Weird (dumb) question about odds.

Quote: Ahigh

What, are you developing "age progression" photoshop software on the side as well these days?

I had a few moments to continue this.

As I said, I've no objection to how anyone accounts for his money or measures his gambling experience. However, when it comes to expressing and comparing the edge (house advantage) of the various bets I think it's important to understand how it's most commonly expressed and how different expressions can sometimes be misleading.

Like it or not, the house advantage of craps bets is most often expressed as the average percentage lost per dollar wagered. Our host, Michael defines the house edge as:

"The ratio of the average loss to the initial bet." https://wizardofodds.com/gambling/house-edge/

So, what is the average loss? It's the net amount won or lost when summing all probable outcomes of the initial bet, right? Well, what is the initial bet? Does it include money you bought-in for that's still in your rack? Does it include money in your pocket? Does it include money on a different bet? If so, then why didn't Michael define it as the average loss to the amount wagered on ALL bets? Fact is, the initial bet is the full dollar amount wagered on the bet in question and not on any other bets. This amount determines what the house will earn.

Furthermore, the house advantage is typically expressed per resolution (meaning per winning or losing outcome, not including pushes.) Indeed, the majority of books you've ever read on craps probably list the house advantage on Place6 as 1.52%, right? Well, that's the average loss per resolution and has become the defacto standard which most people think about when you talk about "house advantage". In my opinion it makes the most sense since the house gains the advantage through wins and losses and not from bets that push. This really boils the house advantage down to it's core elements.

A person can certainly measure his average loss against his total outlay (return on investment), against a number of events, against a tick of the clock, or any other metric he chooses regardless of how many wagers it may entail. It may provide him with very useful information but it will NOT change the underlying house advantage of the bets he employs and it's NOT comparable to the defacto standard house advantage.

I think you'd agree that comparing the loss per ROLL of one wager against the loss per RESOLUTION of another wager would be improper and potentially misleading. It would be comparing apples to oranges. Yet this improper comparison is exactly the same type of thing that happens when some folks compare the loss per resolution of combined wagers to the loss per resolution of single wagers. Without realizing it, they're using the term "resolution" differently.

$12 Place6 bet:
On any win, the dealer multiplies $12 by 7/6 and pays $14
On any loss, the dealer takes $12

$6 Place6 and $6 Place8 bets:
On any win, the dealer multiplies $6 by 7/6 and pays $7
On any loss, the dealer takes $12

In both cases, the full amount wagered (the initial bet) is $12. However, in the case of the combined bet, does the dealer base his 7/6 payoff on the full amount wagered? No! So does this conform to our "common" understanding of house edge? No! Does it make any sense to compare it to the standard edge? No!

(Side note: if the bets in the combination win and lose at the SAME time then the full amount wagered would apply to every resolution and the combined edge would naturally be comparable with single wagers.)

What typically happens with folks who claim that combined bets reduce the edge, is they divide their net loss by the full amount wagered for every resolution even though the full amount wagered (initial bet) does not always resolve. It should by now be obvious that such a calculation does not represent the same thing as the common house edge and it certainly cannot be used to claim that the edge has been lowered.

Was Ahigh's math correct? Sure. Was his edge per resolution correct? Sure, as long as you understand that his definition of resolution is different and not on a par with the standard house edge.

Ahigh's post clearly indicates that the Place6/Place8 combination lowers the edge to less than either Place bet alone and it seems I'm not alone in reading it that way. But I'll grant that words can be tricky and it's possible he may have meant something else so I asked him several times to clarify: Does the Place6/Place8 combination lower the house advantage to less than either bet alone? He won't say but I hope others who are in doubt will understand that numbers can be misleading. Bet combinations may make a fun strategy but they won't lower the house advantage.

Quote: MrV

Quote: Ahigh

What, are you developing "age progression" photoshop software on the side as well these days?

lol

Quote: Steen

I think you'd agree that comparing the loss per ROLL of one wager against the loss per RESOLUTION of another wager would be improper and potentially misleading. It would be comparing apples to oranges. Yet this improper comparison is exactly the same type of thing that happens when some folks compare the loss per resolution of combined wagers to the loss per resolution of single wagers. Without realizing it, they're using the term "resolution" differently.

