2
$\begingroup$

There's this !dice command in a discord server I'm in, and it has a $\frac{1}{6}$ chance of winning with a $5.4$ times payout. $5.4 \frac{1}{6} = 0.9$ times profit so I know in essence you can't profit over sheer time.

However me and some other people have made thousands without much effort simply by starting out with a bet of $\$5$ (fake money you earn by chatting) and increasing it by $\$5$ until we win, leaving us with a increase in profit around $\frac{9}{10}$ times (no math on the $\frac{9}{10}$, off the top of my head estimate).

The server owner says it's only luck but we've done it successfully every time. Is this actually a profitable method and if not is there one?

  • 0
    Ah, the good old Martingale strategy. It only works as long as you can afford the ever-increasing bets, unless the random number generator isn't as random as it would like to be. – 2017-01-05
  • 0
    The random number generator is JavaScript's `Math.random();`, so pretty random if not perfect. – 2017-01-05
  • 0
    If you start w/ $5 and go 10, 15, 20... won't you have a net loss even if you win on 20? That's a 30% chance of profit, not 90%? – 2017-01-05
  • 0
    If I win on 20 I've spend \$30 and get \$108, seems pretty worth it to me – 2017-01-05
  • 0
    I'm silly, didn't read 5.4. The actual probability is 84%, lose money on the 10th. – 2017-01-05

2 Answers 2

1

If you start out with a large amount of capital, you will indeed have a high probability of getting a small positive return, and a small probability of losing everything. On the average, since it is an unfair game, you lose money. But since it's only fake money, who cares?

  • 0
    At the end of the week the person with the most fake money gets $10 of IRL money and all the fake money is reset, makes quite a few people care surprisingly. – 2017-01-05
  • 1
    If only the person with the highest return gets it translated into something real, while everybody else gets nothing, this may have interesting optimal strategies. Reminds me of [How to Gamble If You Must](http://store.doverpublications.com/0486780643.html). – 2017-01-05
  • 0
    There's also a pot where the percent fake money you put in relative to all the money that's been put in is the chance of you winning and winning that gives you a head start on the next week equal to the pot's size, and there are investments to increase passive income (via chatting) and to unlock a 50% win with x2 return command that's the only option that doesn't have a 0.9x return. This server has quite a few gambling features I don't mention. – 2017-01-05
  • 0
    I'll probably post another question on which order I should buy the investments in to be the most efficient, since it's a different enough topic from this question. – 2017-01-05
0

The optional sampling theorem in martingale theory says that the optimal strategy for an unfair game in which you have only finite capital is never to play.

  • 1
    'optimal' is pretty loaded here. – 2017-01-05
  • 0
    https://math.dartmouth.edu/~pw/math100w13/lalonde.pdf – 2017-01-11
  • 0
    I know the one. What I'm saying is life is not always just about expectation value. What if there was an game that lost money on average, but paid off when the stock market tanked? – 2017-01-12
  • 0
    Apart from correlations with outside events, I can think of plenty negative EV games that I and most others would gladly play. (Of course it would have to be irrational in some sense to play them an arbitrarily large number of times.) – 2017-01-12