[HN Gopher] Monte Carlo Methods or Why It's a Bad Idea to Go to ...
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Monte Carlo Methods or Why It's a Bad Idea to Go to the Casino
Author : chkas
Score : 127 points
Date : 2021-11-14 15:02 UTC (7 hours ago)
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(TXT) w3m dump (easylang.online)
| intrasight wrote:
| Go to a "Monte Carlo Night" fundraising event. You get all the
| fun of a casino and do good at the same time.
| reidjs wrote:
| I understand gambling at Casinos as a fun novelty with your
| friends. But as a legitimate way of making money? Seems so risky.
| Especially when gambling online seems pretty straightforward. Or
| even better, gambling a percentage of your income on stocks or
| cryptocurrencies seems like it should fulfill the same addiction
| with less potential for completely destroying yourself
| financially.
| chrsig wrote:
| >seems like it should fulfill the same addiction with less
| potential for completely destroying yourself financially
|
| I don't think this is accounting for the role that risk plays
| into the addiction.
| reidjs wrote:
| That's a good point. The potential for destroying yourself
| financially may be a meaningful part of the addiction. At
| least at a casino you may be more restricted, you can't use
| credit cards for example, while margin trading on Robinhood
| lets you gamble using credit.
| sokoloff wrote:
| I've definitely seen people take credit card cash advances
| from ATMs in casinos.
| halikular wrote:
| The only casino game worth playing is poker. Everything else is
| a scam.
| Mikeb85 wrote:
| Poker isn't really a casino game though, as you're not
| playing against the house.
| crehn wrote:
| Put a large sum on black in roulette. If you lose, place
| double on black. Repeat until you win once or end up
| bankrupt, then go home.
| IkmoIkmo wrote:
| It's the antithesis of gambling.
|
| If you bet $10 on black and win straight away, earning $10,
| and go home with $20, and stay home for the rest of your
| life and never walk into a casino again, then yes, you won.
| But you're not really a gambler. You're actually the
| opposite of a gambler, one that never enters a casino
| again. Of course you gambled $10, but the amount is
| meaningless.
|
| If instead you gambled a meaningful amount, say $50k, then
| indeed it'd be truly gambling something meaningful. But if
| you'd lose, you'd have to double it to $100k. If you lose
| that, $200k. It spirals out of control quickly if you're
| actually betting meaningful amounts.
|
| And the amounts must be meaningful. After all, if you bet
| $10, lose a few and eventually win and go home with $80,
| the strategy requires you to never gamble again. If you
| come back because $80 isn't meaningful, you're really just
| starting over at a meaningful amount, that could make you
| win enough to never make you come back. But at that point,
| you're talking about significant risks (e.g. betting $50k
| and losing 4 coin unfavourable (47% / 53%) tosses in a row,
| and you've lost a total of $750k and need to risk losing
| another $800k to walk away with a profit of just $50k, by
| flipping another unfavourable coin toss)
|
| If you were Jeff Bezos, of course you could bet a million
| and walk away with an eventual win before running out of
| money. But the amount of money isn't meaningful to Bezos.
| In the same way a kid with $40 of savings could bet $50
| cents and walk away with 50 cents of profit by winning the
| 5th round. But that doesn't make any meaningful difference
| if it ends there. If the kid comes back to gamble, the
| strategy falls apart, as the house always wins in the end
| if people keep coming back.
|
| And that's precisely why the strategy doesn't actually work
| for anyone. To win any meaningful amount, you'd have to bet
| a meaningful amount. And to do that, is incredibly risky as
| there's a good chance you'll run into your limit before you
| win. And even if you win, that experience will likely pull
| you back in to try to repeat it, the gambler mindset
| eventually will lose.
|
| How quickly do you run into your own limit, and the limit
| of the casino? After all, the odds are against you.
|
| Technical note: your final game winnings are never more
| than the first game winnings. That's why the first bet must
| be meaningful.
