complicated come bet house edge question

I have studied the house edge calculations for the pass and come bets at the wizard of odds site extensively. The house edge of 1.4% for each bet is based on winning when a 7 or 11 hits, losing when a 2,3,or 12 hits AND the resolution of an established point. This works the same way when someone comes to the crap table and put money on the come bet when a point is established. HOWEVER, what about when a player has a pass line bet, a point is rolled, and he now wants to place a come bet (this is the strategy many have used--pass line with odds and come bets with odds). At this point, the come bet may win on a 7 but the pass line will lose. The bettor puts down a come bet but does not want a 7 to be rolled. How does this affect the house edge calculation on the come bet because you now win on and 11 or the ON point, push (lose pass line but win come bet) on a 7, and lose on 2,3,12?
The current house edge calculation is 8/36 + 9648/35640 or 244/495 (to win) versus 251/495 (to lose)
The complicated fraction (9648/35640) is based on rolling a point and rerolling that point before rolling a 7.
Can the wizard or anyone with savvy in probability answer my question?

Whodat

I followed you right up to the point where you applied the passline 7 loss to the come bet's house edge. Are you sure you want to do that? I don't think this situation affects the house edge on either the come bet or on the passline bet. They both exist, separately, and they both have separate house edges and different win conditions.

You could determine the outcome distribution of a combined "pass + first come bet when the pass wasn't natural" bet, but it wouldn't serve any purpose other than to gauge the variance of that combination. The pass and come bets are independent wagers and the house edge is identical between them. The only outcome that resolves both wagers at the same time is a 7, and depending on the state of the come bet that could either be a pass loss + come win or pass loss + come loss. Of course, it's also possible to resolve a pass bet and have a come bet still working.

Bottom line, it's easiest to deal with each bet independently.

nice little question

Quote: whodat

How does this affect the house edge calculation on the come bet

i say
it does not "affect the house edge calculation on the come bet"

now you are trying to figure out after one bet has started its journey
but not resolved and another starts.
the come bet knows nothing about the pass line bet as does the pass line bet knows nothing about the come bet as the dice do not even know about either bets.

the bets are independent and the house edge as you calculated is every possible path that can be taken to a resolution
BEFORE the dice are rolled and considering every possible roll after that that results in a bet being resolved.

plus, when i simulated this a few years ago, it showed no difference in the house edge
just the ev changed due to the fact that more than 1 bet could be resolved per pass line decision

now i have seen a craps roll while a come bet sat in the come box and thought the dealer did not pick it up as a losing bet
that can change the house edge for the come bet (it was not my come bet)

maybe some one will bring some math to the plate for you

Very interesting i was thinking about the same thing

I was researching 'safer' bets and how to stay at the table longer

One thing i found was betting pass line and when a point is made place a come bet to block a 7

Slowly but surely i am learning this game

Of course after the come bet moves to a number you can still 7 out but its still interesting

As another member here told me if that 3rd roll is a 7 then you lose pass line plus you lose on the number where the come chips went

Quote: mustangsally

now i have seen a craps roll while a come bet sat in the come box and thought the dealer did not pick it up as a losing bet
that can change the house edge for the come bet (it was not my come bet)

That was of course, a dealer not paying attention and without boxman support. How to take advantage of such a situation remains the big question. It won't happen again in most cases and/or if you were to make the come bet a larger amount in an effort to take advantage of their inability to keep up with the game. It isn't cheating IMHO to take advantage of a dealers mistake. I've done it many times on a busy table when betting the don't pass. I've been paid on a pass line winner more times than I can count and usually leave the table after it happens. I'm not cheating, just taking advantage of gifts or comps given to me. Call me a dirtbag if you wish, but trust me, taking $500.usd from Donald Trump at the Taj Mahal didn't make me cry or lose sleep.

Thanks for all the responses. I understand that if you were to look at the events as independent then the HE is 1.4 regardless. Unfortunately they are somewhat dependent in my mind because the roll on the come bet can affect the outcome of the pass bet + odds. Logically without looking at independent bets, when you place a come bet after a pass line bet has been in place you are really hoping that the 7 does not roll because you would win your come bet and lose your pass line + odds bet for a negative outcome. So in actuality, you want either an 11 or a point number (2 + 3 + 4 + 5 + 5 + 4 + 3) or 26/36. The advantage of a pass line or a come bet lies in the natural being rolled on the first roll. After that it has a horrible EV. If you place a come bet hoping that a 7 would not be rolled it defeats the purpose of the advantage. Makes me rethink whether I want to just play pass line + odds as opposed to establishing multiple points.