Thank you!

As for Ahigh, it's not that he 'doesnt realize it', he's a pretty smart guy, nor do I think he is up to something pernicious. We do get posts from people who are trying to mislead due to various motives, but that's not Aaron IMO. However, to pick at him some myself, he is a bit too proud of his smoke and mirrors and leaves it to the reader to discover the basic facts of your paragraph above.

Quote: NowTheSerpent

If we're talking EV per bet resolved then the total amount bet would be $30*11 + $1*36 = $366 and a total loss of $10 would give an EV = -2.7322%.

Yes, of course, I fully agree. Expressing the average loss as a function of the action is how I would figure it too.

I hope you can see now from my other posts that I was trying to show that Ahigh's method of expressing the average loss per resolution (without regard to which bet has action) is NOT on a par with the standard house advantage and does NOT represent a decrease in the edge.

The point was: If anyone thinks that Ahigh's method of expressing the edge points the way to better bet combinations, then the Place6/Twelve would be superior to Place6/Place8.

Quote: Steen

Yes, of course, I fully agree. Expressing the average loss as a function of the action is how I would figure it too.

I hope you can see now from my other posts that I was trying to show that Ahigh's method of expressing the average loss per resolution (without regard to which bet has action) is NOT on a par with the standard house advantage and does NOT represent a decrease in the edge.

The point was: If anyone thinks that Ahigh's method of expressing the edge points the way to better bet combinations, then the Place6/Twelve would be superior to Place6/Place8.

Quote: Ahigh

When you lower the number of rolls to resolve a bet, you lower the edge per resolution.

You say that you didn't compare anything, that I'm putting up straw men. But what's that word you wrote there ... "lower"? Seems to me you've used it many times. That word describes either the change in something from a beginning state to an ending state, or the difference between the states of separate things. In either case, it's a COMPARISON of states!

Quote: Ahigh

You do understand that a resolution of a bet depends on the definition of the bet. And the definition of the bet defines the number of rolls for the bet.

Well, the house defines the resolution of a Place6 bet. Would you call it a fixed definition? I would. It doesn't change based on the weather, how much you wager, what other wagers you have, how many times you lost, etc. And so the average number of rolls to resolve the Place6 is also FIXED. Certainly you must agree because you said so yourself.

Quote: Ahigh

I defined the bet to be a bet that you can roll a six or an eight before a seven.

No problem, you can define all the bets you like. But again, it's a fixed definition and so the average number of rolls to resolve your bet is also FIXED.

So what exactly have you lowered? The average number of rolls to resolve Place6 is fixed and the average number of rolls to resolve your fantasy bet is also fixed. You haven't lowered anything but your use of the word "lower" implies that you have. Or do you mean that the average number of rolls to resolve your fantasy bet is by definition lower than the average number of rolls to resolve Place6? But that's a comparison. I thought you said you weren't making a comparison.

And what about those other words you used, "resolve" and "edge"? Did you explain in your original post that they have different meanings in the Place6 versus fantasy bet comparison? Since I just explained it in another post I'll forego the explanation here.

Quote: Ahigh

The differences in the way people look at "resolved bets" are the source of the confusion.

Oh, so you agree that the term "resolution" is being applied diffently? That's just what I said, so then why are you squawking about straw men? The resolution of your fantasy bet is different than the Place6 bet and therefore the edge that you compute is non-standard. This makes your comparison (without explanation) misleading.

and is this really Ahigh?

or maybe this is really Ahigh

removed
silly

When you lower the number of rolls to resolve a bet, you lower the edge per resolution.



I think we are begining to see a complete lose of common sense on this board and lacking any
conversation which is relevant to the game of craps, we are seeing sentences like the one above.


The house edge on your bets do not change with the number of rolls before a resolution, if you have
a $10 bet on a 10, that edge is the same on each roll, no matter how long it takes to either hit the
10 or the 7.

