intuitively usable by the majority of the gambling public. ELPH (in bets) is more relevant than either HE or EoR. Telling someone the house edge on the passline is 1.41% isn't intuitively relevant, and telling them that the house edge of the passline plus 3/4/5x odds is 0.37% is misleading. But if you tell someone they'll average a half-bet loss per hour -- regardless of whether they take odds -- that's very easy to understand.

However, I think the optimal approach would be to use more than one statistic. We can use ELPH to communicate the average rate of loss per hour in bets, and another to communicate the likelihood of being ahead after an hour. That's where variance comes in, and that's how it becomes clear that certain bets have a better chance to get ahead than others. And since someone may also want to know the expected bankroll swings (e.g., to better plan their buyins), I propose a triplet:

a) ELPH (in bets)
b) 2-SD range over an hour (+/- # bets)
c) Chance of being ahead after an hour (of flat betting)

So, for any given proposition, we can evaluate hourly expected loss in units, +/- 2SD in units, and the probability of a net gain. That seems to serve the purpose better than a single ratio that, frankly, has proven very misleading.

Quote: MathExtremist

Like I said before, I think the most relevant comparison is expected loss per hour.

It isn't often that I disagree with ME, but this is one of those times. To address why, I think we need to answer the question about why people gamble in the first place. I contend the usual motive for most table game players is they are buying excitement, or adrenaline. Those players won't get a sufficient fix if it takes too long between hands. For them, it will take $x of total bets to get their fix. My advice is to minimize the expected loss of that action.

I'm sure somebody will counter with the example of the pai gow poker/tiles player who is plays more for the social experience and/or the challenge of the game itself. Your metric may be more appropriate for those players, but I think they are in the minority, and even they would get bored if the game were too slow.

Finally, let's look at a practical example? Which is the better bet in craps:

A) Field, where both 2 and 12 pay 2 to 1. House edge = 5.56%. Average rolls to resolve = 1.
B) Hard 4 or 10. House edge=11.11%. Average rolls to resolve = 4.

I contend the answer is A. By your logic, the answer should be B, because the expected loss per roll is 2.78%, thus it will lose half as much as the field bet per hour. Do you agree the answer is B?

Quote: Wizard

It isn't often that I disagree with ME, but this is one of those times. To address why, I think we need to answer the question about why people gamble in the first place. I contend the usual motive for most table game players is they are buying excitement, or adrenaline.

I agree, but then you compared the field (boring) to the hard 10 bet (exciting). There isn't a single dice player on the planet who thinks winning a field bet is more exciting than hitting a hard 10. Hitting a hard 10 is one of the most cheer-inducing outcomes in craps. When was the last time you heard a table full of players cheer because a field number rolled?

Quote:

Those players won't get a sufficient fix if it takes too long between hands. For them, it will take $x of total bets to get their fix.

I disagree. I don't think thrill seekers are looking at total wagering volume, I think they're looking at what they're betting on. If you ask 100 dice players which is the more exciting bet, the hard 10 or the field, you'll end up with 100 to zero in favor of the hardway.

Quote:

Finally, let's look at a practical example? Which is the better bet in craps:
A) Field, where both 2 and 12 pay 2 to 1. House edge = 5.56%. Average rolls to resolve = 1.
B) Hard 4 or 10. House edge=11.11%. Average rolls to resolve = 4.
I contend the answer is A. By your logic, the answer should be B, because the expected loss per roll is 2.78%, thus it will lose half as much as the field bet per hour. Do you agree the answer is B?

Yes. There is no question that a player both loses less (in bets per hour) and has a more exciting time by betting the hard 10 rather than the field. One must ignore both of those facts in any definition of "better" that suggests the field is a better bet. And considering that most Strip craps tables are $10, while the hardways can usually be bet for $1, the $1 hard 10 bettor loses at 1/20 the hourly rate of a $10 field bettor.

Look at it another way and suppose you were a casino operator. Which bet (Field or Hard 10) would you rather have your players betting on? Is the answer the same or different as what you consider to be a "better" bet for the player?

The bottom line is that I disagree with your foundation -- I don't think players care about their total handle. I think they care about playing time. For most casual gamblers (my target audience here), playing time is fixed. Whether that's a night out or a weekend in Vegas or AC, there is a limited period of time between when they get to start gambling and when they have to stop and go home. To use your example, the simple fact is that it's impossible for a dice player to make $1 or even $10 hard 10 bets all weekend long and wager the same total amount as a $10 field bettor, so an approach that assumes handle is equal isn't reflective of reality.

