Hello Darkness My Old Friend

Simon and Garfunkel fans will recognize the refrain, though for me it's my 'new' friend.

I've been playing Craps in Casinos for about 18 years now, from the start having at least begun to search the internet for the smartest ways to play ... probably found Wizardofodds.com right away. And the Wizard has always said that it only seems like the better free odds are on the Don't Pass bets because they allow you to bet more on the free odds. A common example is if 3x4x5x is the max allowed Rightside, they typically allow you to go as high as 6x on the Don't. 

Quote: wizard

... the don't pass [free odds] look deceptively significantly better. The main reason it is less is the odds multiple is relative to your bet taking odds, and the win when laying odds.

However, this contains one assumption: that you always take max odds. I have known this for years, but assumed that if you didn't max the odds, but took similar odds, you'd lose that HE advantage. I only recently examined this, since I was balking at 6x odds with $15/25 table minimums that seem to be the new thing around me. I was doing 4x Darkside instead and assuming this put me against a similar HE as 3x4x5x Rightside. 4x Rightside is in fact similar, -0.374% vs -0.347%, mind these are combined bet odds HE.... but to my surprise 4x Don't odds are lower, -0.273% HE. As far as average bet and total action, I think these are likely similar, playing Craps using 4x odds Rightside or Darkside. But the HE is lower ... I am surprised this is never mentioned! 

I'm currently aiming for $2000 in total action during a session. That difference would mean only about a buck and half in expectation. More importantly, I also wonder about the variance.

Quote: wizard

Although the player may bet more laying the odds, the variance is still the same. For example, if the point is a 4, and the table allows 3X odds, the variance is the same betting $30 with a 1/3 chance to win $60, or $60 with a 2/3 chance to win $30

I'm thinking the variance Darkside may be lower as well when the player does not max it out at 6x as the example here is doing. Note that this does not contradict the Wizard! His example is for maxing odds. This lower variance I can be less confident about ... but I am really thinking it is with 4x DP betting vs 4x Pass betting, as the former gets you less than even money, the latter more than even money, while bet size is the same.  You can vote. I forgot to make it a poll

Formulas and quotes taken from the links and formulas also are at my last blogpost


https://wizardofodds.com/games/craps/appendix/1/


https://wizardofodds.com/games/craps/basics/

I've been betting $3 PL with $3, $4, $5 odds or $3 DP with $6 odds with the same $100 stake for a month now. Multiply that by 5 and it'd be a $500 stake. Multiply that for a $30 table for a $30 PL with $30, $40, $50 odds or $30 DP with $60 odds and it'd be a $1,000 stake. I'm not getting anywhere but there's been some ups and downs. I sit out while two hot shooters in a row rack up 6 points between them and FOMO. I'm on the Do side while there's six point 7-outs in a row. Maybe it does average out to zero, but missed bets make it all lopsided.

Odious…. How much you bet on the ‘free’ odds, whether on pass or don’t pass, is irrelevant to the house edge. Those bets have no house edge. You are subject to the house edge SOLELY on your pass line or don’t pass bets. Period.

Of course your variance will be higher the more you bet on the free odds.

Have fun!

Quote: ChumpChange

… missed bets make it all lopsided.

I don’t doubt that seems so, but I thought picking when to bet and when not to has zero impact on the house edge, along the lines of you can’t predict when a streak will begin nor when it will end.

Quote: SOOPOO

Odious…. How much you bet on the ‘free’ odds, whether on pass or don’t pass, is irrelevant to the house edge. Those bets have no house edge. You are subject to the house edge SOLELY on your pass line or don’t pass bets. Period.

Of course your variance will be higher the more you bet on the free odds.