|
| Say you bet $10 and lose, bet $20 and win, you made $10
| profit. Say you lost the $20 too and bet $40, you again
| still made $10 as you made 80 - (10+20+40). Suppose you
| lost the $40 too, and the $80, and the $160, and the $320,
| and the $640, and now bet $1280 and win $2560... subtract
| 1280+640+320+160+80+40+20+10, and again, you only walked
| away with $10.
|
| In other words, to walk away with something meaningful like
| $10k, you may end up having to wager 1.2 million after 7
| coin toss losses.
| lexapro wrote:
| >If you were Jeff Bezos, of course you could bet a
| million and walk away with an eventual win before running
| out of money.
|
| Are there really casinos with no maximum bet? Usually
| there is a maximum so you run into the problem that at
| some point you can't double anymore and have to take the
| loss, even though you would have enough money left.
| spapas82 wrote:
| For reference; this system is called Martingale
| https://en.wikipedia.org/wiki/Martingale_(betting_system).
| It is used for a lot of years; there's even a refernece of
| it in the Dostoyefsky novel "The Gambler":
| https://www.cambridge.org/core/books/abs/dostoevsky-in-
| conte....
|
| Also beyond roulette I've heard of various martingale
| variations in different gambling games. For example, a
| common system here in Greece is play martingale on draws on
| a soccer league (like the World cup or the Euro Cup): Pick
| the first game and bet on draw (no matter what the teams
| are). If you win you'll get 3x (that's what the draw
| usually gives); if you lose, double it and bet draw at the
| next game. This is a good system if you can afford
| doubling. I remember a Euro some years ago where there were
| like 15 games without a draw ; consider that if you started
| with 1 euro you'd need to bet ~ 32 0000 euros in the 15nth
| game ...
| paulcole wrote:
| What you're describing is a Martingale method. It also has
| the issue of running into a table's max bet. Overall it's
| one of the dumbest gambling "systems" out there -- and
| that's saying something.
| bena wrote:
| Also, red/black isn't 50/50. It's slightly under.
| [deleted]
| agys wrote:
| This "system" is addressed in the blog post (under: "New
| Strategy: we double the bet after each loss").
| rileymat2 wrote:
| Given the rake, it is also a loser unless you have a big
| advantage from skill.
| sokoloff wrote:
| During the TV-fueled boom of no-limit hold'em and around
| Chris Moneymaker's WSOP main event win, friends and I would
| travel every year to Vegas to play in the side games and
| satellites leading up to the WSOP. Staying in the (now
| gone) Imperial Palace for $25/night, it was relatively easy
| to beat the single-table satellites by enough to pay for
| the flights the first Friday and then grind out an overall
| profit on the rest of the days.
|
| That's a special case of "big advantage in skill" in the
| sense that the WSOP/TV boom drew a bunch of players with
| way more aspiration than skill/experience and the games
| were easily beatable by players of typical home game winner
| level of skill as a result.
| jedberg wrote:
| The IP is only gone in spirit -- the building is still
| there, they just renovated it and jacked the price.
|
| But you can still get cheap gross rooms at Circus Circus!
| halikular wrote:
| Yeah, but it tends to be lower in online casinos. And you
| clearly know the percentage.
| mfringel wrote:
| The typical big-casino rake isn't that large. From memory
| (it has been 2 years since I've physically been in a poker
| room), the typical rake at a full 9-player table at the
| Encore (Everett, MA, USA) worked out to ~$12-15/hour per
| person.
|
| For a professional dealer, good chips, and a continuous
| flow of players, that seems like a pretty fair price to
| pay.
| listenallyall wrote:
| If all the players sit down with $1000 and play for 5
| hours, the casino will have taken approx. 6% of the total
| bankroll. It's not about what is fair, it's whether you
| are actually skilled enough to beat the other players AND
| the rake over the long term. Most people can't.
| mason55 wrote:
| > _scam_
|
| Or just paying for entertainment. Craps pass line is under
| 1.5% per bet placed with even money odds if you're backing up
| your bet. For a $15 pass line bet you're paying the house
| $0.25 per bet. Even at 10 bets/hour it's $2.50/hour for
| entertainment, which is super cheap. And toss in a couple
| free drinks and it comes out to be very cheap entertainment.
