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1 vote (11.11%)
8 votes (88.88%)

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mustangsally
mustangsally
Joined: Mar 29, 2011
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February 14th, 2012 at 2:42:25 PM permalink
from:ask-the-wizard
about half down

Hi, if person A makes 1000 consecutive bets on the pass line without backing up his bet, and person B makes 1000 consecutive bets on the pass line and he takes 100X odds whenever possible,
doesn’t each person lose the same amount of money?
— Blake Haas from Thousand Oaks

The Wizard.
Yes. I can just imagine the follow up question to be why I recommend taking the odds if doing so doesn’t help to win more.

What I suggest is betting less on the pass so that your need for action is mostly met by a full odds bet. For example if you are comfortable betting about $90 per bet, and the casino allows 5x odds, then I would drop the pass line bet to $15 and bet $75 on the odds. That will lower the overall house edge from 1.414% to 0.326%.

Wow!
Sally says that "taking the odds DOES help to win more." Looks like I am "at odds" with the Wizard's statement.

(The Wizard does a great job on explaining how to make a better pass line bet with odds but leaves out the reason why other than lowering the house edge. Many just see that it is lower because you are betting more. That is true.)

First, the question by Blake
it is not a fair comprison.
This is the ever so classic mistake made in statistics of comparing apples to oranges.
(I should know. I broke the rules maybe a zillion times and at times still do)

Why?,it does not represent commensurate risk.

Steen, in WinCraps talks about it and I will make my comments about that later on and Alan Krigman also seems to be the only one "out there" that says it gives the player the best chance to win more. OK, Alan Shank, "goatcabin" has also tried to drive home this point.

But the WORLD is stuck on EV and EV only, IMO.
They do not want to consider variance (SD). Too hard or too much work, I guess.


I will show this with the math first that "by taking the odds does help to win more."

But what really is the eye opener is the simulation results.
Simulation results can really drive home a point way better than just straight math for most folks.
It blew my mind!
I'm OK now.
--------------------------------------------------------------------------------------------
Craps: Pass no odds or Pass 100x odds. same loss - revisited
1000 pass no odds $5 bets
$5000 total action.

1000 pass 100X odds $5 bets (average bet $338.33)
total action $338,330

By total resolved action (handle) these bets are not even close to being the same.
If the average bet by the NO odds player was to be $338.33 to have the same handle as player B. Hands down, player B losses less by EV.
-4.78
-0.07
per bet made.


Putting Bankroll aside for now, even tho' it is very important and the topic will make for a new thread,
The better story is:
ev/sd (this is an approxamation for the binomial distribution)
-70.71 same EV for both players.
Player A std dev = $158.10
ev/sd = -0.447235501
0.327352515 chance of being even or showing a profit. (about 100 out of 305 players)
(exactly 0.3388132 even or ahead; 0.3159887 being ahead after 1,000 wagers)

Player B std dev = $15,936.89
ev/sd = -0.004436691
0.498230022 chance of being even or showing a profit.
(about 1000 out of 2007 players)

What boat would one rather be in if bankroll was not a concern?
Silly.
----------------------------------------------------------------------------------------------------


From Steen at WinCraps Help section.
Free to everyone to download and have on their computer.

"Another frequent use of this concept is to demonstate the effect of taking or laying odds.

For instance, there are those who claim that odds bets do nothing to affect the outcome of the game.
They point out that if you bet $5 on the Pass Line you'll lose an average of 7.05 cents per decision (1.41% of your wager) whereas if you also take $10 odds you'll still lose an average of 7.05 cents per decision.
You're risking more money to lose the same amount, so why take odds?

Well, for one thing that's not a fair comparison.

Betting $5 flat on the Pass Line does not represent commensurate risk with betting $5 flat and taking $10 in odds.

By adding $10 odds to the same $5 flat bet you're increasing your action.
To figure the average action of $5 flat with $10 odds we have to consider resolutions on the come-out roll which produce only $5 action and resolutions after points have been established which produce $15 worth of action.

Hence, 12/36 of the time the flat bet portion alone resolves on the come-out producing action of $5 * 12/36 = $1.67 and 24/36 of the time both the flat and odds bets resolve after points have been established producing action of $15 * 24/36 = $10. Add them together and we find that $5 flat/$10 odds produces an average action of $11.67 per decision.

