Joined: Nov 2, 2022
• Posts: 2
November 2nd, 2022 at 2:44:09 PM permalink
We have been having a lively debate about the odds of a particular Craps dice odds situation over in a large Facebook group.

The debate is over likelihood of outcome.

Some have stated that there are MORE ways to roll EITHER a 6 or 8 than a 7.

To me this makes sense. There are 6 ways to roll a 7. There are only 5 ways to roll a 6 or 8. BUT, if wanting a 6 OR an 8, there would be more ways for that to come up then a 7. i.e. 10 ways for a 6 OR 8, but only 6 ways for a 7.

Why would this be wrong?

Thank you.
TigerWu
Joined: May 23, 2016
• Posts: 4627
November 2nd, 2022 at 2:46:36 PM permalink
What is the logic from people saying the odds of a 7 are more likely?
unJon
Joined: Jul 1, 2018
• Posts: 3858
November 2nd, 2022 at 2:51:52 PM permalink
Chance of 6 or 8 before 7 = 10/16.
Chance of 7 before 6 or 8 = 6/16.

Doesn’t make it a good bet to place the 6 and 8 for a roll, of course, because of how much you win 10/16 of the time versus how much you lose 6/16 of the time.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
Ace2
Joined: Oct 2, 2017
• Posts: 2095
November 2nd, 2022 at 4:22:31 PM permalink
Are you sure you’re not referring to the probability of rolling a 6 AND an 8 before two 7s?

That one is somewhat counterintuitive since you’re more likely to roll the 6 and 8 first
It’s all about making that GTA
Wizard
Joined: Oct 14, 2009
• Posts: 24899
November 2nd, 2022 at 5:30:32 PM permalink
Quote: Ace2

Are you sure you’re not referring to the probability of rolling a 6 AND an 8 before two 7s?

That one is somewhat counterintuitive since you’re more likely to roll the 6 and 8 first

That's what I was going to say. If you roll two dice, keeping a count of totals of 6, 7, and 8, you're more likely to see both a 6 and 8 before you see two 7's.
“Extraordinary claims require extraordinary evidence.” -- Carl Sagan
odiousgambit
Joined: Nov 9, 2009
• Posts: 8964
November 2nd, 2022 at 5:35:54 PM permalink

We have been having a lively debate about the odds of a particular Craps dice odds situation over in a large Facebook group.

The debate is over likelihood of outcome.

Some have stated that there are MORE ways to roll EITHER a 6 or 8 than a 7.

To me this makes sense. There are 6 ways to roll a 7. There are only 5 ways to roll a 6 or 8. BUT, if wanting a 6 OR an 8, there would be more ways for that to come up then a 7. i.e. 10 ways for a 6 OR 8, but only 6 ways for a 7.

Why would this be wrong?

Thank you.

if the casino offered a bet that *either* 6 or 8 would come before 7, then the fair odds would be 3:5 [6:10] . They would probably have you lay 2 units to earn 1, to have a house edge.

But they don't have that bet. You can bet 6 to come before 7, or 8 to come before 7, bets that are independent. Some of your brainstorming friends may imagine that betting both on 6 and 8 at the same time creates a 6:10 situation that pays 7 to 6. This is a fallacy.

So this is my differing view of what might be going on here in all this discussion in the OD's group.
Last edited by: odiousgambit on Nov 3, 2022
The Dice, the cards, they not only have no sense of justice but are seemingly endowed with a sense of cruel irony. This devolves from the 'nature of random'. Ironically, don't you see.
Joined: Nov 2, 2022
• Posts: 2
November 3rd, 2022 at 6:30:50 AM permalink
Perhaps I should clarify a bit.

The argument by some is that there is a 27.78 % chance a 6 OR an 8 would be the result of a single dice roll. While only a 16.67% a 7 would be rolled.

The other side of the argument basically states that you can only have one result, not two. Therefore, your odds don't change.

My take is that while the 2nd argument is true, YOUR MONEY is saying that it will be one OR the other, therefore your odds of winning ONE of your individual bets is 27.78%.
ChumpChange

Joined: Jun 15, 2018
• Posts: 3653
November 3rd, 2022 at 8:19:18 AM permalink
So should I be betting the PB 6 or the PB 6 & 8? I could bet \$48 on the PB 6, or \$24 on the PB 6 & 8 each. Somebody else is shooting the dice so I won't be dice influencing my wins, and I won't have a PL bet. If I want to half-press my bet on a win though, I'll be looking for 2+ hits on the same number in either scenario.
odiousgambit
Joined: Nov 9, 2009
• Posts: 8964
November 3rd, 2022 at 10:30:19 AM permalink

Perhaps I should clarify a bit.

The argument by some is that there is a 27.78 % chance

10 chances for that, 6 chances for a 7 rolled, is all that matters. If something else is rolled it's the same as if it was never rolled.

Quote:

.... a 6 OR an 8 would be the result of a single dice roll. While only a 16.67% a 7 would be rolled.

So not realizing the above gets you this place that has no meaning

Quote:

The other side of the argument basically states that you can only have one result, not two. Therefore, your odds don't change.

My take is that while the 2nd argument is true, YOUR MONEY is saying that it will be one OR the other, therefore your odds of winning ONE of your individual bets is 27.78%.

I guess you can say it's trying to apply single roll betting probability to a multi-roll bet. This does not compute.
The Dice, the cards, they not only have no sense of justice but are seemingly endowed with a sense of cruel irony. This devolves from the 'nature of random'. Ironically, don't you see.
Ace2
Joined: Oct 2, 2017