| halikular wrote:
| That's a case for entertainment. In poker real money can be
| made, although hard. All other ways of making money in the
| casino has been cracked down on.
| User23 wrote:
| The strip casinos don't care about individual advantage
| play if you're playing with black chips or less[1]. I've
| watched an older pit boss make fun of an obvious counter
| by calling the count out for him. Now if you're wonging
| and doing other team stuff then sure expect to get
| cooled.
|
| Edit: the real key way to view it is that much like
| bartenders, casino staff are fundamentally providing
| recreation. The ones that are good at their jobs will
| provide a solid experience for a reasonable price.
|
| On the other hand anyone with a gambling addiction needs
| to stay away. A good rule of thumb is to treat your
| entire trip bankroll as entertainment budget that you're
| willing to spend all of.
|
| [1] For all I know they might not even care if the
| counter's base bet is melons, but my experience is
| limited to black chip range since losing won't hurt and
| it's enough to get the dopamine hit plus sign off on nice
| comps.
| jedberg wrote:
| The only way to win at the casino is with a player's card. If you
| play perfect strategy and have them track all your play, they
| comps they give you should be close to what you lose. But you
| have to play for a long time to get the comps and have the odds
| work out, and most people don't.
|
| In other words you have to be pretty rich already and have a deep
| bankroll to get the breakeven comps.
|
| Otherwise, consider your losses the fee for the entertainment. :)
| daneel_w wrote:
| I'm not sure why people are surprised or educated when this
| reality is explained to them. Surely there's not a single man
| alive who really believes that slots etc. offer a 50/50 chance of
| winning? The house always has an edge of one or several
| percentiles, which make up their average profit margin of every
| dollar that passes through the establishment. These days casinos
| prefer to not call it an edge in their favor, but rather paint it
| in a prettier and somewhat delusive light by using the term "RTP"
| - return to player.
| kqr wrote:
| One strength of Monte Carlo methods that's often overlooked is
| their robustness to changing specifications.
|
| A coworker told our team about a puzzle relating to sizes of
| pizzas. Most people came up with clever solutions that all
| depended on things like uniform density, perfect circularity,
| etc. Probably good approximations to real world pizzas. But one
| of us suggested a Monte Carlo based method and the beautiful
| thing about it was that it would work even without all those
| assumptions. As long as the pizzas have an area when viewed from
| above, it works.
| mbil wrote:
| Neat! I think a martingale strategy would also have been fun.
| jstx1 wrote:
| The post doesn't really shed much light on it, it feels like a
| missed opportunity to explain things well.
|
| There's two main effects:
|
| - Negative expected value (EV)[1]. The games are set up in a way
| that on average you're likely to lose money. This is true for
| every game where you play against the house, otherwise the game
| wouldn't be there. Poker is different because your EV depends on
| how you play relative to other people.
|
| - Bankroll management and risk of ruin[2]. Even in a fair game,
| if you start with a short bankroll, you're likely to go broke.
| For example, let's say two of us flip a completely fair coin and
| bet $1 on each flip. The expected value for both players is $0.
| Now if one of us starts with $5 and the other $1000 and we play
| repeatedly, the person with the smaller amount is almost
| guaranteed to go broke in a long series of flips. This what
| happens when you play against the house and it's the main reason
| why people lose money when they gamble in casinos.
|
| [1] https://en.wikipedia.org/wiki/Expected_value
|
| [2] https://en.wikipedia.org/wiki/Risk_of_ruin
| confidantlake wrote:
| [Edit] As has pointed out I have misread the parent comment and
| agree with it. Leaving my original response below.