Quote: Wizard

Which is the better bet in craps:

A) Field, where both 2 and 12 pay 2 to 1. House edge = 5.56%. Average rolls to resolve = 1.
B) Hard 4 or 10. House edge=11.11%. Average rolls to resolve = 4.

I contend the answer is A. By your logic, the answer should be B, because the expected loss per roll is 2.78%, thus it will lose half as much as the field bet per hour. Do you agree the answer is B?

IMO,
Depends on the 'meaning' of the word 'better'

and what $$$ are resolved vs. at risk in a players mind


Over 100 rolls per hour with $5 wagers every roll
A:
total resolved $action $500 (exactly)
total $ at risk: $500
EV: -$27.78

B:
total resolved $action $125 (average)
total $ at risk: $500
EV: -$13.89

Per hour per roll,
B is better with a lower EV
because both risked the same $$$ over 100 rolls.
The numbers do not lie.

But per bet resolved or total action - equal action between two different type bets
A is better easily.
B would have to play longer to have the same resolved action of $500
and that $500 action will have an EV of -$55.56
twice as high as the field
the numbers do not lie

It still depends on how you want to look at it.
From the inside out (from the casinos view)
or
the outside in (the players view)

Quote: MathExtremist

I agree, but then you compared the field (boring) to the hard 10 bet (exciting).

only your opinion

Quote: MathExtremist

There isn't a single dice player on the planet who thinks winning a field bet is more exciting than hitting a hard 10.

sure there are. I for one. Maybe you do not know I am a Dice player.
My late wife was also one.
The last 10 years I have dealt Dice at casino night parties for 4 hour sessions without any break,
the largest excitement I have witnessed, again only my opinion,
comes from hitting the Field.
It IS the action bet.

Quote: MathExtremist

Hitting a hard 10 is one of the most cheer-inducing outcomes in craps.
When was the last time you heard a table full of players cheer because a field number rolled?

Last Saturday.
A real $$$ game, a craps tournament (please do not invite yourself)
with 16 players and over 90% of these type of events are won by the Field bettors.
One event was won by a player making $1000 Place 8 and hit 3 in a row. That is the exception

Many that have played Craps do not like it at all because of all the waiting for bets to resolve.
Pass line, odds, place 6&8 , all the hardways,

no winners yet, this is so boring!

I have heard that many times from both sides of the table.
That has been a common complaint heard by me after I turned 21.

Quote: MathExtremist

Look at it another way and suppose you were a casino operator. Which bet (Field or Hard 10) would you rather have your players betting on?

Given the same amount of total bets, the hard ways. Given the same amount of time and average bet, the field. Whatever gives me the greatest expected profit. I'm certainly going to comp the hard way bettor better, all other things being equal.

Quote:

The bottom line is that I disagree with your foundation -- I don't think players care about their total handle. I think they care about playing time.

I think we're going to have to agree to disagree. If playing time were paramount, then I would be singing the praises of bingo, live keno, and lottery tickets. What my readers can expect from me is advice on what is the best value per dollar bet.

Quote:

If you ask 100 dice players which is the more exciting bet, the hard 10 or the field, you'll end up with 100 to zero in favor of the hardway.

Not if I were in the sample pool. I would get an equal amount of excitement winning $10 nine times as $90 once.

I am really appreciating the quality of the discussion here. For my purposes, as a casual gambler, and trying to bring out a new game, I think EoR is the best available comparison head-to-head when evaluating 2 games. It takes into account the total exposure the player has for optimum play, follow-on bets, and concentrates on the base game payout factor. Time is of interest to the casino for drop purposes, and to the player for the boredom factor, but I don't think time is the primary consideration when compared to bankroll and the perception of how quickly it's being drained on a losing streak.

I think if a person takes 10 minutes to lose 100 or 2 hours, from the player's point of view, if that's their dollar limit, that's when they get up. Certainly they had more entertainment value from the 2 hours of play, but the primary dictate when losing is bankroll. Time definitely affects the perception of and eventual return to the game by the player, but bankroll and volatility are IMO more important. EoR strips the unnecessary elements for consideration while improving on the HE calculation. This seems especially important to me when a casino is considering bringing on a new game to replace an existing game; there is such a proliferation of forced bets and bet escalation within the game, I don't know how else they can make a critical calculation about the drop potential.