Have fun!
link to original post

I don't know if you realize this has been beat to death, but I'll try again

If you see someone who is betting $50 on the Pass, and he wants some advice, you can suggest to him he bet the table minimum instead, then add the free odds to make the combined bet $50. Here the betting makes more sense and he even benefits from reducing his total action

If you see a different guy betting the table minimum, and suggest to him he *adds* the free odds, you're not doing him any favors ... he hasn't reduced the HE and he's increasing his total action

If you see the latter guy wanting more action ... and eventually that's everybody I ever met, and see him making middle table bets to get more action ... that's what he will likely do btw, it's what he will see tons of players do... and suggest to him to cut that out and do free odds instead, you're lowering the HE but he's keeping his total action probably about the same

the suggestion to not do free odds at all but just bet the table minimum sounds OK, but nobody, nobody, does that for very long. The Standard Deviation of the Pass Line bet is very close to 'one'. It's mindlessly boring

Quote: SOOPOO

Odious…. How much you bet on the ‘free’ odds, whether on pass or don’t pass, is irrelevant to the house edge. Those bets have no house edge. You are subject to the house edge SOLELY on your pass line or don’t pass bets. Period.

Of course your variance will be higher the more you bet on the free odds.

Have fun!
link to original post

This is a misguided post, SOOPOO.

Soopoo is not totally off base if he's just observing the typical craps player ... so the caution he gives about free odds doesn't come from nowhere

What I see is most players learn to play from other players and from the dealers. So they are introduced to the idea of getting a lot of other action besides the basic bet right away. And, wouldn't you know it, this means he's likely to have the wrong idea about the free odds. Most likely he'll play the free odds too, probably at about 2x level. But he's just adding another bet. In other words, he's got a bunch of favorite bets and the free odds are *added* sometimes. If he plays them and declines to make one of his other bets when he does, that's the right way to do it, but that's not what I see.

So I guess I can't make sense to Soopoo because he imagines maybe you can just play the Pass or the Don't and add no other action. But I am saying that just isn't the way anybody is going to play ... everybody is going to want more action. The smartest way to do it is with the free odds. If you want to say beware, say beware of the variance, you might not be able to take it

We got sidetracked from a question I was asking: all things being equal , is the variance less playing the Don't?

My point is, if you compare playing darkside going max odds, often 6x, to playing say rightside 3x4x5x or roughly equal 4x, maybe it is the case that the variance is comparable. But what if you play darkside with 4x odds? The HE is lower and I suspect the variance as well. Anybody know?

Quote: odiousgambit

We got sidetracked from a question I was asking: all things being equal , is the variance less playing the Don't?

My point is, if you compare playing darkside going max odds, often 6x, to playing say rightside 3x4x5x or roughly equal 4x, maybe it is the case that the variance is comparable. But what if you play darkside with 4x odds? The HE is lower and I suspect the variance as well. Anybody know?
link to original post

The variance of dp/dc with max odds is definitely higher than the variance of p/c with max odds. If on a 3x4x5 table you, say, use only 4x odds with dp/dc bets, the dc/dp variance will drop down a bit and probably be close to full odds on p/c bets. Not sure how close...maybe still a bit higher.

Whatever odds are used, on either side, the overall HE will not change...The HE will be based on the flat bets only, with the dp/dc bets having a slightly lower HE than the p/c bets.

Quote: UP84

Quote: odiousgambit

We got sidetracked from a question I was asking: all things being equal , is the variance less playing the Don't?


My point is, if you compare playing darkside going max odds, often 6x, to playing say rightside 3x4x5x or roughly equal 4x, maybe it is the case that the variance is comparable. But what if you play darkside with 4x odds? The HE is lower and I suspect the variance as well. Anybody know?
link to original post

The variance of dp/dc with max odds is definitely higher than the variance of p/c with max odds. If on a 3x4x5 table you, say, use only 4x odds with dp/dc bets, the dc/dp variance will drop down a bit and probably be close to full odds on p/c bets. Not sure how close...maybe still a bit higher.

Perhaps you can correct the following reasoning: It seems to be true that bets that pay more than even have a higher variance than lay bets. In Craps, see link, the hardways etc have a standard deviation value of 2 or 3 or so, while betting on the 2 or 12 will get you up to 5.09! The only listing I see for a lay bet there, placing to lose on 4 or 10, has an S.D. of 0.69! I just have been led to believe that it's common sense that betting on something that has a high payoff is what big variance is all about, and to do the opposite is to lower variance, with evidence. 