What does change is your loss expectation , but that is not edge. the faster you have a resolution, the
less money you have exposed to the edge. Now resolution does not have to be positive, so it could be
said that the faster you have negative resolutions, the less money you have.

Say you have bet a hard 8 and if it takes 2 rolls or it takes 10 rolls the house edge is
9.09%. You cant say well if i hit a hard 8 on the third roll, the house edge is only 6%.


Dicesetter

Quote: dicesitter

When you lower the number of rolls to resolve a bet, you lower the edge per resolution.



I think we are begining to see a complete lose of common sense on this board and lacking any
conversation which is relevant to the game of craps, we are seeing sentences like the one above.


The house edge on your bets do not change with the number of rolls before a resolution, if you have
a $10 bet on a 10, that edge is the same on each roll, no matter how long it takes to either hit the
10 or the 7.

What does change is your loss expectation , but that is not edge. the faster you have a resolution, the
less money you have exposed to the edge. Now resolution does not have to be positive, so it could be
said that the faster you have negative resolutions, the less money you have.

Say you have bet a hard 8 and if it takes 2 rolls or it takes 10 rolls the house edge is
9.09%. You cant say well if i hit a hard 8 on the third roll, the house edge is only 6%.


Dicesetter

Yes. A complete lose of it. Finally someone who gots it. I thot there were nuns.

I hates to be to the linguistic police, but the correct phrase is: I thots there were nuns.

Quote: Ahigh

That is absolutely true making the assumption that you only have one bet at a time that has an edge!

If you consider the combination of all bets on the table as one bet, the (weighted) edge per roll is the only sane way to proceed. Multiplying the weighted edge per roll by the average bet amount is the best way to calculate average cost for playing the game. And it is a function of the number of rolls, not a function of the number of bets placed unless you always and consistently bet the bet until resolution (something I don't personally do FWIW).

Some examples of bets that I take:

$110 even working. -- combination of buy the 4 and 10 for $25 each and a $30 six and a $30 eight. This combo-bet pays $49 for a four or a ten and $35 for a six or an eight. Each payment costs exactly a $1 vig.

Edge per roll is ( ( 50/110 ) * 0.33 + ( 60/110 ) * 0.46 ) = 0.401 -- better than the pass line with no odds, plus .. compared to the pass line, I am only committed for a single roll.

If I "hit it and quit it" meaning that I bring the bet down on the first hit, it lasts for 1.63 rolls. So the bet that isn't marked on the table that I can roll any even box number before a seven is only a 1/160 edge when I hit a four or a ten and a 1/146 edge when I hit a 6 or an 8. The 4 or 10 is 6/16th of the win events and the 6 and 8 is 10/16th of the win events. So the edge per bet resolved on this bet that I am creating here is ((1/160)*(6/16))+((1/146)*(10/16)) = 0.66% per resolved bet. If you and your thinking that edge per bet resolved is the best way to go, then I advise you to follow through and create some of your own bets and take those bets because you can get a much lower edge by putting more money at risk! I'm pointing out that I don't think that way because looking at edge per bet resolved makes an assumption that you will be done with a single resolved bet. Instead I don't look at it that way. I look exclusively at edge per roll and I try to make the fewest number of bets possible keeping my edge per roll low (minimize hedging) and try to win in as few tosses as possible and go with a profit if I can get it.

Here's another bet that I look at in terms of two bets combined...

Hard 8 for $1 and place the eight for $30:

Edge per roll is ((1/31) * 2.78) + ((30/31) * 0.46) = 0.535% edge per roll -- you can focus on the hard 8 having a high edge, or you can look at the total edge being relatively low. Increasing the edge per roll from 0.46% to 0.53% is a 15% increase in the edge. I consider the combination of these two bets a single bet. That's just how I look at it. Sure it's not on the felt, but I'm betting on the eight, and I get paid a little more if it comes hard.