Thanks for letting me join in; all is JMHO.

Quote: Wizard, in response to what bets he (as a casino operator) would rather take bets on

Given the same amount of total bets, the field. Given the same amount of time and average bet, the field. Whatever gives me the greatest expected profit.

Exactly. The greatest expected profit, between the field and the hard 10 bet, comes from the field. So how can it be that a bet that's better for the casino is simultaneously "better" for the player?

Quote:

I think we're going to have to agree to disagree. If playing time were paramount, then I would be singing the praises of bingo, live keno, and lottery tickets. What my readers can expect from me is advice on what is the best value per dollar bet.

I didn't say playing time was paramount -- some people want a quick game, others want to take their time. What I meant to convey was that playing time is more fundamental than the number of individual wagering transactions because those transactions happen at a varying rate. It makes far more sense to compare the expected loss by playing blackjack for an hour and bingo for an hour than it does to compare the expected dollar loss of a single blackjack wager vs. a single bingo session.

Ultimately, I think you put too much emphasis on money vs. time. Money is an artificial and replenishable human construct. Time is neither -- it is the only thing we cannot create or obtain. In the grand scheme of things, a time-based metric is the only fair way to allow us to compare costs effectively, not only between different wagering propositions but between wagering and non-wagering activities. If time is your denominator, we can accurately compare the cost of going to a movie, a ball game, bowling, playing blackjack, playing keno, etc. Revenue per time-unit is the way everything else is measured and reported from an operational standpoint -- win per day, win per month, etc. That's true of land-based gaming, online gaming, and virtually every other business. It's not at all inconsistent to use revenue per time to evaluate bets, either. If anything, I'd say a purely EV-based approach is more anomalous than a time-based approach.

Quote: MathExtremist

Exactly. The greatest expected profit, between the field and the hard 10 bet, comes from the field. So how can it be that a bet that's better for the casino is simultaneously "better" for the player?

I misspoke earlier. I meant to say, "Given the same amount of total bets, the hard ways. "

Quote: MathExtremist

What I meant to convey was that playing time is more fundamental than the number of individual wagering transactions because those transactions happen at a varying rate. It makes far more sense to compare the expected loss by playing blackjack for an hour and bingo for an hour than it does to compare the expected dollar loss of a single blackjack wager vs. a single bingo session.

I simply disagree. I get asked all the time what are the best bets in the casino. For 15 years I've been saying those with the lowest element of risk, and I'm not about to change my tune now. I might add that you don't see me promoting betting strategies/systems like the Craps 5 Count, in the interests to slowing down the game. I assume you would endorse such strategies.

Quote: MathExtremist

Ultimately, I think you put too much emphasis on money vs. time. Money is an artificial and replenishable human construct. Time is neither -- it is the only thing we cannot create or obtain. In the grand scheme of things, a time-based metric is the only fair way to allow us to compare costs effectively, not only between different wagering propositions but between wagering and non-wagering activities. If time is your denominator, we can accurately compare the cost of going to a movie, a ball game, bowling, playing blackjack, playing keno, etc. Revenue per time-unit is the way everything else is measured and reported from an operational standpoint -- win per day, win per month, etc. That's true of land-based gaming, online gaming, and virtually every other business. It's not at all inconsistent to use revenue per time to evaluate bets, either. If anything, I'd say a purely EV-based approach is more anomalous than a time-based approach.

I'm looking at things from the perspective of the player. While I don't talk about time much, I assume the player does value time by wanting to get his gambling over with quickly. For example, Mary and Steve come spend two nights in Vegas. Steve puts an emphasis on gambling and Mary on dining, shopping, and shows. Both would prefer to be together, but recognize some time must be spent apart, lest one or both go home unfulfilled. My advice to Steve would be to play a fast-paced game, with a low element of risk, to scratch his gambling itch as quickly and cheaply as possible, to spend more time with his sweetheart, and hopefully get lucky at nighttime.

Quote: Wizard

I'm looking at things from the perspective of the player. While I don't talk about time much, I assume the player does value time by wanting to get his gambling over with quickly. For example, Mary and Steve come spend two nights in Vegas. Steve puts an emphasis on gambling and Mary on dining, shopping, and shows. Both would prefer to be together, but recognize some time must be spent apart, lest one or both go home unfulfilled. My advice to Steve would be to play a fast-paced game, with a low element of risk, to scratch his gambling itch as quickly and cheaply as possible, to spend more time with his sweetheart, and hopefully get lucky at nighttime.