Quote: whodat

Thanks for all the responses.
I understand that if you were to look at the events as independent then the HE is 1.4 regardless. Unfortunately they are somewhat dependent

no
you understand wrong
in other words
not correct

they are either dependent or independent events (bets)
never somewhat
math is not like that

the bets are independent events by their definition
the house edge will never change
=========================
what changes when making more than one bet will be the expected value of X bets and the variance
but you ask about the house edge and that can never change

it is that simple

I would pay you real cash to
simulate this and you will see who may be right
you name your price for your time
or

you can do a thought experiment right now

I make 1 pass line bet
the roll = 6
you make a come bet
the roll = 8
the Wizard makes a come bet
the roll = 9

3 bets are made in total and the house edge has not changed for one bet

what is the difference if 3 bets are made from 3 players or 3 bets are made by one player
same house edge
different ev and variance is the answer

again, i say
they are not "somewhat dependent" events
even if you think they are

and if you feel awful thinking about them because

there are many other and better bets to be made, in my opinion
next

Trying to give a simple answer, you can never combine any number of +HE bets to get a -HE bet. You can play with variance and payouts based on your total bet, but you are never changing the odds on the individual bets. But there are different sets of odds based on whether or not the come point is established.

The House Edge is the expected loss when placing the bet (and letting it run its natural course), so as you make the Pass Line bet the House Edge takes effect (you've already lost the 1.4c). When you subsequently make the Come Bet the cost is the same.

The difference between this and (say) making two Pass Line bets is their outcomes are related. An immediate 7-out is a stand-off and a later 7-out (i.e. neither point is made) makes both bets lose. If you have established two points then there's a better chance of making at least one of them and a long roll probably means both the Come and Pass win.

Thus the variance of {Pass then Come} is higher than {Pass Pass}, but the cost (House Edge) is the same.

Thank you Charliepatrick for your more simple explanation. I mistakenly used the term "dependent" when I really want to use "related." I tried to understand it from a probability standpoint but it became too complicated when I tried to adjust the 2nd roll (come bet roll) to account for immediate 7 (stand-off), win on the pass line when you roll the point (i.e. 5 on come out, then 5 on come bet, etc), win the come bet with an 11, etc. It's just that from a psychological standpoint, we are rooting for the 7 on the come out roll because we have an advantage over the house but don't root for it on the come bet even though theoretically we have the same advantage.

Thank you for your response but the thought experiment with three different bettors does not answer my question because the money each person puts at risk is independent of the other person. The variance and relation explanation provided by patrick makes a lot more sense.
It does not make any sense for you to pay me "real cash" to simulate EV and variance because if I could do that I would not be asking this question on the forum.
I joined the forum to ask questions that I have a hard time understanding and that maybe someone can give some insight into. Although your answer is helpful, it sounds somewhat condescending "no you are wrong in other words not correct."
I am just asking a question. There is no need to be judgmental in your answer. I am not that stupid.

Quote: richbailey86

Very interesting i was thinking about the same thing

I was researching 'safer' bets and how to stay at the table longer

One thing i found was betting pass line and when a point is made place a come bet to block a 7

Slowly but surely i am learning this game

Of course after the come bet moves to a number you can still 7 out but its still interesting

As another member here told me if that 3rd roll is a 7 then you lose pass line plus you lose on the number where the come chips went

Then what?

Make 5 pass, after point is established make a 5 come, after it moves make a 10 come, after it moves make a 20 come?

You are golden as long as 2, 3, or 12 never rolls. Oh wait, that's the HE.

Quote: whodat

Thank you Charliepatrick for your more simple explanation. I mistakenly used the term "dependent" when I really want to use "related." I tried to understand it from a probability standpoint but it became too complicated when I tried to adjust the 2nd roll (come bet roll) to account for immediate 7 (stand-off), win on the pass line when you roll the point (i.e. 5 on come out, then 5 on come bet, etc), win the come bet with an 11, etc. It's just that from a psychological standpoint, we are rooting for the 7 on the come out roll because we have an advantage over the house but don't root for it on the come bet even though theoretically we have the same advantage.

I make pass line and come bets,often continuous, when my bank roll allows. I like the high variance but it is not fun when it goes against you. Your comment on rooting for the 7 on the come out is not usually true for most regular craps players. We are happier to never see a 7 because it will be trouble much more of the time for the money making bets than what you make on your naked passline bet with no odds. Aggressive players will have hardways and place bets working all the time and will lose on that come out 7.

Quote: whodat

Thank you for your response but the thought experiment with three different bettors does not answer my question because the money each person puts at risk is independent of the other person. The variance and relation explanation provided by patrick makes a lot more sense.
It does not make any sense for you to pay me "real cash" to simulate EV and variance because if I could do that I would not be asking this question on the forum.
I joined the forum to ask questions that I have a hard time understanding and that maybe someone can give some insight into. Although your answer is helpful, it sounds somewhat condescending "no you are wrong in other words not correct."
I am just asking a question. There is no need to be judgmental in your answer. I am not that stupid.

FWIW, whodat, MustangSally gives everybody a similar flippant "hard time" when she responds. It's not personal. She's not the only one. Not defending what she said or even how she said it, but it's up to you to decide if you want to use the info she provided, or even have a conversation with her or anyone else. She usually backs up what she says with a math explanation, as she did here, but not everybody agrees with her, either on what she says or how she says it. Again, she's not the only one.

I say this because we do moderate for personal insults, and I wanted you to know I looked at this. I don't believe it rises to that level. Welcome to the forum, and please do continue to ask your questions.

