### A Reward Problem to the Consecutive Heads In a Run

#### Abstract

#### References

Bloom, D. M. (1996). Probabilities of Clumps in a Binary

Sequence. Math. Mag., volume 69, pages 366–372.

Feller, W. (1968). An Introduction to Probability Theory and Its

Application, volume 1, 3rd ed. Wiley.

Finch, S. R. (2003). Feller’s Coin Tossing Constants. Mathematical

Constants, pages 339–342. Cambridge University Press.

Ford, J. (1983). How Random is a Coin Toss? Physics Today,

volume 36, pages 40–47. Gordon, L., Schilling, M. F. and Waterman, M. S. (1986). An Extreme Value Theory

for Long Head Runs. Prob. Th. and Related Fields, volume 72,

pages 279–287.

Havil, J. G. (2003). Exploring Euler’s Constant. Princeton

University Press.

Hirose, H. (2016). Learning Analytics to Adaptive Online IRT

Testing Systems “Ai Arutte” Harmonized with University

Textbooks. 5th International Conference on Learning Technologies and Learning Environments, pages 439–444.

Keller, J. B. (1986). The Probability of Heads. Amer. Math.

Monthly, volume 93, pages

–197.

Mood, A. M. (1940). The Distribution Theory of Runs. Ann. Math.

Statistics, volume 11, pages 367–392.

Schilling, M. F. (1990). The Longest Run of Heads. Coll. Math. J.,

volume 21, pages 196–207.

Schuster, E. F. (1994). In Runs and Patterns in Probability:

Selected Papers (Ed. A. P. Godbole and S. Papastavridis), pages

–444. Kluwer.

Spencer, J. (1986). Combinatorics by Coin Flipping. Coll. Math. J.,

volume 17, pages 407–412.

Full Text: pdf