So it raises the question, how does this not hold up for the cited situation?
https://wizardofodds.com/gambling/house-edge/

Quote:

Whatever odds are used, on either side, the overall HE will not change...The HE will be based on the flat bets only, with the dp/dc bets having a slightly lower HE than the p/c bets.
link to original post

More on that later.

Quote: UP84

Quote: odiousgambit

We got sidetracked from a question I was asking: all things being equal , is the variance less playing the Don't?

My point is, if you compare playing darkside going max odds, often 6x, to playing say rightside 3x4x5x or roughly equal 4x, maybe it is the case that the variance is comparable. But what if you play darkside with 4x odds? The HE is lower and I suspect the variance as well. Anybody know?
link to original post

The variance of dp/dc with max odds is definitely higher than the variance of p/c with max odds. If on a 3x4x5 table you, say, use only 4x odds with dp/dc bets, the dc/dp variance will drop down a bit and probably be close to full odds on p/c bets. Not sure how close...maybe still a bit higher.

Whatever odds are used, on either side, the overall HE will not change...The HE will be based on the flat bets only, with the dp/dc bets having a slightly lower HE than the p/c bets.
link to original post

The variance of DP with 6x odds (24.1357) is nearly identical to that of PL with 3-4-5 odds (24.1634). The DP variance would be the same as PL if a DP bet was an exact mirror of PL, but it isn't since that would give the DP bettor a 1.41% advantage over the casino. It's an exact mirror except for how 12s during comeout are treated, and that's what causes the tiny discrepancy in variance

The HE on the line bet doesn't change but the overall HE decreases with more odds since a larger portion of the total bet is not exposed to HE

Quote: Ace2

The variance of DP with 6x odds (24.1357) is nearly identical to the that of PL with 3-4-5 odds (24.1634). The DP variance would be the same as PL if it a DP bet was an exact mirror if PL, but it isn't since that would give the DP bettor a 1.41% advantage over the casino. It's an exact mirror except for how 12s during comeout are treated, and that's what causes the tiny discrepancy in variance

have you read my response? Why isn't the variance less, the odds bet darkside being a lay bet?

where are you getting your variance figures from?

Quote:

The HE on the line bet doesn't change but the overall HE decreases with more odds since a larger portion of the total bet is not exposed to HE
link to original post

this is the thing people who don't play Craps don't get. They seem to think you might play the pass or the don't and decline to have other action. Nobody plays like that, which is I guess why they don't know, they don't play. If you are going to get more action, then no HE on that is the best you can do. All other extra action has house edge, some awful.

Quote: odiousgambit

My point is, if you compare playing darkside going max odds, often 6x, to playing say rightside 3x4x5x or roughly equal 4x, maybe it is the case that the variance is comparable. But what if you play darkside with 4x odds? The HE is lower and I suspect the variance as well. Anybody know?
link to original post

Compared to 6x, playing DP with 4x odds raises overall HE from 27 bips to 37 bips and drops variance from 24.14 to 12.71. 4X on DP would be comparable to 4 * 2/3 = 2.67x odds on PL. Compared to 3-4-5x, playing PL with 2.67x odds raises overall HE from 37 bips to 51 bips and drops variance from 24.16 to 12.33 (pretty close to 12.71 for 4x DP). If you're going to lay 4x on DP make sure you're flat betting in multiples of 6.

6x is the other side of 3-4-5x. No matter what the point is, your PL odds are paid at 6x your flat bet, which is why you lay 6x if you're betting DP

Quote: Ace2

Quote: odiousgambit

My point is, if you compare playing darkside going max odds, often 6x, to playing say rightside 3x4x5x or roughly equal 4x, maybe it is the case that the variance is comparable. But what if you play darkside with 4x odds? The HE is lower and I suspect the variance as well. Anybody know?
link to original post

Compared to 6x, playing DP with 4x odds raises overall HE from 27 bips to 37 bips and drops variance from 24.14 to 12.71. 4X on DP would be comparable to 4 * 2/3 = 2.67x odds on PL. Compared to 3-4-5x, playing PL with 2.67x odds raises overall HE from 37 bips to 51 bips and drops variance from 24.16 to 12.33

thank you!