Now let's compare that to the $5 flat bet without odds.
It produces the same amount of action on every decision, so obviously the average action per decision is $5.

So to make a fair comarison we can either reduce the $5 flat/$10 odds bets to something that produces an average of $5 action per decision or we can increase the $5 flat bet to something that produces an average action of $11.67 per decision. The later seems to be the easiest, so to make bets with commensurate risk we can compare $5 flat w/$10 odds to $11.67 flat without odds.

Now we can clearly see the effect of the odds bet because the $11.67 flat bet loses an average of 16.46 cents per decision which is much higher than the 7.05 cents per decision of the $5 flat bet with $10 odds.

The correct conclusion is that taking odds reduces your average loss per dollar of action."

Not, The correct, but
A correct conclusion.
------------------------------------------------------------------------------------------------------
Now let the simulation results speak for themselves.

Parameters:
10 million unit bankroll bankroll. (when bankroll is not an issue, players do win more. The key is to have a proper bankroll so the issue of busting is minimal)
100,000 pass line wagers.
10,000 players for each method of play.
No odds
3,4,5,X odds
10X
20X
100X
For the NO odds pass line player it would take, on average, 1 in 258,522 players to show a profit.
None showed a bankroll increase after 100,000 wagers. No surprise there.
The data shows how many actually had a profit after 100,000 wagers. The more odds taken the more they won.

GAMBLSIM by Steve Fry (another cool craps program. I think Steve and Steen know each other)

NO Odds
Simulation of Craps Pass Line Wagers
Odds Multiplier . . . . = 0
Session Bankroll . . . =10000000.00
Win goal to quit session=***********
Max. Decisions to quit = 100000
No. Sessions simulated = 10000
Starting Random seed . = 3211234
------------------------------------
All bets are a single unit
------------------------------------
Simulation Results per Session
------------------------------------
Avg. No. games played . = 100000.00
Avg. No. games won . . = 49289.65
Avg. No. games lost . . = 50710.35
Avg. No. dice rolls . . = 337564.35
Avg. Total amount bet . = 100000.00
Bankroll was busted . . = 0.000% of the time ( 0)
Win goal was met . . . = 0.000% of the time ( 0)
Bankroll decreased . . = 100.000% of the time
Bankroll increased . . = 0.000% of the time

3x, 4x, 5x Odds
Simulation of Craps Pass Line Wagers
Odds Multiplier . . . . = 3x, 4x, 5x
Session Bankroll . . . =10000000.00
Win goal to quit session=***********
Max. Decisions to quit = 100000
No. Sessions simulated = 10000
Starting Random seed . = 3211234
------------------------------------
All bets are a single unit
------------------------------------
Simulation Results per Session
------------------------------------
Avg. No. games played . = 100000.00
Avg. No. games won . . = 49289.65
Avg. No. games lost . . = 50710.35
Avg. No. dice rolls . . = 337564.35
Avg. Total amount bet . = 100000.00
Avg. amount bet on Odds = 277760.93
Bankroll was busted . . = 0.000% of the time ( 0)
Win goal was met . . . = 0.000% of the time ( 0)
Bankroll decreased . . = 82.320% of the time
Bankroll increased . . = 17.660% of the time


10X Odds
Simulation of Craps Pass Line Wagers
Odds Multiplier . . . . = 10
Session Bankroll . . . =10000000.00
Win goal to quit session=***********
Max. Decisions to quit = 100000
No. Sessions simulated = 10000
Starting Random seed . = 3211234
------------------------------------
All bets are a single unit
------------------------------------
Simulation Results per Session
------------------------------------
Avg. No. games played . = 100000.00
Avg. No. games won . . = 49289.65
Avg. No. games lost . . = 50710.35
Avg. No. dice rolls . . = 337564.35
Avg. Total amount bet . = 100000.00
Avg. amount bet on Odds = 666627.11
Bankroll was busted . . = 0.000% of the time ( 0)
Win goal was met . . . = 0.000% of the time ( 0)
Bankroll decreased . . = 66.690% of the time
Bankroll increased . . = 33.310% of the time

