As a martingale is a model of a fair game, and using optional stopping theorem assumes that you are dealing with a martingale, is it even possible to use optional stopping to find stopping time in an unfair situation? And how? (In conncetion to the Gambler's Ruin, finding probability of winning and loosing)

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    $\begingroup$ Are you familiar with super- and sub-martingales? $\endgroup$ – aduh Sep 10 '16 at 18:13
  • $\begingroup$ Somewhat, but i don't completly see how one can use them. $\endgroup$ – User123456789 Sep 17 '16 at 18:12

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