This is what I'm coming up with for misses in a row and amount what needs to be bet to get back what is lost up to that point. Looks rough for anything over $1

1 1.10 X
2 3.41 X
3 8.26 X
4 18.45 X
5 39.84 X
6 84.77 X
7 179.11 X
8 377.23 X
9 793.28 X
10 1666.99 X
11 3501.78 X
12 7354.83 X

I just found the probability forum here on 2p2.
Saw where someone lined this:
https://stattrek.com/online-calculator/binomial.aspx
in another discussion..

For the 220, which is correct AFAIsee

You then divide by 2^12... 4096 I get without calculator

So 220 divided by 4096

I think there is a factorial formula for cumulative... Ie 3 heads or less

The pyramid is 100% based on this.. Your 220 is on the pyramid

Thanks. I wrote up a post before my last one that apparently didn't go through.

If I'm reading your data correctly, I see the bell curve shape.
Looks like 23% of the time you get 3-in-a-row 6 times out of 12 flips. That would be the...mode? And then 38% of the time we get +1/-1 (61% of the time, total). 85% of the time it will happen 4-8 times. It is concerning that 3 in a row happens 10 times, 2 in 100 times and 11 times 29 in 10,000.

For my case, a round would be a quarter of play. 3 rounds a game(Q2-Q4 skipping Q1), 12 rounds would be 4 games.

Having 6 in a row (24% of the time) looks like we basically have 3 scenarios, x= 1 unit

@ -110 odds
Worst case
G1Q2 miss -1.10X
G1Q3 miss -3.41X
G1Q4 miss -8.26X (cumulative)

G2Q2 miss -18.45X
G2Q3 miss -19.84X
G2Q4 miss -84.77X

G3Q2 hit win +85.77X

and

G1Q2 miss (N/A)
G1Q3 hit + 1x
G1Q4 miss no action

G2Q2 miss -1.10x
G2Q3 miss -3.41x
G2Q4 miss -8.26x

G3Q2 miss -18.45x
G3Q3 miss -39.84x(cumulative)
G3Q4 hit win +40.84x

and best case

G1Q2 hit + 1x
G1Q3 miss no action
G1Q4 miss no action

G2Q2 miss -1.10x
G2Q3 miss -3.41x
G2Q4 miss -8.26x

G3Q2 miss -18.45x (cumulative)
G3Q3 hit +19.45x
G3Q4 no action

7 misses would be up to -179.11x cumulative loss, 8 -> -377.23x, 9 -> -793.28x, 10 -> -1666.99x, 11 -> -3501.78x with each one being divided into 3 scenarios depending on if the first miss happens in Q2 (worst case), Q3 (best case) or Q4.


I'm guessing it wouldn't make a difference but I wonder if playing Q1 would change the numbers a bit. It sort of seems like it would because Q1 you have two teams who set the stage for the Q1 total score odd/even. Then Q2,Q3,Q4 are played according to that. Then Q1 of the next game, two different teams set the stage for Q1 and Q2-4, in my mind, are played off of that Q1 result.

Thinking about it mathematically though seems like Q4 from 1 game carried over into Q1 of the next game shouldn't make a difference since it's a coin flip each time. It's just if G1Q1 is 'odd' then I'm going to be playing 'even' for each of the following G1Q2-4 until it hits since I"m betting against 'odd' hitting 4 times in a row. If it does, then it kind of feels like G2Q2 resets, in a sense, and it doesn't make sense to get against it hitting again although technically it is the 5th coin flip in a row and we would still be betting against odd hitting for the fifth time in a row.

I'm guessing this is what it means when we say the coin flips are independent. Like, I could pick any 3 Qtrs at random from various games in the day and still expect the same chance of them all hitting the same value vs. if I pick any 3 that are played consecutively.

In the basketball game scenario though it seems like maybe it isn't entirely 50/50, odd or even, and any difference in those odds does depend on the two teams that are playing in the game.

Either way, interesting info.

Sorry for the confusion about "3 in-a-row 6 times etc " I am just now trying to run the factoral numbers myself and realize I was misunderstanding what it is they were referring to. Instead of 3-in-a-row 6 times, it's just 6 times in a row out of12, correct?

It's too late now to edit my previous post. So out of X rounds/flips/quarters we will hit only 1 'odd' or 1 'even' 0.29% of the time, 4 in-a-row 12.08%, 6 in-a-row ~24% etc. Just making sure I'm reading the numbers correctly.

For 4 quarters I'm getting

1 25%
2 37.5 %
3 25%
4 6.25%

For 3 Qtrs:

1 37.5%
2 37.5%
3 12.5%

Which is what I was thinking since (.5)^3 is 12.5% and (.5)^4 is 6.25%
Thinking maybe I read the "12-rounds" data wrong.

This is saying that for 3 Qtrs all 3 hit the same value 12.5% of the time, only 2 hit 37.5% and only 1 hits 37.5% or in other words, 87.5% hit rate.

If I don't play Q1 and then bet against the other 3-Qtrs being the same value, that's the same as playing all 4Q, no, since I am essentially betting against all 4 being the same? Skipping Q1 and betting on Q2-Q4 should have a 93.5% win rate, correct?

can Q4 of the previous game be factored in to say consider it to be a case of N=12, and so on?
I'm still a little confused as to if this concerns quarters that hit in-a-row or just total quarters.

e.g. For N=3, I see now that 3=12.5% is the only value that is important to me - those are the odds of 1 unique value hitting all 3 remaining times...(which if Q4 of another game has hit, or Q1 of the current game, those factors don't matter at this point.) There are 3 remaining Qs and 1/8 chance of a "miss."
(So does skipping Q1 of a 4Q game always make it become an N=3 scenario?)

How do I apply higher values of N to the problem? Do they matter? Was I using N=12 correctly earlier?

Also I am going to look back at some of the earlier responses on probability but up to this point do I factor in regression using this factoral method?