20X Odds
Simulation of Craps Pass Line Wagers
Odds Multiplier . . . . = 20
Session Bankroll . . . =10000000.00
Win goal to quit session=***********
Max. Decisions to quit = 100000
No. Sessions simulated = 10000
Starting Random seed . = 3211234
------------------------------------
All bets are a single unit
------------------------------------
Simulation Results per Session
------------------------------------
Avg. No. games played . = 100000.00
Avg. No. games won . . = 49289.65
Avg. No. games lost . . = 50710.35
Avg. No. dice rolls . . = 337564.35
Avg. Total amount bet . = 100000.00
Avg. amount bet on Odds = 1333254.23
Bankroll was busted . . = 0.000% of the time ( 0)
Win goal was met . . . = 0.000% of the time ( 0)
Bankroll decreased . . = 58.800% of the time
Bankroll increased . . = 41.140% of the time


100X Odds
Simulation of Craps Pass Line Wagers
Odds Multiplier . . . . = 100
Session Bankroll . . . =10000000.00
Win goal to quit session=***********
Max. Decisions to quit = 100000
No. Sessions simulated = 10000
Starting Random seed . = 3211234
------------------------------------
All bets are a single unit
------------------------------------
Simulation Results per Session
------------------------------------
Avg. No. games played . = 100000.00
Avg. No. games won . . = 49289.65
Avg. No. games lost . . = 50710.35
Avg. No. dice rolls . . = 337564.35
Avg. Total amount bet . = 100000.00
Avg. amount bet on Odds = 6666271.13
Bankroll was busted . . = 0.000% of the time ( 0)
Win goal was met . . . = 0.000% of the time ( 0)
Bankroll decreased . . = 52.510% of the time
Bankroll increased . . = 47.490% of the time

I was really surprised by the sim results. Aren't you. Maybe I am just too young.
-------------------------------------------------------------------------------------------------------
added:
Bankroll and ev stats

No Odds
Std-dev ending bankroll = 316.53
Skew of ending bankroll = -0.81
Kurtosis end bankroll = 11594.79
Average expectation EVI = -1.421%

345X Odds
Std-dev ending bankroll = 1559.03
Skew of ending bankroll = -0.04
Kurtosis end bankroll = 87.79
Avg Odds change in b/r = -34.57
Average expectation EVR = -0.385%

10X Odds
Std-dev ending bankroll = 3430.73
Skew of ending bankroll = -0.03
Kurtosis end bankroll = 2.64
Avg Odds change in b/r = -75.42
Average expectation EVR = -0.195%

20X Odds
Std-dev ending bankroll = 6603.40
Skew of ending bankroll = -0.02
Kurtosis end bankroll = -1.48
Avg Odds change in b/r = -150.84
Average expectation EVR = -0.110%

100X Odds
Std-dev ending bankroll = 32003.70
Skew of ending bankroll = -0.02
Kurtosis end bankroll = -1.58
Avg Odds change in b/r = -754.21
Average expectation EVR = -0.032%
---------------------------------------------------------------------------------------------------------
In conclusion
The odds bet in Craps does help to win more.

Why?
ev/sd

ev stays the same as sd increases.
That is what players need in the end. Less luck to win.
This is nothing new. Alan, "goatcabin" has many posts about this.
I was going to link to a few, but lost my link list. He does have some nice posts in his Blog.
Another day.

Now on to the bankroll requirements in another thread to see what kind of bankroll is needed to sustain a low "bust rate" for different average bets and bankrolls.
There will not be any "blue sky" rules of thumbs.

Sally says this was a long a** post.
I got excited.

Now for Valentine's Day fun!
Yeah!
I Heart Vi Hart
MathExtremist
MathExtremist
Joined: Aug 31, 2010
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February 14th, 2012 at 4:44:58 PM permalink
Quote: mustangsally

from:ask-the-wizard
about half down

Hi, if person A makes 1000 consecutive bets on the pass line without backing up his bet, and person B makes 1000 consecutive bets on the pass line and he takes 100X odds whenever possible,
doesn’t each person lose the same amount of money?
— Blake Haas from Thousand Oaks

The Wizard.
Yes. I can just imagine the follow up question to be why I recommend taking the odds if doing so doesn’t help to win more.

...

Sally says that "taking the odds DOES help to win more." Looks like I am "at odds" with the Wizard's statement.
[snip]

I was really surprised by the sim results. Aren't you. Maybe I am just too young.

In conclusion
The odds bet in Craps does help to win more.