|
| For number 2 it depends on strategy. The strategy you outlined
| has you risk $5 to win $1000. Of course in a fair game you will
| go broke most of the time. For every time you win you should
| lose 200 times to come out even. But you can easily take the
| reverse strategy. Bet $5 if you win, leave. If you lose double
| your bet, if you go down $1000 dollars leave. In this case you
| are almost guaranteed to win. But the times you do lose you
| lose enough to make up for all of your wins.
|
| EV is EV, it doesn't change based on who has the larger
| bankroll. The casino doesn't magically get an edge because they
| have more money. They get the edge because the game odds are in
| their favor.
| stavros wrote:
| I don't think you're talking about the same thing as the GP.
| If you bet $5 and lose, you can't double your bet, you have
| no money (which is exactly the GP's point).
|
| It's a random walk, and it's much more likely to take you to
| -$5 way before it takes you to +$1000.
| confidantlake wrote:
| Yes exactly, completely agree with you. I am seeing this
| does not matter. It is not why a casino makes money.
| [deleted]
| kqr wrote:
| Well... that's bordering on oversimplifying it.
|
| The key distinction is whether you count the EV of a single
| wager, or the expected growth of compound returns.
|
| As you say, the single-wager EV is independent of bankroll
| provided you can afford it in the first place. This is also
| what most people mean when they say EV, and indeed the common
| mathematical definition of it.
|
| However, skilled risk takers know that the arithmetic EV
| isn't what matters more generally. What matters in the long
| run is geometric EV, or expected growth of compound returns.
|
| And for geometric EV, bankroll absolutely matters. The larger
| your bankroll, the better your geometric EV. I suspect this
| is what the parent comment referred to.
|
| (However, when the wager shrinks in comparison to your total
| wealth, the arithmetic EV approaches the geometric EV by
| Taylor series approximation. For "everyday affairs" (as I
| think Bernoulli put it) you can think of them as equal.)
| confidantlake wrote:
| I would have to disagree that I am oversimplifying it. We
| are talking about a casino vs a player. Most players
| betting $5 at a time are not losing because of bankroll
| considerations. They are losing because the game they are
| playing is negative ev for each individual bet.
|
| A casino would much rather play against a player with
| $1,000,000,000 than a player with $5. Sure the player with
| $5 is going to go broke nearly 100%. And the player with
| more money will never go broke betting $5 at a time, they
| will die from old age way before that happens.
|
| The fact that a player with only $5 has almost a 100%
| chance of ruin is absolutely not why a casino is making
| money. A casino is always going to want a player with a
| lower risk of ruin than a higher one. When a player goes
| broke they can no longer make money from them.
|
| Do people really think a casino would prefer someone going
| broke 100% of the time with $5 then a player going broke 0%
| of the time with $1,000,000,000? That they are making money
| because of players losing their bankrolls and unable to
| bet?
| kqr wrote:
| Aha, I see what you're saying. You're right, but I still
| think you're reading something into the top-level comment
| that isn't there.
|
| The way I understand it, they're not saying "casinos make
| money because their counterpart is going broke" (and
| you're right that they don't.) They're saying "in the
| casino vs. player situation, the player will almost
| always run out of bankroll before the casino does, and
| therefore the casino does not risk ruin, even in highly
| volatile games."
| confidantlake wrote:
| I reread the parent and the article and see what you are
| saying. I agree that I misread the top level comment, and
| they were correct. (I only looked at the first roulette
| example where bankroll did not even exist). Thanks for
| pointing this out.
| newaccount74 wrote:
| From my (limited) experience watching folks at the
| roulette table, I think there are two kinds of players.
|
| There's the players making small bets, they win a bit,
| lose a bit, and at the end of the day they may go home
| with a bit more or a bit less money than they came with.
| The casino wins on average because of the 0.
|
| Then there are the gamblers. They come to the table, make
| a few large bets, and within a few minutes they lost
| their monthly salary (or whatever was the limit on the
| ATM). They lost because the player will continue playing
| until they can't.
|
| I'm pretty sure that you could make a completely fair
| roulette, and the house would still win big every day.
| I'm not sure why there aren't any fair roulettes, though.
