pass line + odds

If I place a passline bet, where the house edge is 1.41% and add a 5x odds bet, with no house edge, does that reduce the house edge to 0.28%?

for the overall bet yes....but to get to the point where you can place odds...your pass line bet is no longer 1.41% HE

Actually house edge on a passline bet with 5x odds is .00326 per "bet made" or "bet resolved". See the WoO article on Craps strategy here.

Maybe I'm not thinking clearly at the moment -- doesn't the house edge on a post-comeout, passline-plus-5x-odds wager depend upon the point number? Isn't the edge on a 4 or 10 point worse than on a 6 or 8 point? I haven't looked at the strategy page that Ayecarumba linked, but the quoted edge might be a composite that doesn't apply to any specific point.

Did I get this confused somewhere?

The Wizard's page is where I came up with the question. On his page, he points out that house edge on a passline bet is 1.41%, and an Odds bet offers no advantage to the house. So I figure if I bet a unit on a passline bet and 5x on the point, then I reduced the house edge to 0.28%. But another poster offered a different %?

The previously quoted figures were combined.

Here is the full description from the Wizard of Odds Craps Appendix:

Quote: Wizard of Odds Craps Appendix

Combined Pass and Buying Odds
The player edge on the combined pass and buying odds is the average player gain divided by the average player bet. The gain on the pass line is always -7/495 and the gain on the odds is always 0. The expected bet depends on what multiple of odds you are allowed. Lets assume full double odds, or that the pass line bet is $2, the odds bet on a 4, 5, 9, and 10 is $4, and the odds on a 6 or 8 is $5.

The average gain is -2×(7/495) = -14/495.

The average bet is 2 + (3/36)×4 + (4/36)×4 + (5/36)×5 + (5/36)×5 + (4/36)×4 + (3/36)×4] =
2 + 106/36 = 178/36

The player edge is (-14/495)/(178/36) = -0.572%.

The general formula if you can take x times odds on the 6 and 8, y times on the 5 and 9, and z times on the 4 and 10 is (-7 / 495) / [ 1 + ((5x + 4y + 3z) / 18) ]

Quote: 135steward

The Wizard's page is where I came up with the question. On his page, he points out that house edge on a passline bet is 1.41%, and an Odds bet offers no advantage to the house. So I figure if I bet a unit on a passline bet and 5x on the point, then I reduced the house edge to 0.28%. But another poster offered a different %?

It's because you don't always have the opportunity to bet 5x odds. The reduction you observe in house edge is as a percentage of your total wager, not in actual dollar terms. A $5 passline bet costs about 7c regardless of the size of your odds wager because the odds wager has 0 cost.

removed
silly

You guys are great! Thanks for your help!

My 2 cents:
The pass-ODDS bet is the best bet in the house and generally under-utilized by the players. Why bet all those place bets, instead bet more on the odds with its 0 house advantage. Not as much action with just pass-odds, but generally better $ results. Most casinos, at least in Misssissippi, have at least 10x and many have 20x odds. Concentrate on a betting scheme on the odds portion for a better chance of a winning session.

Here is one betting scheme on the odds portion that has worked well overall for me and using it now: I divide my session bankroll into two groups. First is $5 pass and level $25,26 odds using a $300 buyin. IF lose that, then second buy-in of $500 for $5 pass and level $50 odds. Once get in the positive overall with the $50 odds at the end of the latest shooter's hand, then start anew. Win goal is $150 for this $800 total session bankroll. The cumulative odds thing seems to often kick in after an extended losing bout and the larger odds bet helps with the recovery. On the good days will stay within the first buyin, some days will get into the second buy-in and it is not unusual to get into the second buy-in. Overall this wins about 9 out of 10 sessions, about as good as it gets in this game.

Anyone else have an odds scheme with good results? Many odds schemes are possible and not saying above is the best, but this is a good one for small wins with LOW RISK.

At an Even amount table... such as $2 or $10, ect. Pass line always places 5x the Pass Line bet, and Don't Pass always places 6x the Don't Pass Line bet.
This resolves as expected for a PassLine w/Odds wager: $2/$10 that pays either $20 on the 4-10, $15 on the 5-9, or $12 on the 6-8 plus $2 for the Line bet.
For the "dark-side" it resolves differently: $6 for the 4-10, $8 for the 5-9, or $10 for the 6-8 plus the $2 for the DP line.