This is a wonderful example of how English and math don't play well together.

"The odds bet in Craps does help to win more" has two interpretations. One is that "more" means "more often". Two is that "more" means "more money".
The first is true. The latter is not.

The sim results clearly showed that taking higher odds resulted in a greater frequency of winning sessions. That's not surprising -- it's all about variance. In the same way, betting $38 at a time on a single roulette number will show a higher chance of a winning session over N spins than betting $1 at a time on 38 different roulette numbers (which has 0% chance of winning, ever).

However, the sim did not show (a) the chances of dipping below a certain fixed amount, say 50000 units, nor (b) the mean of all the sessions. Just as I would expect the chance of a bankroll increase to increase with odds, I would also expect (a) to increase. I would also expect (b) to remain level.

Visually, what you're doing is taking a tall, narrow bell curve and squashing it into a short, wide bell curve. Imagine the giant foot from Monty Python's Flying Circus stepping on it. The zero point doesn't change, and neither does the mean (N*EV, which is less than the zero point), so it makes sense that some part of that squashed bell curve is now above the zero point. The more you flatten it (that is, the greater the variance), then more of the curve is to the right of zero.

So I don't think you disagree with the Wizard at all. I think you were saying two different things and that English got in the way of clear communication.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
slackyhacky
slackyhacky
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February 15th, 2012 at 12:01:46 PM permalink
Nice post sally
odiousgambit
odiousgambit
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February 15th, 2012 at 12:33:43 PM permalink
The statement "taking the odds does not help a player to win more" seems to be a common denouncement to dissuade a certain degree of stupidity that can set in for a player. I'm sure someone who takes questions from the public like the Wizard can tell you there is a lot of stupidity generated about this. I can think of a thread here not too long ago where the OP was asking what the odds were of getting to a million dollar bankroll; he was supposing they were pretty good using 100x odds. I think he was planning on trying it with something like a $5 passline bet with 100x odds. Such a person needs to come down out of the clouds.

It is true however that if you risk the same amount in "total action" as you term it, you have made your betting much smarter and can expect to lose less at the HE. This logically means shorter sessions in order to keep total action the same; very, very much so at 100x. If, however, you merely increase your total action by not shortening the session [yes, probably betting out of comfort zone] then you are just being an idiot.

So I will say I agree with both you and the Wizard. How diplomatic is that? [g] But I voted for the top phrase, as I think it should stay a common denouncement.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
guido111
guido111
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February 15th, 2012 at 1:09:49 PM permalink
Quote: mustangsally


Now let the simulation results speak for themselves.

Parameters:
10 million unit bankroll bankroll. (when bankroll is not an issue, players do win more. The key is to have a proper bankroll so the issue of busting is minimal)
100,000 pass line wagers.

20X Odds
Simulation of Craps Pass Line Wagers
Odds Multiplier . . . . = 20
Session Bankroll . . . =10000000.00
Win goal to quit session=***********
Max. Decisions to quit = 100000
No. Sessions simulated = 10000
Starting Random seed . = 3211234
------------------------------------
All bets are a single unit
------------------------------------
Simulation Results per Session
------------------------------------
Avg. No. games played . = 100000.00
Avg. No. games won . . = 49289.65
Avg. No. games lost . . = 50710.35
Avg. No. dice rolls . . = 337564.35
Avg. Total amount bet . = 100000.00
Avg. amount bet on Odds = 1333254.23
Bankroll was busted . . = 0.000% of the time ( 0)
Win goal was met . . . = 0.000% of the time ( 0)
Bankroll decreased . . = 58.800% of the time
Bankroll increased . . = 41.140% of the time


20X Odds
Std-dev ending bankroll = 6603.40
Skew of ending bankroll = -0.02
Kurtosis end bankroll = -1.48
Avg Odds change in b/r = -150.84
Average expectation EVR = -0.110%

I find the 20X odds player very interesting. Very possible and realistic.

The sd (for $1 bets) reasonable for a $5 bettor with a big and proper bankroll.

And over 41% showing a bank increase AFTER 100,000 pass decisions? That is impressive.
I have to look at that again.

