See a Horn, Bet a Horn---What is the probability?

[Bankerdude80]

As I continue to re-read Grafstein's Dice Doctor, I am finding a few topics to explore further. Now we all know
know who is attributed the "See a Horn, Bet a Horn" slogan whether correctly or not.
I did notice that Grafstein also embraces this betting method for those that have to have prop action.

Grafstein basically says wait until you see a horn bet rolled, then bet $1 each ($4) total on the horn. If the shooter
continues to roll horn numbers, continue to press the horn (doubling the initial bet) each time. To me, this sounds
like "See a Horn, Bet a Horn". So my question is a twofold :

1) What is the probability of rolling two consecutive horn numbers?

2) What is the probability of rolling three consecutive horn numbers? Four?

My further analysis was to see how to minimize the exposure to the high edge (HA) this type of betting carries. To minimize the
grind down on the bankroll what if we change this betting method slightly by decreasing our initial exposure by 50%.

A) See a Horn, bet $2 on the C&E
B) If a craps number is rolled, parlay the the bet to $8 and move it to the Horn.
C) If an eleven is rolled, you can move $8 of the payout to the Horn, and add the difference to your rack. Or, you can parlay
it to a $12 Horn, and rack the remaining. Or, power press to a $16 Horn.
D) Continue partial pressing if the Horn numbers keep rolling.

Is this a valid method of betting the See a Horn, Bet a Horn strategy? I know it's still a grind down.

The payouts on a $4 Horn exceeds the payout on the Any Craps (part of C&E) bet.

(Payouts may vary by casino)
Any Craps typically pays 8 for 1.

Horn Bet 2 pays 30 for 1
Horn Bet 3 pays 15 for 1
Horn Bet 11 pays 15 for 1
Horn Bet 12 pays 30 for 1

Is the initial extra $2 towards the Horn really worth it over the long run? What if we don't see repeating Horn numbers?
By the same token, if we see repeating Horn numbers what are we losing?

[ComeOut7]

The horn has the same probability as the seven.....1/6.....SO....What about a 4,8,12,16,20,24 progression? That's a fun play that has won for me numerous times....
Ground rules
Wait until you see a horn before starting
And always stop by the 24 dollar roll....Otherwise it will not pay for itself unless you up the bet on the 11/3....

Good Luck,,,

[Mad Professor]

~The probability of a randomly-thrown Horn-number on any given roll is 16.67% (1-in-6).

~The probability of two consecutive randomly-thrown Horn-numbers is 2.28% (1-in-36).

~The probability of three consecutive randomly-thrown Horn-numbers is 0.46% (1-in-217).


MP

[heavy]

The odds of throwing four consecutive aces is approximately one in 1.67 million. The odds of throwing six consecutive 12's or six consecutive 2's is roughly one in 2.17 billion. I've done it. I've done that too. Just saying. Anything is possible.

[London Shooter]

But you have rolled the dice 3 billion times in your life

Actually, here's a good question. Have you got any kind of broad estimate of how many rolls you may have had over the years?

[heavy]

Ah, the old "personal long run" question. Seems like I went through that exercise one many years ago. I'd do it again if I weren't up against the clock getting some prep work done at home before heading back up North tomorrow for 2 weeks. Let me just way that if you're only counting live casino rolls - no where near that "billion" number.

[mssthis1]

This is a little off topic but I had a Randies gone wild day in Kansas City on Saturday.

Saturday at noon I was scheduled to play round 1 in a BJ tournament, We decide to go to the TR casino to play for a bit and burn off our coupons. Get in and only 1/2 a table open and its full. I go play BJ for a bit. Play a couple shoes of double deck, lose 3 in a row so off I go.

In the meantime they have opened another table and my preferred spot at SR1 is open. Watch 1 shooter who tosses 8 or 9 times so I decide to gingerly play on the randies. 1st two generate enough winners to breakeven. Then this lady gets the dice and carefully sets a 3V, A2 set, and then heaves the dice down the table and they rebound back to the boxman, Another Randie, oh boy. Then the weirdest thing I have ever seen happened. Her first comeout roll was a six, then it went like this, 11, 6, 8CO, 11, 8, 7, 5CO, 11,5, 7, 4CO, 11, 4, 7, 9CO,11 9, 7. If you're paying attention she has a 5 fire, not one box number and 5 yo's. I don't have a fire bet and I have to go for the BJ tournament so I decide to pickup all my chips and head for the cage. I didn't even color as I didn't want to create an EDE. I watch 1 more roll and it's a comeout 10. I don't know what she tossed after that but she tossed the ten while I was at the cage, I could hear the screaming. Nobody had over $1.00 on the fire.

Whats the odds of that?

My afternoon was even more interesting, I plan on starting a Randies gone wild thread when I have more time.

[heavy]

Tossing back to back aces or twelves is a much more manageable one in 1296.