Now I'm not saying people that don't do this have anything wrong with them, but I am saying that looking at the weighted edge per roll is just another way of analyzing the game where you don't get all upset about one leg of a complex series of bets having a high edge if the weighted average is sufficiently low .. it's a big picture sort of way to look at the game that to me is perfectly sane.

The correlary is that you will never find me betting a single $5 bet on the four on my or anyone else's roll. That's a 6.66% edge and 1.66% edge per roll! TERRIBLE!!!

My cutoff point is 1.00% edge per roll. And generally speaking, I don't usually take bets that sum up to more than 0.8% edge per roll under any circumstances. I have recently made exceptions for playing crapless in order to get bigger pays on crap numbers, which on a regular table, I have no low edge way to get paid on the 12, and the only low edge way to get paid on an ace-deuce is from a DC bet.

Ahigh, I found this post from "Biased Dice: the science begins" in which you were the OP. After blowing the dust off of it and applying it here I'm interested in clarification, if you wouldn't mind. It may help some of us that are lost trying to follow. Please elaborate. Thanks.

Quote: MaxSwelle

Ahigh, I found this post from "Biased Dice: the science begins" in which you were the OP. After blowing the dust off of it and applying it here I'm interested in clarification, if you wouldn't mind. It may help some of us that are lost trying to follow. Please elaborate. Thanks.

To me, it's all pretty clear. Maybe if you asked a question?

I got it. Really

Anybody who doesn't understand isn't going to. It's a waste.

Many don't even understand why they want $6 odds on a 5/9.

I give.

There are none so blind as those who will not see !

Waxed poetic, as usual. It has become so clear to me however-right before my eyes.

Quote: MaxSwelle

Waxed poetic, as usual. It has become so clear to me however-right before my eyes.

Do appreciate the quote. You bet on the dice. Resolution is a tricky concept for some here.

Per roll and done easy.

Quote: Ahigh

Do appreciate the quote. You bet on the dice. Resolution is a tricky concept for some here.

Per roll and done easy.

I'd take it over a triple paying 12 Field any day.

To further illustrate the point, let's use some extreme bet amounts at a table with extreme limits:

$12,000,000,000.06 Place6 bet:

5 ways to roll 6, win $14,000,000,000.07 = $70,000,000,000.35
6 ways to roll 7, lose $12,000,000,000.06 = -$72,000,000,000.36
20 ways to push = $0
--------------------------
Net = -$2,000,000,000.01
Net per dollar wagered = -$2,000,000,000.01/$12,000,000,000.06 = -1.67%
Net per dollar wagered per resolution = -1.67%/11 = -1.5151%

Now let's compare this to the following combination:

$12,000,000,000 Place6
$0.06 Place8
-----------------------------
$12,000,000,000.06 Total wager

The total amount wagered remains the same, but before we figure the edge on this combo, what does your gut feeling tell you about the 6 cents that was moved to the Place8 bet? Is it significant? Will it affect the edge on the $12 billion Place6 bet or do you think the house edge will for all practical purposes remain the same?

5 ways to roll 6, win $14,000,000,000 = $70,000,000,000
5 ways to roll 8, win $0.07 = $0.35
6 ways to roll 7, lose $12,000,000,000.06 = -$72,000,000,000.36
20 ways to push = $0
--------------------------
Net = -$2,000,000,000.01
Net per dollar wagered = -$2,000,000,000.01/$12,000,000,000.06 = -1.67%
Net per dollar wagered per resolution = -1.67%/16 = -1.0416%

Wow, according to Ahigh's rationale, moving a paltry 6 cents to the Place8 still LOWERS the combined edge per resolution to 1.0416%!! Happy days are here again! Are you moved?

What has really happened here? The math is correct yet an insignificant restructuring of the wager still drove the edge per resolution down. Can you see now that it's because the term "resolution" doesn't mean the same thing as it did with Place6 alone? When we think about the house edge, we normally understand a resolution to mean that the whole wager resolved, whereas Ahigh uses it to mean that some part of it resolved, even if that part is insignificant!