Quote:

[that's] (pretty close to 12.71 for 4x DP). If you're going to lay 4x on DP make sure you're flat betting in multiples of 6.

6x is the other side of 3-4-5x.

it is the 'other side' but it seems to be connected to making it easy for the dealers to remember what the payoff is. Somebody somewhere must have argued at some point not to allow such high free odds, but was shot down due to the 'easy for dealer' factor? Seems that way to me anyway.

Quote:

No matter what the point is, your PL odds are paid at 6x your flat bet, which is why you lay 6x if you're betting DP
link to original post

You mean if it's 3x4x5x Rightside. But you don't have to do this, and I have concluded I don't necessarily want the high variance. 12.33 suits me fine. And the HE is lower than going 4x Rightside. I'm surprised this is being discussed for the first time [first time I've seen it that is].

PS: you don't mean "paid at 6x" I don't think. Set at 6x, but pays a varying less than even

Quote: odiousgambit

Perhaps you can correct the following reasoning: It seems to be true that bets that pay more than even have a higher variance than lay bets. In Craps, see link, the hardways etc have a standard deviation value of 2 or 3 or so, while betting on the 2 or 12 will get you up to 5.09!

You're reasoning would hold true IF you were betting the same amounts. But you are betting 6x on DP not 3-4-5.

Here's a simple example, If you buy the 4 for $25, commission on win only (pays $49), the return is 1/3 * 74/25 = 98.67% and the SD is (1/3 * 2/3)^.5 * 74/25 = 1.3954. If you were to bet the other way, laying the 4, you'd lay $50 to win $24, the return is also 98.67% (2/3 * 74/50) and the SD is (1/3 * 2/3)^.5 * 74/50 = 0.6977. So the SD for laying is half BUT your bet amount is double, resulting in the same total SD. Same concept for DP vs Pass...you are betting more in odds (the opposite of PL odds) on DP

I believe all the "rightside/wrongside" bets are structured this way. You have the same long-term expectation and variance on either side (or essentially the same since PL and DP flat bets are close to, but not exactly opposite)

Btw it's easy to calculate variance for any odds amount

Quote: odiousgambit

You mean if it's 3x4x5x Rightside.

PS: you don't mean "paid at 6x" I don't think. Set at 6x, but pays a varying less than even
link to original post

I have no corrections to make.

Whether you're betting 3x odds on 4/10, 4x odds on 5/9, or 5x odds on 6/8, a PL odds win pays 6x flat. Which is why the inverse (DP) is to lay 6x for every point number, on which an odds win will pay 3x, 4x or 5x depending on the point

I'll see if I can study that and do it

bear in mind I'd be happy to go 6x at a $5 table, most times too at a $10 table, but $15 and $25 make for bets that are too big. Even 3x4x5x Rightside I balk at max odds when $15/25.

Quote: SOOPOO

Odious…. How much you bet on the ‘free’ odds, whether on pass or don’t pass, is irrelevant to the house edge. Those bets have no house edge. You are subject to the house edge SOLELY on your pass line or don’t pass bets. Period.

Of course your variance will be higher the more you bet on the free odds.

Have fun!
link to original post

That concept might hold true if, for instance, you're normally a $100 passline bettor that then decides to add 3-4-5x odds "just to get more variance at no additional cost". You’d still be a $100 bettor in terms of HE but now a $500 bettor in terms of variance! For low-edge games, you won't even notice the HE in the short term, but a 4.92 factor increase in variance is HUGE.

What that bettor should do is stay around his $100 total level by betting $25 on the PL, which will give him an average total bet of $94.44 including 3-4-5 odds. For about the same amount of action, his total cost of play will be around 74% lower since 74% of his total action is no longer exposed to any HE.

Also, the standard deviation for $25 plus 3-4-5 odds is only 23% higher than the SD for $100 with no odds since the base bet is 75% lower. The general belief is that playing max odds means huge variance, but it's actually not much of an increase if you are just reallocating your total bet amount from flat to odds. The only reason it does increase is because odds wins are paid at more than even money while PL is always even money. Average odds win pays about 2.5 for 1, a 25% increase over 2 for 1 on passline, hence the SD increase