It is very common to see high rollers bet $100 on the line and back up with odds. 2, 3, 4 and 5X odds.
They could be a strong force if they placed the min on the line and the max odds. even 10X to 20X.
boymimbo
boymimbo
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February 15th, 2012 at 1:17:13 PM permalink
It's about the variance. When you put odds bets on, you are subjecting yourself to more variance, in both directions. Over 100,000 trials, the variance is such to allow a win.
----- You want the truth! You can't handle the truth!
odiousgambit
odiousgambit
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February 15th, 2012 at 1:20:15 PM permalink
Quote: guido111

And over 41% showing a bank increase AFTER 100,000 pass decisions? That is impressive.
I have to look at that again.



I have had similar results running Wincraps. You need to be at 10x odds or more to get these impressive runs. If you add in breaking even [and losing a very small amount] yes, I have been impressed. Some losers are awful to behold too, though.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
guido111
guido111
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February 15th, 2012 at 1:41:35 PM permalink
Quote: boymimbo

It's about the variance. When you put odds bets on, you are subjecting yourself to more variance, in both directions. Over 100,000 trials, the variance is such to allow a win.

Yep. I guess I never really looked at trials over 100k.

Here is 100K pass line bets
$5 flat bet
ev:-7070.71
Prob = prob of being even/ahead
Oddssd:100,000ev/sdprob1 in
0$1,580.98-4.4723550143.86814E-06258522.0105
1$2,993.17-2.3622766110.009081542110.1134571
2$4,518.70-1.5647641470.05881911117.00127711
3$6,072.75-1.1643337060.1221444018.187031022
345X$7,772.30-0.9097320440.181481925.51019076
4$7,637.92-0.925736760.17729145.64043153
5$9,208.55-0.7678411320.2212907874.518940947
6$10,782.26-0.6557724210.2559852823.906474592
7$12,357.86-0.5721628030.2836058433.526020448
8$13,934.71-0.5074167170.3059312293.268708467
9$15,512.44-0.4558087610.3242637523.083909301
10$17,090.80-0.4137142140.3395417082.945146285
20$32,889.08-0.2149864820.4148889292.410283645
40$64,504.91-0.1096150220.4563573482.191265253
50$80,314.88-0.0880373280.4649235042.150891472
60$96,125.31-0.0735571830.4706813712.124579518
80$127,746.89-0.0553493490.4779300742.092356299
100$159,368.94-0.0443669080.482305972.073372636


and 1 million pass line bets.
The higher odds make it all possible.
ev stays the same and the sd goes up.
Nice.

ev:-70707.07

Oddssd:1,000,000ev/sdprob1 in
0$4,999.50-14.142828351.03401E-459.67106E+44
1$9,465.25-7.4701745554.00443E-142.49724E+13
2$14,289.40-4.9482187053.74479E-072670378.518
3$19,203.72-3.6819464680.000115738640.801192
345X$24,578.16-2.876825320.002008489497.8866038
4$24,153.24-2.9274366760.001708843585.1911814
5$29,120.01-2.4281268580.007588517131.7780569
6$34,096.49-2.0737344760.01905198952.48795878
7$39,078.98-1.8093376490.03519928228.40967064
8$44,065.44-1.6045925480.05429175118.41900429
9$49,054.65-1.4413938630.07473672213.38030326
10$54,045.86-1.3082792170.09538931110.4833549
20$104,004.40-0.6798469490.2483006884.027375072
40$203,982.43-0.3466331360.3644334742.743985034
50$253,977.94-0.2783984750.3903532452.561782214
60$303,974.92-0.2326082380.4080328152.450783279
80$403,971.13-0.1750300110.4305280262.322729158
100$503,968.84-0.1403004810.4442112922.251180954
guido111
guido111
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February 15th, 2012 at 1:42:56 PM permalink
Quote: odiousgambit

I have had similar results running Wincraps. You need to be at 10x odds or more to get these impressive runs. If you add in breaking even [and losing a very small amount] yes, I have been impressed. Some losers are awful to behold too, though.

I agree. Now it will be interesting to work with the RoR formula and get some bankroll numbers that would match this kind of play.
jamminbeh
jamminbeh
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February 15th, 2012 at 11:15:33 PM permalink
if $5 was bet on the pass line every time, you will lose the same amount (not percentage) of money on average whether you back the bet up or not. Backing the bet up has no house edge and no player edge, so it won't affect the amount of money won or lost. That's all the wizard was saying and that's all I was asking about.

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