Pass line is a true 5x, the Don't Pass is really laying 3-4-5. The House advantages are 0.327% Pass, 0.273% Don't Pass. One needs a 5x table or higher to do this.
IMHO a very simple wagering system.

Quote: dwm

The cumulative odds thing seems to often kick in after an extended losing bout and the larger odds bet helps with the recovery.

No such thing as "cumulative" odds. The odds are the same on EVERY roll. They don't change if you are losing or winning. Increasing your bet is actually worse for you even though you might see a positive winning session.

Quote:

Anyone else have an odds scheme with good results? Many odds schemes are possible and not saying above is the best, but this is a good one for small wins with LOW RISK.

Not a bad way to play. A lot better than making stupid Field bets and hardways. :)

Quote: dwm

Here is one betting scheme on the odds portion that has worked well overall for me and using it now: I divide my session bankroll into two groups.

First is $5 pass and level $25,26 odds using a $300 buyin.

Simulation of Craps Pass Line Wagers
Odds Multiplier . . . . = 5
Session Bankroll . . . = 60.00
Win goal to quit session= 30.00
No. Sessions simulated = 1000000
Starting Random seed . = 321321
------------------------------------
All bets are a single unit
------------------------------------
Simulation Results per Session
------------------------------------
Avg. No. games played . = 61.73
Avg. No. games won . . = 30.43
Avg. No. games lost . . = 31.31
Avg. No. dice rolls . . = 208.42
Avg. Total amount bet . = 61.73
Avg. amount bet on Odds = 195.32
Bankroll was busted . . = 36.617% of the time ( 366174)
Win goal was met . . . = 63.383% of the time ( 633826)
Bankroll decreased . . = 36.617% of the time
Bankroll increased . . = 63.383% of the time

Quote: dwm

IF lose that, then second buy-in of $500 for $5 pass and level $50 odds. (100b-10X)

Simulation of Craps Pass Line Wagers
Odds Multiplier . . . . = 10
Session Bankroll . . . = 100.00
Win goal to quit session= 60.00
No. Sessions simulated = 1000000
Starting Random seed . = 321123
------------------------------------
All bets are a single unit
------------------------------------
Simulation Results per Session
------------------------------------
Avg. No. games played . = 67.50
Avg. No. games won . . = 33.27
Avg. No. games lost . . = 34.23
Avg. No. dice rolls . . = 227.87
Avg. Total amount bet . = 67.50
Avg. amount bet on Odds = 375.62
Bankroll was busted . . = 40.382% of the time ( 40382)
Win goal was met . . . = 59.618% of the time ( 59618)
Bankroll decreased . . = 40.382% of the time
Bankroll increased . . = 59.618% of the time

Quote: dwm

Once get in the positive overall with the $50 odds at the end of the latest shooter's hand, then start anew.

Win goal is $150 for this $800 total session bankroll.

OK. Your rules of play are now in stone.

Quote: dwm

On the good days will stay within the first buyin, some days will get into the second buy-in and it is not unusual to get into the second buy-in. Overall this wins about 9 out of 10 sessions, about as good as it gets in this game.

From my sims above, one has a ~63% chance of winning $150 before the second buy-in.
You may be winning 9 out of 10 session in your short term play but that will not last.
Closer to 8 out of 10 or 82 out of 100 at best for long term play.

Let us look at 100,00 players playing this method. (I have some time to kill today)

63,383 risked $800 and won $150 on their very first try!
14,644 go home broke! I heard a few say "freakin' dmw!
21,973 back to even. Do they continue?
Freakin' yes, they are Craps players!
21,973 players... what happened?

13,927 finally made their $150.(77,310 total have a $150 profit)
8,044 Buy-in again for $500!
3,218 bust out finally after getting back to even one time.
17,862 total have now gone home broke!

4,826 are back to even.
What should they do?
3,059 finally make their $150 on their third try!(80,369 total have a $150 profit)

1767 players left buying in for their last $500 again!
774 bust out!(18,637 total have gone home broke!)

993 players are now left and back to even!
630 FINALLY win $150! (80,999 total have a $150 profit)
363 again buy-in for their last $500.
145 BUST out!
(18,782 total have gone home broke!)

218 players are now left standing back to even.
They go to the bar and drink until sober!
(sure, I have this in WinCraps, but just to lazy to push the button, this was entertaining!)
So, maybe 82,000 would hit $150 profit.
82 out of 100 sessions.
82*150 = 12,300
18 * -800 = -14,400
OK.

