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I hope you're not going to hate me for my bad phrasing of this question, because I'm not a mathematician. So, the problem goes like this:

We have an unknown number of gamblers, and each of them has different amount of cash - from few bucks to few thousand. The goal is to transfer money to one individual(no matter who) - all the money, or a given sum.

Those players, however, cannot exchange money or interact with each-other in any way, but each of them can gamble with the casino.

When gambling with the casino, one has 47.5% chance of doubling a bet and 52.5% of losing the bet.

What is the best and most reliable way to do this and loose as little to the casino as possible?

Edit: A real life example - Imagine there are many players that want to cash out their points but neither one of them has anything near the minimum cash-out amount, so they come together and try to figure out a strategy to gamble until someone has enough points to cash-out and then split the money

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    $\begingroup$ How is this going to transfer money to the given individual? The given individual is either going to gain money from the casino or lose money to it (more likely the latter) via that individual's bets, not from anyone else's. $\endgroup$
    – Robert Israel
    Commented Sep 4, 2018 at 22:46
  • $\begingroup$ Ok, the word transfer might be a bit out of context but you get the idea, one must hold all or a given amount of cash at the end $\endgroup$
    – Nikolai Frolov
    Commented Sep 4, 2018 at 22:52
  • $\begingroup$ This is not clear. You could have each person bet all their money. Then, with probability $\approx .86$ at least one person will double their money. At that point, all winners could cash in and split the proceeds. But if only one person wins, this represents a significant loss. Is that what you wanted? $\endgroup$
    – lulu
    Commented Sep 4, 2018 at 23:25
  • $\begingroup$ Worth noting: Since the bets are so unfair, it is generally wiser to place big bets...as you limit the "fees" that are constantly being extracted in the form of unfair odds. $\endgroup$
    – lulu
    Commented Sep 4, 2018 at 23:26
  • $\begingroup$ This may work better if the players can place opposite bets. For example, gambler 1 bets on red at roulette while gambler 2 places a equal bet on black on the same wheel at the same time. But this does require them to interact in some way to coordinate the bets. $\endgroup$
    – David K
    Commented Sep 4, 2018 at 23:28

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