Probability of rolling Hard 8 (three or four times) before a Seven

First, I searched around and I apologize in advance if these question been answered before.. ( I could not find it).. Was trying to find what is the percentage chance of Hard 8 rolling three or four times before a Seven out? Also, it would be nice to know the percentage difference with the hard 8 turned on and off on the come out roll.

Additionally, to compare the percentage chances of, five or six point Fire Bet, Small All Tall and Three of the same number Hardway (let's say 8 for example) rolling before a Seven. Hope that made sense..It's a tough one..Thanks in advance!

Quote: VegasHardway

First, I searched around and I apologize in advance if these question been answered before.. ( I could not find it).. Was trying to find what is the percentage chance of Hard 8 rolling three or four times before a Seven out? Also, it would be nice to know the percentage difference with the hard 8 turned on and off on the come out roll.

Additionally, to compare the percentage chances of, five or six point Fire Bet, Small All Tall and Three of the same number Hardway (let's say 8 for example) rolling before a Seven. Hope that made sense..It's a tough one..Thanks in advance!

1.) Whether or not you have the bet on during a CO roll is immaterial to the probability.

2.) There are six ways to roll a Seven and one way to roll a Hard Eight, thus, the probability of one Hard Eight before a Seven is 1/7. However, it is important to remember that Soft Eights also cause a Hard Eight to lose, and there are four ways to roll those. Therefore, the probability of rolling a winning Hard Eight is 1/11.

Two Hard Eights w/o Loss: (1/11)^2 = 0.0082644628 or 1/0.0082644628 = 1 in 121 (Approximately)

Three Hard Eights w/o Loss: (1/11)^3 = 0.0007513148 or 1/0.0007513148 = 1 in 1331 (Approximately)

Four Hard Eights w/o Loss: (1/11)^4 = 0.00006830134 or 1/0.00006830134 = 1 in 14,641 (Approximately)

You could also look at House Edge per roll, but what I wrote above assumes you are going to leave the bet up until it either wins or loses.

3.) You're welcome, nothing tough about it.

4.) With those other bets in comparison, you should be more concerned with either House Edge per Roll or, I would suggest, House Edge per bet resolved. The Fire Bet is always terrible even compared to Hardway bets, but the Small/Tall/All might have a lower house edge depending on how it pays v. how the Hard Eight pays. This can differ from casino to casino.

5.) If you're looking to make a big score and that is your primary concern, then the lowest House Edge and Expected Loss mechanism with which to do that would be to pick one of the lowest House Edge bets on the Table (Pass/Don't Pass with or without Odds...though the Odds will change your bet structure) and to press your bets after wins. You could even do a full Reverse Martingale and you'll expect to lose less money in the long run, though you will still inevitably lose given enough trials.

Let us know if you you ever witness 18 hard eights in a row...

Mission146, Thanks! that was fast (your good). Just to explain the motivation for the question.. I was interested in the percentage chances that a person would have to parlay a Hardway number i.e. (8) three or four consecutive times before a seven. I have rolled the Small All Tall (Small 2dollar, All 1dollar, Tall 2dollar) once (DI or luck--I'll never tell) and on the same night almost did it again but missed rolling the 2 and the 12,(go figure the toughest numbers to roll) before the 7 out.
The reason I asked, is not trying to make a "Big Score" because experience shows that doesn't happen often, but if your going to gamble -- just curious on the betting option. Your answer confirms what I thought, if I'm reading it correctly, it's a better (positive) percentage bet to Skip the fire bet and go for the 1 dollar Hardway parlay 3x if luck repeats (4x parlay repeater would be extremely lucky), I think that's what your answer stated, if reading it correctly.

Also, a side note of interest, I bet a Three way 7 on the come out roll, the 7 rolled four times in a row and I parlayed the seven three times in a row. After the third seven in a row parlayed, moved the 375 to the horn... Lesson learned!!! What are the percentage chances of four 7's in a row..Thanks again!

VegasHardway,

Thanks for the compliment, I've seen many Craps questions on here so I can usually put together responses pretty quickly. I should really just categorize the answers I have given and keep a file with all of them to copy/paste, probably just have to change a few words.

My answer does indicate that the Hardway bets have a lower house edge than do the Fire Bets, yes, but Pass/Odds or Don't Pass/Odds have lower house edges than Hardway bets, by far. What's wrong with parlaying (Reverse Martingale, essentially) the Pass Line at a reduced expected loss?

Four sevens is easy, a seven happens 1/6 rolls, so (1/6)^4 = 0.00077160493 or 0.077160493% or 1 in 1,296.

By the way, Hop Bets usually have a worse house edge than Hardway bets.

Good point on the Pass/ Don't line parlay. The thinking was (lowest amount of money at risk 1 dollar) 1 dollar on the Hardway paid at 10 for 1 parlayed 3X in row is a 900 -1,000. Let's see.. a 5 dollar pass line with 10X odds (50...55 dollars at risk) parlayed 3X would be a 1,000? if you get the 4 or 10 as the point for the 3 parlays? Maybe, I'm figuring the payoffs wrong?

I understand your point, but you have a greater probability of success with a PL parlay. Furthermore, that $1 on a Hardway results in a greater expected loss than even a $5 PL bet.

Quote: VegasHardway

what is the percentage chance of Hard 8 rolling three or four times before a Seven out?

It depends on how many rolls one sees in a session.
say 100 rolls per hour.
more rolls... better chances

Here is data I have
from doing the math. (In excel, of course)

Easier to get Hard6 or Hard8
just a few more $$$s

actually easier to get a Hard4 run (or Hard10)
than a 6 or 8.
shooters are funny that way too.

Oh, yes
look how many rolls it takes on average and the probabilities
to get a feel how often these events occur.

Quote: VegasHardway

Also, it would be nice to know the percentage difference with the hard 8 turned on and off on the come out roll.

that makes no difference, in agreement with another and doing the math and simulations.
Sally

have fun