Timid Play when Large Bets are Profitable

David Gilat, William Sudderth

Research output: Contribution to journalArticlepeer-review


The total variation of a simple, symmetric random walk with absorbing barrier at zero, is stochastically larger than the total variation of any other nonnegative, integer-valued supermartingale with the same initial position. This strengthens a result of David Freedman on the optimality of timid play for maximizing the time to bankruptcy in certain gambling situations.
Original languageEnglish
Pages (from-to)573 - 576
JournalAnnals of Probability
Issue number4
StatePublished - 1977
Externally publishedYes


  • decision theory
  • dynamic programming
  • gambling theory
  • martingale
  • Simple random walk
  • timid play
  • variation


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