Krapstuff - Streaks

Streaks.math

1r. Heads streak (for at least 1 of length X or more)

using the R code below

(this basic version differs from the Home page version as the code will NOT print the raised matrix)

call function like this: runs.r(5, 20, 0.5)

where run.r function = runs.r (run length, # of trials, trial prob of success)

press Run (or enter key)

One can a new call in the R Console and press enter

Note: Do NOT enter values with seperators. example: 10,000 is 10000. do not use the comma (,)

1 million is 1000000 (or better 1e6 or 10^6) and not 1,000,000 (code uses , for something else)

2r. Average number of trials for a run (streak)

with 2 or 3 outcomes, success or failure or a tie.

runs.mean3(run length, probability of success, probability of a tie)

examples: runs.mean3(5, 0.5) #fair coin flip call (tie default = 0)

runs.mean3(5, 949/1980, 55/1980) is for the don't pass bet in craps

3r. Heads or Tails streak (or both)

R code using Markov chain. p(heads) does not have to equal p(tails)

***** see section 4r. for Heads AND Tails *****

for Heads or Tails streak (NOT both)

some math required: (p(Heads) + p(Tails)) - (2 * p(Heads & Tails))

more to follow...

4r. Heads and Tails streak (heads 1st then tails or tails 1st then heads)

R code using Markov chain. p(heads) does not have to equal p(tails)

returns:

print(headsT.run) heads run 1st then tails run

print(tailsH.run) tails run 1st then heads run

print(tailsH.run + headsT.run) both possibilities

5r. Average (mean) number of streaks (runs) in N trials table. X and X or more