| Drdrdrq wrote:
| Speculation: because it would draw attention to where the
| real profit comes from?
| User23 wrote:
| Powerball tickets have negative EV _after taxes_ , but I'm
| willing to spend a grand total of about $20 a year on them by
| playing when the jackpot is north of half a billion. Because
| the $20 loss has absolutely no effect on my quality of life,
| but the win would.
| fallingknife wrote:
| Typically, when the jackpot is up in that range, the tickets
| actually have a positive EV.
| wbc wrote:
| Super unlikely, the main reason is at that point many
| people buy tickets and it becomes more and more likely the
| jackpot is split between multiple winners [0].
|
| Actually the largest Powerball at $1.586 billion was split
| between 3 people [1]
|
| [0] https://chance.amstat.org/2020/02/lottery-
| ticket/jackpots-ev... [1] https://apnews.com/article/archiv
| e-6d98eff765c9e2f4b68367131...
| laurent92 wrote:
| Isn't that a "gateway drug" effect? I'm similarly afraid of
| sometimes having wine alone, because I know it's addictive.
| Nbox9 wrote:
| Gambling has a similar distribution to most markets. 20% of
| the gamblers generate 80% of the gambling revenue. Most
| people that gamble don't ruin their life. Most people that
| drink don't ruin their life/health.
|
| There's some ethical concerns where the gaming industry
| (and liquor industry) will market more towards problem
| users or in ways to generate more problem users, but buying
| $20/lotto tickets a month isn't a guaranteed start of a
| problem, nor is having wine alone sometimes.
| HWR_14 wrote:
| That's just measuring the EV in Utils as opposed to Dollars.
| bluecalm wrote:
| My favorite fact about the law of large numbers is that the more
| you play the higher expected distance from the expectation is.
|
| This sounds counterintuitive to many so it's worth considering
| for a bit.
|
| The law of large numbers says that the number of successes
| divided by the number of tries converges. It doesn't mean the
| number of successes converges to expectation - quite the
| contrary.
|
| For example when you flip a coin and go up a unit every time it's
| heads and down one unit every time it's tails your expected
| distance to 0 is sqrt(n) where n is the number of flips.
| Similarly when you play poker your expected distance from real EV
| to what you actually get is going to increase the more you play.
|
| With this mind it's not correct to say the amount is already
| close to calculated results with more tries as the article says.
| Try it, you will get numbers farer away from the expectation the
| more times you play!
| kqr wrote:
| That's a nice way to look at it. In an example, for someone who
| was as confused as I:
|
| If you're playing a perfect good blackjack strategy, even
| without counting cards, you have a small edge over the house
| (if I remember my Thorpe correctly.) Let's call it 0.5 %.
|
| So if you play 100 hands, you can expect to win 51 of them.
| However, sometimes you might win 59, or 63, sometimes only 45
| or 37. But you'll be reasonably close to 51. If you won fewer
| than 36 hands or more than 66 I'd be surprised. So in the worst
| case you win 15 hands fewer than your expectation, and in the
| best case you win 15 hands more.
|
| If you instead sat day and night and played 10,000 hands,
| you'll still be expected to win the same fraction: 5,050.
|
| But you might win 5,073, or 5,168. Or win 5,012, or win 4,931.
| With this large number of hands, you might well win 150 hands
| fewer than you expected to, or 150 hands more!
|
| Relatively speaking, you're closer to the expectation with the
| additional trials. With 100 hands, you might win anywhere
| between 36 % and 66 % of them. With 10,000 hands, you'll
| probably win between 49 % and 52 % of them.
|
| But when you're playing 100 hands, the difference between 36
| and 51 % is only 20 hands. When you're playing 10,000 hands,
| the difference between 49 % and 51 % is 200 hands! In terms of
| actual absolute money won or lost, you're more likely to end up
| farther away.
|
| ----
|
| And the reason, of course, is that while the expectation grows
| linearly when you increase the number of hands, the variation
| shrinks with the square root of the number of hands.
