Probability of not having 2 wins in a row

Hi, I already know the probability of losing X number of coin tosses in a row (50% for 1 flip, 25% for 2 flips, etc.).

Can someone tell me the formula of losing X number of coin tosses in a row, WITHOUT winning two in a row (instead of only one)?


To clarify my question, there is this negative progression which goes like this:
1,1,1,2,2,3,4,5,7

If this bet is won at ANY point, parlay it and wager both bet and win, or two units. If this wins, start from the beginning.

Example:
Bet A (1check): lost
Bet B (1check): lost
Bet C (1check): lost
Bet D (2checks): won
Bet E parlay (2 checks plus the 2 checks just won): won.
You're now ahead by two checks.

I would like to know the odds (probability) of going from 2 flips to 50 flips WITHOUT winning two in a row. All I need is the formula and I could work it out. But if anyone has a chart, that will be fine also.

Thanks for your help!

It's the same. Flipping a coin:

TTTT is the same as TTHH which is same as THTH or HHHH or TTTH or THTT etc. I can't think of a general formula for what you're looking for, other than if you do X flips, there'll be 2^X possible sequences and each will have probability 0.5^X.

I'm sure someone like TheDonGuy will come up with some super simple formula. :(

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I would like to know the odds (probability) of going from 2 flips to 50 flips WITHOUT winning two in a row. All I need is the formula and I could work it out. But if anyone has a chart, that will be fine also.

Thanks for your help!

Fibonacci numbers work great when the probability of success AND failure are 50% exactly.
this will help out:
Fibonacci numbers streaks


for any other probability use a spreadsheet like this one
my Excel in Google

https://goo.gl/Af59ca

it is for a run of 2 in a row
so make a column and subtract the values from 1

thank you for sharing
Sally

Thank you, Sally. This is what I was looking for!

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Example:
Bet A (1check): lost
Bet B (1check): lost
Bet C (1check): lost
Bet D (2checks): won
Bet E parlay (2 checks plus the 2 checks just won): won.
You're now ahead by two checks.

I think I disagree with your 2 check net profit.
after betC, profit = -3
bet D wins at 2 so 4 total for next bet
4 wins for 8 total, but profit = 8-2 or 6

6 + -3 = 3 total profit for the parlay win
unless there is a tip in there I did not see

looks fun to play at Craps dpass
more thrills than flat betting
I would say

good luck
Sally

Yes, you are correct, it is 3 units profit. I was in error. Thanks for pointing that out!