Thanks BBB. I understand completely. If I had been here for a while then I would not have taken the comment the wrong way. I am just "slightly sensitive" :) to comments about my intelligent level--as I am sure everyone is.

Quote: whodat

The variance and relation explanation provided by patrick makes a lot more sense.

MAYbe
but the house edge does not always equal the expected value of 1 bet
bet size matters

but opinions are free
you can choose the ones you like and discard others
like
6C2 (where order does not matter)

Quote: whodat

It does not make any sense for you to pay me "real cash" to simulate EV and variance because if I could do that I would not be asking this question on the forum.

MAYbe you did simulate this on your own and got a HE = 1.39% and wanted to share your results
I have simulated this by making exactly 1.5 million pass and come bets without odds and the HE was 1.43%, higher than 1.41%
see i can share too (2)
i made the cash offer cuz i like doing things that way and i find many like getting cash for doing something
a win-win

nows,
it looks to be true that 2 successive line bets are correlated

one math guy, not to be named here (sure give a guess), shows that for the next 2 rolls of the dice, the 1st being a pass line come out roll
the ... here it is
"15.7. Correlation between successive line bets.
Consider the player who bets
one unit on the pass line at the come-out roll, and then one unit on come if the
second roll is a point roll, or on the pass line if the second roll is a come-out
roll. Let X1 (resp., X2) be the player’s profit from the first (resp., second)
bet. Find the correlation between X1 and X2."

Answer: −0.00614789 (not yet verified by me)
looks inviting to say the least little thing

Quote: whodat

I joined the forum to ask questions that I have a hard time understanding and that maybe someone can give some insight into.

that is nice

Quote: whodat

Although your answer is helpful, it sounds somewhat condescending "no you are wrong in other words not correct."

this is exactly the teaching methods used in higher learning environments, in other words,
my math professors in college used this approach
one MAY kick, scream and cry (boy, did I ever!)
but sooner or later it sinks in
wow! that was cool

Quote: whodat

I am just asking a question.

yes, you asked about changing the house edge
and that still does not change except in a situation like one i pointed out.

Quote: whodat

There is no need to be judgmental in your answer.

thank you for sharing your opinion
i do (DUE) not see it the way you do (or BBB does)

the reason is simple too
i travel much faster through space (time) than do most (that MAY include you)

again, i am told i am a lucky girl

Quote: whodat

I am not that stupid.

not enough information (well, i know i am stupid about lots of stuff)
so i go with you for now on that

have fun!
be good

Thanks for your response MS. I am interested in the experimental correlation result. Just a quick question. If the correlation shows a small negative value, AND it can be verified by you or other math whizzes, does that mean that it would be better to stick to just the pass line bet and not try to make multiple come bets?

Thanks

Quote: whodat

If the correlation shows a small negative value, AND it can be verified by you or other math whizzes, does that mean that it would be better to stick to just the pass line bet and not try to make multiple come bets?

Thanks

yes it is a small negative value (the range being -1 to 0 to 1)
that example came from a college text book by SN Ethier
and it looks to cover just 2 rolls of the dice starting with a come out roll
and 2 bets (P,C or P,P)

i do not really know the purpose of it, but i mentioned just because i saw it,
or how important it is as a bit of knowledge.

i do know the chances are 2/3 * 2/3 to have a P,C points after 2 rolls
sure not the favorite at 4/9
but of course there are many possible outcomes from 2 rolls trying to make 2 line bets (pass/come)
as they are contract bets, they are made to be resolved

MAYbe ME or Don wants to tackle it

i only have played touch football a few times
and when boys and girls play touch football together, it is just a matter of time B4 it becomes tackle football

Your expected return value of a $20 PL with no come bet is the same as a $10 PL+$10 come bet. The addition of any odds makes no difference too.

Quote: Morgue

Your expected return value of a $20 PL with no come bet is the same as a $10 PL+$10 come bet. The addition of any odds makes no difference too.

nice opinion
buts, this is meaningless in my opinion

no REAL craps player thinks about HIS average loss per bet
they play to have fun and win money.

ands
actually you failed to say what does change is the variance and the probability distribution
way more important to a craps player, imo
but more of a challenge to the average (or below average) person attempting the math, i DO (DUE) say
============================================
one $20 pass line bet, in my opinion, has a way higher prob to win $20
than
a $10 pass and $10 come trying to win $20 (it is what the player WANTS)
of course, one MAY just end up with 2 pass line bets too (2 or 1+1 or 3-1)
============================================
variance rules at craps
leave the "expected return value" only folks to their losing ways, i say
right?

one is either a lifetime winner
or
a lifetime loser

can not be both

and can not choose which one to be
hey, it is the game rules
how about smoking that in a pipe and telling the world what colors you see

i would like that
thank you for sharing!
Mully

Doesn't Lifetime loser + lifetime winner =breakeven player?
Perhaps one could have been both.
What if Sally starts gambling when she turns 21, over the next 30yrs she incurs losses
of 500k, continues 2 gamble 4 30yrs more and wins 500k. Was she a lifetime
winner or loser?