|
| The reason they converge in the law of large numbers is not
| that the variation shrinks as you play more hands -- the reason
| they converge is that the expectation outgrows the variation,
| which makes the latter seem small relative to the former.
|
| This is also why the distance traveled in a random walk is
| dominated by variation in the short term and bias in the long
| term. When you have a small enough time step, the square root
| is greater than the line.
| citizenpaul wrote:
| A good reason not to go to US casinos in vegas is there are too
| many stories of casinos blocking payout due to "exploiting"
| games. If you win you win or you dont. Doesnt matter how its up
| to the casino to validate that their game works and is exploit
| free. You already put your money down so they might as well just
| use a gun to take it at that point.
| atian wrote:
| There are few industries with as many eyes as the gambling
| industry in the US. This needs some context.
| jedberg wrote:
| I've never heard of this, other than someone breaking the slot
| machines. And they make it very clear that if you don't use the
| slot machine they way it is intended, you void your play.
|
| I've been scammed at foreign casinos before in the Caribbean,
| but never in the US.
| denysvitali wrote:
| I guess this is more related to card counting
| kqr wrote:
| This holds a life lesson: you haven't actually "won" until
| you've managed to get the other party to pay you. Goes in
| casinos as well as finance and business.
|
| Corollary: the best way to win is the one where others don't
| care or don't even realise you have won. Try to find a niche
| others don't care about and find in it regular, small wins.
| Don't go into a highly contested arena and try to win big. Even
| if you think you have won, you'll never get paid that way.
| krisrm wrote:
| The related article on blackjack (linked at the bottom) was also
| a great read. I've never felt like I really understood card
| counting but it makes a lot more sense now. Also explains why I
| don't go to the casino :)
| listenallyall wrote:
| Card counting 101: unlike dice or roulette where every outcome
| is entirely independent, blackjack has "memory"... all the
| cards that have previously been discarded are unavailable in
| future hands. Blackjack starts out with a casino advantage of
| only about 0.3 to 0.7%. When a lot of 5s (and to a lesser
| extent, 6s and 4s) have been used already, that can move the
| advantage up to about 2 percentage points into the players
| favor, therefore, going from -0.5% to as high as +1.5%. The
| idea is to bet as little as possible under normal
| circumstances, and then for the hands where the advantage has
| shifted to the player, increase the bet as much as the casino
| will allow. So for example in theory, 40 hands x $10 x -0.5% +
| 3 hands x $500 x +1.0% is net positive. But not a lot, and good
| luck getting a 50x bet spread past a halfway decent pit boss.
| kqr wrote:
| > for the hands where the advantage has shifted to the
| player, increase the bet as much as the casino
|
| ...and your bankroll...
|
| > will allow.
|
| ----
|
| You can still go bust on a 1.5 % edge, after all, if you
| overbet.
| listenallyall wrote:
| If your bankroll isn't sufficient to withstand significant
| volatility, yes, you shouldn't start counting cards in the
| first place.
| teej wrote:
| Just beware - the expected value of the authors simulated
| blackjack counting is quite good. This is due in part to the
| crazy "spread" (the ratio of max bet to min bet) of 100-to-1.
| This illustrates the profitability of the model well, but it's
| unrealistic.
|
| A more typical spread of 10-to-1 ekes out an expected value of
| ~0.5% (see https://wizardofodds.com/games/blackjack/card-
| counting/high-...). When I was counting, I could barely hit
| $15/hr expected value. Hardly worth the effort, I found it very
| demanding to keep track of the count at Vegas dealer speeds and
| play perfect blackjack for hours on end.
| ReaLNero wrote:
| How did you manage to card count without attracting
| attention, even after playing for hours?
| kqr wrote:
| At $15/hour, I'm sure the casino will let them sit for days
| if they want. It's peanuts and shows other non-counters a
| player winning, meaning good publicity for the casino
| that's surely worth more than $15/hour.
| listenallyall wrote:
| Because he wasn't winning. Even if they noticed, he wasn't
| a threat.
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