Now if only I can see that quantified!! Is this the reason you like video poker?? LOL

Quote: tringlomane

Now if only I can see that quantified!! Is this the reason you like video poker?? LOL

If anything, that is a reason not to like video poker. The advantages are usually razor thin, so you have to put in long hard hours to make up for it.

This is pretty lousy evidence to quantify my theory...

Quote: Vamos a Las Vegas by Los Tigres del Norte

Pero no estoy solito,
my honey is with me
so after we get tired,
nos vamos a dormir.

This song alternates between English and Spanish, as a joke. To translate it all into English, which I'm sure Nareed and Paco will find many faults with:

Quote: Wizard translation

But I am not single,
my honey is with me
so after we get tired,
we go to bed together.

full lyrics.

Quote: Wizard

I misspoke earlier. I meant to say, "Given the same amount of total bets, the hard ways. "

Fair enough, but you certainly accept that the house makes more money on a $10 field bettor than a $10 hardway bettor over the same period of time, whether you measure that in rolls, hours, or months.

Quote:

I simply disagree. I get asked all the time what are the best bets in the casino. For 15 years I've been saying those with the lowest element of risk, and I'm not about to change my tune now. I might add that you don't see me promoting betting strategies/systems like the Craps 5 Count, in the interests to slowing down the game. I assume you would endorse such strategies.

Not at all. Standing at a dice table holding one's chips isn't "playing." Neither is sitting at a blackjack table not betting. The question, to me, is "what does it cost to play"? I can answer that question very easily: 1 bet per hour, 2 bets per hour, etc. There is nothing controversial about that because it is an objective measurement, if somewhat variable due to the effects of game speed. If everyone played a fixed amount of handle or a fixed number of bets, for example by buying in once and never replaying winnings, then you may have a point. But that's not the way people play. Gamblers generally either play until they've busted out, until some large win occurs, or until some loosely-defined time period has elapsed. The problem with EoR is that it may mislead someone into thinking they're playing a lower-cost bet than they are. Why should it matter that the EoR percentage of a single bet in game A is lower than in game B if the dollar cost of playing game A is actually higher than game B?

Quote:

I'm looking at things from the perspective of the player. While I don't talk about time much, I assume the player does value time by wanting to get his gambling over with quickly.

With all due respect, I strongly disagree that most players want to get their gambling over with quickly. Suppose a typical blackjack player spends money getting to Las Vegas, sits down at a blackjack table, and wins the first 10 hands in a row (with a few doubles, splits, and naturals for good measure). They're not going to hang it up for the weekend. Neither is a VP player who hits quads on their first play.

I would even go further and say that anyone who feels gambling is something to be gotten over with quickly should not be gambling at all. If it's not entertaining, or if it's a chore, don't play. But if it *is* entertaining, why would you want it to be over quickly?

Quote: MathExtremist

Fair enough, but you certainly accept that the house makes more money on a $10 field bettor than a $10 hardway bettor over the same period of time, whether you measure that in rolls, hours, or months.

I agree, of course.

Quote:

Not at all. Standing at a dice table holding one's chips isn't "playing."

Neither is a hard 10 bet on all the rolls that are not a 7 nor 10.

Quote:

With all due respect, I strongly disagree that most players want to get their gambling over with quickly.

Everyone is different, but I think the average Vegas visitor doesn't want to gamble the whole time, but do other things as well.

Quote:

Suppose a typical blackjack player spends money getting to Las Vegas, sits down at a blackjack table, and wins the first 10 hands in a row (with a few doubles, splits, and naturals for good measure). They're not going to hang it up for the weekend. Neither is a VP player who hits quads on their first play.

They might. Many gamblers go in with the goal to win $x or lose $y, whichever happens first.

Quote:

I would even go further and say that anyone who feels gambling is something to be gotten over with quickly should not be gambling at all. If it's not entertaining, or if it's a chore, don't play. But if it *is* entertaining, why would you want it to be over quickly?

In my opinion, most table game players are playing for the rush rather than for entertainment. Macau is a good example. Few players there seem to be having any fun. You won't seem much talking. Instead, the vast majority act like they just don't want to be bothered.