Now again ... Ahigh's math is still correct and it's true that a $12 billion Place6 bet and 6 cents Place8 bet will lose 1.0416% per resolution, but knowing what you know now about the term "resolution" can you see that it doesn't give us a clear picture of the house edge and to say that the edge of Place6/Place8 combo is lower than the edge of Place6 alone is completely misleading?

I try to point this pitfall out in my help file in my explanation of expected value. My recommendation to avoid it is to express the edge as the average loss per dollar of action, and I define action to be the amount that was wagered on a bet that wins or loses. It's the amount of money directly responsible for an outcome, it's the "initial wager" which the dealer pays or takes. If you've bet $22 inside and a 6 is rolled, the action is $6 because the dealer uses it to calculate the $7 payoff. He could care less what you have on other wagers and a player having only a $6 Place6 earns the exact same amount that you do.

May I reply for Aaron?

just show that the ev ?
thats really what matters..

place 6
win 5/36 * 7 = .97
lose 6/36 * 6 = 1
total = .03
.03/6 = .005
or .02778/6 = .00463

place 6/8
win 10/36 * 7 = 1.94
lose 6/36 * 12= 2
total = .06 (we have two place bets so /2 =.03)
.06/12 = .005
or .05556/12 = .00463

Quote: bahdbwoy

just show that the ev ?
thats really what matters..

place 6
win 5/36 * 7 = .97
lose 6/36 * 6 = 1
total = .03
.03/6 = .005
or .02778/6 = .00463

place 6/8
win 10/36 * 7 = 1.94
lose 6/36 * 12= 2
total = .06 (we have two place bets so /2 =.03)
.06/12 = .005
or .05556/12 = .00463

I think I showed that many posts ago :)

Quote: Steen

Wow, according to Ahigh's rationale, moving a paltry 6 cents to the Place8 still LOWERS the combined edge per resolution to 1.0416%!!

If you think that's how I would calculate things, I can understand why you would attack me.

I'll give you points for creativity, anyway.

Quote: odiousgambit

May I reply for Aaron?

Yes, I fully understand. It just appears that some other folks were taken in by his argument (or leaning toward it) and I thought they might be interested to know why it doesn't hold water.

Quote: Ahigh

If you think that's how I would calculate things, I can understand why you would attack me.

I'll give you points for creativity, anyway.

Oh, that's right, you would calculate it using edge per roll together with the average number of rolls to resolve. So ...

$12,000,000,000 Place6
$0.06 Place8
-----------------------------
$12,000,000,000.06 Total wager

5 ways to roll 6, win $14,000,000,000 = $70,000,000,000
5 ways to roll 8, win $0.07 = $0.35
6 ways to roll 7, lose $12,000,000,000.06 = -$72,000,000,000.36
20 ways to push = $0
--------------------------
Net = -$2,000,000,000.01
Net per dollar wagered = -$2,000,000,000.01/$12,000,000,000.06 = -1.67%
Net per dollar wagered per roll = -1.67%/36 = -0.463%

Avg # rolls to resolve = 36/16 = 2.25
Edge per roll x avg#rolls = -0.463% x 2.25 = -1.0416%

Yes, I see now ... -1.0416% is much different calculated this way than -1.0416% calculatd the other way!

Quote: Ahigh

If you think that's how I would calculate things, I can understand why you would attack me.

I'll give you points for creativity, anyway.

Oh, and by the way, I'm not attacking you. I'm attacking your argument.

I can see why you think so though. When someone disagrees with you, you say things like:

- You have a limited perspective.
- You're incapable of understanding.
- You cannot understand things that are outside your current domain of accepted knowledge

When you say things like this, it puts people off. When people say things like this to me, I try to ignore it or minimize it, but sometimes it goads me into responding in kind which is why I had no reservations about calling your argument hogwash.

But honestly, rather than post one-liners, why don't you answer my questions, then address my argument and convince me that you're right? If you can do that, I'll be happy to learn something new.

" If you can do that, I'll be happy to learn something new. " Might be a life turning event for you .