Maxwell’s gambling demon is smart enough to quit while it’s ahead | Hacker News Reader

Maxwell’s gambling demon is smart enough to quit while it’s ahead

arstechnica.com

49 pointspseudolus32 comments

The article lost me on the gambling stuff.

The only winning move when there's a house edge, is not to play. There is no strategy for minimizing your losses (other than not playing or limiting your playing time.) Every bet you place on game with a house edge is progressively dumber.

Technically no if the gambler can keep placing bets which increase in size. A winning strategy is to just keep increasing your bet until you recoup your winnings plus some delta gain.

That only works if you start with unbounded money.

And no limit tables.

Correct, it's called the Martingale strategy. Anyone who doesn't know the name of that strategy and why I doesn't work, shouldn't be gambling. And yet, if they knew that information, then they wouldn't be gambling. I guess nobody should be gambling, but the people who do are the people who don't do the math.

I think you are missing a key element of the equation. It’s not about making money. This isn’t a job replacement, it’s recreation. It’s fun and exciting, it costs money, and we know that.

This is what I think, I gamble - do I care if I win? No. Do I care if I lose? No.

Is it nice if I win? Yes

Will I replace my salary gambling? No

Has it crossed my mind that I can replace my salary gambling? Yes

Has it also crossed my mind to do lots of other careers? Yes

> Has it crossed my mind that I can replace my salary gambling? Yes

It also depends on what you mean by gambling.

Can you replace your salary playing poker? Maybe.

Can you replace your salary playing slots? No.

Does it even work then? I know that a Weiner process will visit all points on the real line with probability 1, but house edge is like a drift term which biases the process to go down. I'd be interested to see some results on this. Clearly, at the limit (house edge = 100% chance of winning), the probability of ever being positive is 0, but what about when the house edge is 1-epsilon?

It only works when the house has no edge. An unbiased random walk expects to cross the original infinitely many times, but a biased walk only finitely many times, as it tends to drift ever further away.

Never mind, I misunderstood the question.

[Even if the game is fair and the house has no edge you may run out of chips before getting ahead. There is no certain way to win in a fair game. If you were certain to win and the opponent certain to lose it wouldn't be fair!]

Well I was talking about tromp's assumption of unbounded money. Of course with finite money the strategy makes no sense.

That's why I said technically and only if the gambler can keep placing bets of increasing size. Obviously this won't work in the real world since the amount a gambler can bet is limited both by how much the other party is willing to wager as well as the amount of money available to the gambler.

If you have an unbounded amount of money to gamble with, why bother gambling?

This isn't a theoretical exercise. I have demonstrated to friends how the Martingale strategy doesn't work in online casinos. The strategy is alluring because the strategy can (but won't always) "work" for hours of play, then then you eventually get hit with an event which wipes you out. Give someone an hour where it works, and they're convinced.

I had that idea and ran the numbers - I'm pretty sure the casino having deeper pockets is part of what gives casinos the edge.

You lost me at "until".

There's no "until" without "if ever".

This isn't a practical strategy, and I do mean "until". The gambler must also be willing to play an unbounded number of games. This is not nearly as big an assumption as the unbounded money assumption since in practice we rely on probablistic processes that may run forever all the time. There is no guaranteed algorithm for generating a number between 1-7 uniformly random using coin flips; all such algorithms can keep generating bad data which can't be mapped to 1-7 (it's just increasingly unlikely).

If there's a skill element don't you just need to be able to outplay the edge?

There's no skill element if there's a house edge. The house edge is how the casino makes money. If there's no house edge, then you're essentially renting services from the casino to run a sort of player market. For example, with poker, the casino takes a percentage of the pot, which is known as the rake.

One possible exception of the above is that at times you may get favorable rules from the casino where you can get a small edge with certain games. One example is blackjack. Perfect play of blackjack does require skill, but perfect play is a ceiling. There is effectively no ceiling (no perfect play) with a game such as poker.

Don't casinos ban players who for example know how to count cards? This would imply that skills may trump the house edge, and thus a bot that would know how to stop (ie how to hide their skill) could stay ahead.

They do in the games where you're playing against the casino (blackjack). However, counting of cards isn't illegal so they ban you for playing too well. In poker the players play against each other and there is no risk to the casino's money.

Blackjack is an oddball game which involves skill and chance. But chance dominates such that it's still likely considered a game of chance.

Skill in blackjack is to play a perfect game. That is, you don't make errors. Counting cards may be considered part of playing a perfect game.

The rules of Blackjack set the house edge. In some cases, a perfect game (including counting cards) could elevate the player such that the player has a small edge. In that case, the player may come out ahead and the casino may eventually stop working with that player. It's rare that a casino hands this to the player as an option though AFAIK. I have heard of casinos negotiating rules with "whales."

Usually, a perfect game won't elevate a player above the line of house edge. Among the rules which narrow the edge is shuffling with multiple decks of cards. If the casino is using multiple decks, then card counting is useless.

That's not true. Sometimes you can make up more on a secondary market (side bets) or are forced to play.

The most mundane example is minimizing your losses to take advantage of comps (typically free drinks). We did this a lot when we were 17-18 to drink extremely cheaply until they changed the rules on us.

Let's not make this more complicated than it is though.

The focus on my post is house edge and how you can't beat it. Many people put up a lot of money on games of chance without understanding this basic idea.

If you do understand this, then go head and proceed to examine how you can still make a trip to the casino pay off.

If you don't understand this, then it's counter-productive to skip it and get right into making money with casino comps, etc.

That depends on your goals.

If you want to maximize your expected average winnings, you are right.

If you want to maximize some percentile, it can be worthwhile to play.

Or if you desperately need 1 million dollars and any amount below that is equally meaningless, and you only have 1000 dollars to start with.

I don't get it... Isn't this stating the obvious? Let's assume you have a dice, if you roll a six, you get 5 times your bet. If you win on a first or second try, it makes sense to stop, from an expected value(EV) point-of-view. But in most of these systems you cannot stop betting forever... So you would start again when things get interesting, which might be the next roll if it is truly random, right? So the only thing they say is to temporarily pause when you are above EV. But when is the best time to start again?

You should expect that over the long term, your losses will equal the house edge. The more you play, the more your losses will approach that of the house edge. In the short term, you'll see lots of variance.

So, the answer to your question is that you should never start. There is never a good time to start. And there's no betting system which gets you over the house edge.

Actual article discussion:

https://news.ycombinator.com/item?id=26284494

Maxwell's Daemon's fatal flaw is that it must consume energy and do work to analyze the state of the system, move the door as particles approach it, etc.

The entire thought experiment is fundamentally flawed, the gedankexperiment of perpetual motion imps.

Yep, said the same about this modified version when this story (in a different publication) was posted a week ago:

https://news.ycombinator.com/item?id=26302918

I've not look beyond that but the headline reminds me of this: https://en.wikipedia.org/wiki/Brownian_ratchet

Is a better way to think about the demon that is is "sorting" the particles? The demon may be able to construct a energy gradient, but only because certain particles had above average energy.

Yet I suppose the random interactions between particles must result in an imbalance. Thus is, at least as a thought experiment, super neat.

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