Where I think we could agree is that advising on the best bets should vary from player to player, according to why they are playing in the first place. I'm not about to preach to the old ladies in the Suncoast bingo room that they should be playing blackjack instead, because the house edge is lower. Likewise, I don't think you'll make many bingo converts at the mini-baccarat table. I seek only to answer the question about how good of a value a bet is, simply in a mathematical sense.

I'm sure Pai Gow has been discussed in some shape or fashion:

How much more do you need to play per hand to get the same comp rating as a $25 BJ player?

Quote: djatc

I'm sure Pai Gow has been discussed in some shape or fashion:

How much more do you need to play per hand to get the same comp rating as a $25 BJ player?

Please don't hijack the thread by changing the topic. If you want an answer to that question, find a pai gow thread or start your own.

Quote: MathExtremist

So how can it be that a bet that's better for the casino is simultaneously "better" for the player?

Hey! We are not talking about a zero-sum game. The casino is there for pure profit; the player is there for entertainment (unless s/he believes s/he has an edge, but I assume we are not in that kind of thread...).

So, yes of course, we are looking for a win-win situation.

Quote: Wizard

If playing time were paramount, then I would be singing the praises of bingo, live keno, and lottery tickets. What my readers can expect from me is advice on what is the best value per dollar bet.

Precisely.

There are two ways to handle this. Either we are looking for an advice as to what game gives the best "fun experience", and then we must include considerations of playing time, nature of the game (craps or bingo?), nature of the bet, risk-aversion and variance, and analyze it all individually with the utility function (aka the preferences) of that specific player.

Or we seek the best "value". But then I have a problem with the "per dollar bet" part. Imagine two games, same speed, same EV, same excitement value. Game A requires 50$ bets, game B only 5$ bets. Typically, game A has larger variance; but this peters out if you play long enough.

• A rational player does not mind about the wager size. To him/her, both games are equivalent.
• Another player shys away from betting 50; he probably is risk-averse, considering (albeit inconsciously) the variance element.
• A third player looks at HE (or EoR) and chooses game A, because House Edge is ten times lower. She actually prefers betting 50.

I personally think the two latter are irrational. But they are rational according to their objectives, surely. Again we are facing subjectivity.


Is there an objective answer? Is there, for that matter, an objective question?

Quote: MathExtremist

Ultimately, I think you put too much emphasis on money vs. time. Money is an artificial and replenishable human construct. Time is neither -- it is the only thing we cannot create or obtain. In the grand scheme of things, a time-based metric is the only fair way to allow us to compare costs effectively, not only between different wagering propositions but between wagering and non-wagering activities.

Beautiful philosophical statement. I love it!

But it is misleading, in our discussion. We ARE discussing value. What has to be seen is that, time or money, each individual values it in a personal way. You can't find a "fair" or "universal" way of comparing those things.

Imagine you tell me that game X has a ELPH of 0.5 "bet" and game Y has an ELPH of 1 "bet". Well, all the info it gives me is that if I make double bets in X, I reach the same ELPH, expressed in money. So what? I personally don't see any comparison of the value of the games. ELPH is more a kind of Table that asks a punter "How much do you want to lose per hour?" and shows the size of wagers s/he must bet in every game. All games are equivalent.

HE or EoR are pretending to point "this game is objectively better than that one". An altogether different proposition.

My gripe is that they fail to provide that service.

Quote: kubikulann

Precisely.

There are two ways to handle this. Either we are looking for an advice as to what game gives the best "fun experience", and then we must include considerations of playing time, nature of the game (craps or bingo?), nature of the bet, risk-aversion and variance, and analyze it all individually with the utility function (aka the preferences) of that specific player.

Or we seek the best "value". But then I have a problem with the "per dollar bet" part. Imagine two games, same speed, same EV, same excitement value. Game A requires 50$ bets, game B only 5$ bets. Typically, game A has larger variance; but this peters out if you play long enough.

• A rational player does not mind about the wager size. To him/her, both games are equivalent.
• Another player shys away from betting 50; he probably is risk-averse, considering (albeit inconsciously) the variance element.
• A third player looks at HE (or EoR) and chooses game A, because House Edge is ten times lower. She actually prefers betting 50.

I personally think the two latter are irrational. But they are rational according to their objectives, surely. Again we are facing subjectivity.


Is there an objective answer? Is there, for that matter, an objective question?

