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Comment by dragonwriter | Hacker News Reader

Even if the odds favor you on each event, if they are < 100% success and you play long enough, you will eventually lose everything. Gambler's Ruin always wins.

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That’s not true at all. If you bet 100% of your bankroll then yes. But you’re not factoring in that you calculate what percentage of your bankroll to bet given certain odds.

If given 51% odds every time you will win considering you manage your bankroll well.

This is well known as “Kelly Criterion”

This also requires some assumptions: That there is no minimum stake and stakes are infinitely divisible. They're important assumptions because finding yourself near zero can easily happen on "full Kelly", especially if it's not a game of perfect information.

This implies that both side of the transaction will inevitibly go bust, bookmaker and gambler alike. It may be true, but it's like saying we're all going to die at some point. The expected times are long enough that it's mostly not worth worrying about.

If the positive-expectation gambler can reduce his stakes he will find a comfortable expected time-to-ruin, which might be hundereds of years if he was able to quantify it. In this position, he should continue to place his bets.

We make hundreds of small positive-ER decisions like this every day and we don't shy away from them for fear of the black swan.

Just not true. Let's say I do a bet of 1 dollar, and I have 50% chance of winning, and I can make 1000 bets every day. If start with 100 dollars it is much more likely to die with a lot of money than broke.

@dragonwriter is right, because we're talking about infinities. There is some non-zero chance you'll flip a coin heads 10,000 times in a row. In an infinite amount of time, that series of events is guaranteed to happen at some point (Poincaré makes sure of that, although it might take billions or trillions of years).

You've defined a fair game [1], one which you're just as likely to win or lose, by the same amount each time. Clearly neither side of this game has an advantage over the other, for any given coin toss. But you expect that long term it will work in your favour?

[1] technically it's a martingale https://en.wikipedia.org/wiki/Martingale_(probability_theory...

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