Easy just to bet $5 with $50 odds all the time.
Just about the same winning session results. Who would have known?

Simulation of Craps Pass Line Wagers
Odds Multiplier . . . . = 5
Session Bankroll . . . = 160.00
Win goal to quit session= 30.00
No. Sessions simulated = 1000000
Starting Random seed . = 321321
------------------------------------
All bets are a single unit
------------------------------------
Simulation Results per Session
------------------------------------
Avg. No. games played . = 159.98
Avg. No. games won . . = 78.86
Avg. No. games lost . . = 81.12
Avg. No. dice rolls . . = 540.10
Avg. Total amount bet . = 159.98
Avg. amount bet on Odds = 528.07
Bankroll was busted . . = 18.315% of the time ( 183147)
Win goal was met . . . = 81.685% of the time ( 816853)
Bankroll decreased . . = 18.315% of the time
Bankroll increased . . = 81.685% of the time

overall, not a bad way to play. most money on the odds bet.

IF you can just increase your pass line win ratio to above 50%, then you would be home free.
How does one do that?
Hey, that is the 64 million dollar question.

7Craps: Thanks for the analysis. Now how is the BEST way to play the odds portion, that is what I am trying to figure.
Those cold streaks will kill a bankroll fast when no points are being made, hmm, negative progression, positive progression, the two buyins that I spelled out and play with level bets per buyin per above, or simply level odds?

Quote: dwm

Now how is the BEST way to play the odds portion, that is what I am trying to figure.

Most will say bet as much on the odds as you can afford every time. Simulations also prove this to be true. But many will never believe it. Too bad.

Unless you can win the pass more than 244/495, LUCK RULES.

But by taking more free odds, one only needs a little luck in one's favor to show a profit even after many trials.

How about 2,000 pass line bets. One could easily make this many in a lifetime of play.
Notice the same ev, but it is the sd (variance) that makes the difference

$5/NO odds average bet $5
ev:-141.41
sd:$223.58
ev/sd = -0.632486512
~26.353451% chance of being even or ahead or ~1 out of 4 or ~2,635 out of 10,000

$5/5x odds average bet $21.67
ev:-141.41
sd:$1,080.17
ev/sd = -0.130918948
~44.7919713% chance of being even or ahead or ~4 out of 9 or ~4,479 out of 10,000

$5/10x odds average bet $38.33
ev:-141.41
sd:$2,417.00
ev/sd = -0.058508025
~47.6671985% chance of being even or ahead ~10 out of 21 or ~4,767 out of 10,000

Do you want to have to best chance of showing a profit after many trials betting the pass? Of course. The odds bet, especially more, gives one the best chance.
Period.

Quote: 7craps

How about 2,000 pass line bets. One could easily make this many in a lifetime of play.

One could easily make this many in two or three months of play!

Math is a stubborn truth, thanks for your time and math expertise.

Quote: WongBo

One could easily make this many in two or three months of play!

Certainly!
about
6752 dice rolls (2,000 * (557/165))
67.5 hours of play (100 rolls per hour. a good clip)

The more one bets, the chance of showing a profit goes down.
That is the effect of the house edge or the "short change" that the casino makes on most all bets.

The pass line is no different. Bet $1 lose $1. Win $1. seems fair to most.

Well, the player should have been paid ~$1.0287 (251/244)
Players get shafted ~2.87 cents on every win per $1 bet. Over time, this adds up to BIG $$$.

Now, 20,000 pass line bets
about
67,515 dice rolls
675 hours of play
5/10x average bet $38.33
ev: -1414.14 (this is how much, on average, one has been "short changed" by the casino payoff)
sd: $7,643.24
ev/sd -0.185018621 ~42.6607215% chance now of showing a profit or 4,266 out of 10,000
instead of
~4,767 out of 10,000 at 2,000 bets.
Always keeps getting worse for the player.

But there is always luck. It never goes away.

Quote: dwm

Math is a stubborn truth.

Well said. Key word is truth.

But, since I like nice casinos I do not mind paying for them thru the house edge.
I like the a/c during the hot summers, the carpet, the perks and even the comps.

Just wish Lady Luck would visit me more than she actually does.
Thank goodness for the internet.

Also true is many want to believe that by making different bets at different times and changing the odds around, going up and down with bets and so on, they can somehow win more than they lose.
It can happen that way. But, just do not count on it.

It is the lifetime LENGTH of play that kills most in the end.