I think there's an objective answer once, as you say, you define the utility function. And I recognize that the utility function is different for different players. I just think that the majority of players are more likely to be concerned about pricing -- if they're concerned about pricing at all -- as a function of how long they get to play rather than on an individual bet basis. The conventional wisdom regarding EV is often misleading, especially when the player has the ability to add to one's wager after the start of the game. The "combined EV" of the odds bet in craps is a perfect example: you can argue that the 1.41% edge on a $10 line bet drops to 0.37% edge when you add 3/4/5x odds, but the expected loss per $10 bet is still 14c. In that case, the ratio has decreased not because the numerator decreased, but because the denominator increased. A gambler who relies on those two statistics, 1.41% and 0.37%, may mistakenly believe they expect a smaller loss by betting odds. That's not true; they just expect a smaller *percentage* loss relative to their total average wager.

I've used the craps vs. blackjack example earlier in this thread, noting that a craps passline player expects a loss of about 0.5 bets/hour while a blackjack player expects a loss of about 1 bet/hour. That means the craps player can bet twice as much (in dollars) over the same period of time for the same expected loss. That's important for comp rating purposes: a $50 craps player is likely to be rated higher than a $25 blackjack player despite the same theo(retical loss). So I would argue that from an economic standpoint, where "economic" includes the whole of the casino experience rather than just individual wagering transactions, knowing one's expected rate of loss per unit time is more important than the percentage expectation of an individual bet.

Quote: kubikulann

Beautiful philosophical statement. I love it!

But it is misleading, in our discussion. We ARE discussing value. What has to be seen is that, time or money, each individual values it in a personal way. You can't find a "fair" or "universal" way of comparing those things.

Imagine you tell me that game X has a ELPH of 0.5 "bet" and game Y has an ELPH of 1 "bet". Well, all the info it gives me is that if I make double bets in X, I reach the same ELPH, expressed in money. So what? I personally don't see any comparison of the value of the games. ELPH is more a kind of Table that asks a punter "How much do you want to lose per hour?" and shows the size of wagers s/he must bet in every game. All games are equivalent.

HE or EoR are pretending to point "this game is objectively better than that one". An altogether different proposition.

My gripe is that they fail to provide that service.

Yes, the intent of the ELPH table would be to make a comparison between two different games from a monetary standpoint. It would then be up to the player to decide whether the cost to play was worth the game experience. Some people like roulette better than they like blackjack, so they should play roulette. If they're in the US, that costs them twice as much per hour as blackjack, given equal bet levels. That's useful information. It doesn't mean, nor is it intended to mean, that roulette is objectively better than blackjack, or vice-versa. "Better" isn't well-defined. ELPH is like TCO (total cost of ownership). One can compute the TCO of a Toyota Prius vs. a Mercedes S550, and the TCO of the Toyota is undoubtedly lower, but some people want to drive a Mercedes. There's nothing wrong with that, just like there's nothing wrong with playing roulette (or slot machines, or keno, or the state lottery). It just costs more to do the latter. My point is that quantifying that cost is a valuable exercise. That shouldn't be particularly controversial.

I do agree that attempting to find an objective definition of "better" is a fool's errand, because "better" is inherently subjective. HE or EoR look at percentage losses on an individual transaction, ignoring how long that transaction takes. But even percentage losses aren't an objective metric because those percentages can be manipulated in a misleading fashion. I gave a craps odds example in a prior post. And one could construct an artificial form of roulette, where the outside bets may only be booked as 10 units but losses only removed 1 unit and wins only paid 11-to-10. As a percentage of total wager, that artificial bet has a better EV than blackjack or craps, but nobody would (or should) argue that it's "better" than either normal roulette or, frankly, craps or blackjack.

Your command is my wish. Here's my new Expected Loss per Hour by Game Calculator.

Thank you kind sir. Element of Risk loses a bit when nobody you try and explain it to knows what the hell you are talking about !

Okay, but, um, it's not an Element of Risk calculator. It's an Average Loss calculator (or for those who prefer the classical but misleading term, an Expected Loss calculator).

I'd like to see a roulette table that spins 55 times an hour.
Even Rapid Roulette and the auto tables aren't that fast.
Average for a real dealer is abour 32, give or take. Slower
whn it's real busy.

I knew people would whine about the default values. But that's why it's a CALCULATOR, not a table. If you don't like the default values, choose your own.