Let's imagine a game with the following parameters:

  • 1.97x payout ratio
  • (Truly) random number is generated each round, ranging from 1 to 100
  • You need to roll under 51 to win (R < 51) - integer only are generated

Is there a way (strategy) to win this game? Knowing that there is no betting limit and we can make as many rolls as we want?

Obviously, we can double down every time we loose but I was thinking about something more subtle like diminishing the bet each time we win and vice & versa so we wouldn't change the edge but may influence the payout ratio to a positive one?

  • $\begingroup$ What do you mean by "win this game" ? Obviously you will never have a positive expected value, do you stop playing once your income is positive ? Would you be happy with 55% chances of leaving the table richer than you joined, even if the gain is lower that your gain is in the other 45 % ? $\endgroup$
    – Evargalo
    Oct 16, 2018 at 12:25
  • $\begingroup$ Relevant answer in this question : math.stackexchange.com/questions/612571/… $\endgroup$
    – Evargalo
    Oct 16, 2018 at 12:30
  • $\begingroup$ Thanks for the speedy answer, yes win the game would mean that the expectations of making a profit are at least 1% higher than making losses. $\endgroup$
    – Linda
    Oct 16, 2018 at 12:31
  • 1
    $\begingroup$ Thanks for the link... very accurate indeed... $\endgroup$
    – Linda
    Oct 16, 2018 at 12:38


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