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Author Topic: Gambler's Conceit  (Read 3179 times)

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Gambler's Conceit
« on: November 07, 2014, 08:11:41 AM »
Quoted from Wikipedia:

Gambler’s conceit is the fallacy described by behavioral economist David J. Ewing, where a gambler believes they will be able to stop a risky behavior while still engaging in it. This belief frequently operates during games of chance, such as casino games. The gambler believes they will be a net winner at the game, and thus able to avoid going broke by exerting the self-control necessary to stop playing while still ahead in winnings. This is often expressed as “I’ll quit when I’m ahead.”
Quitting while ahead is unlikely though, since a gambler who is winning has little incentive to do so, and is in fact rewarded for continuing to do so by their winning. Once in the throes of a winning streak the individual may even become convinced that it is their skill, rather than blind chance, causing their winnings, or good luck on their side, and thus it seems especially senseless to stop while continuing to win.

There is another, more mathematical reason why "quitting when ahead" makes little sense. In casino games, outcomes are an infinite stream of random numbers, and it makes no difference to the distribution and characteristics of the outcomes whether you play all decisions, or skip some in a systematic or random way. So waiting for triggers, and all the rest of it, makes no difference to mathematical probabilities pertaining to various patterns etc.

That being the case, the gambler who attempts to "quit while ahead" does not change anything with regard to his expectation. There could only be an advantage if the gambler had some way of knowing that he was quitting just as things were about to turn bad. And conversely, he would only have an advantage if he were to enter the game just as things were about to turn good. But of course, he cannot ever know either of these.

The wheel does not know whether you are "ahead" or not, that should be obvious.

This is one of the great cliches of gambling, but a little logical thinking reveals it to be a fallacy. It's amazing that it has persisted for so long, and continues to persist.

By the way, I tried posting this topic over at betselection cc, but it seems my contributions are not wanted because I tell the truth. In fact, I was put on moderation recently for being "tactless". XXVV took a dislike to one of my posts and complained to esoito, and now I'm being censored.

It seems that vested interests are holding sway over there. It won't do to have posters posting "nasty negative stuff" when those in authority stand to gain from keeping people ignorant.
« Last Edit: December 28, 2016, 09:30:49 PM by kav »


Conceit Leads to Ruin
« Reply #1 on: November 07, 2014, 07:37:07 PM »
Imspirit writes:

A gambler’s conceit leads to ruin.

Gamber’s conceit is a phrase which describes a gambler’s belief that he is always able to keep his winnings ahead of his losses. When a gambler says, “I’ll stop when I’m ahead,” he is expressing the gambler’s conceit. When a gambler plans to quit playing after making a certain percentage of his bankroll, for example, 10%, he is operating from gambler’s conceit. He thinks he is practicing “good money management,” but underlying this apparently positive discipline is a false sense of invincibility.

Gambler’s ruin is a phrase which describes the fact that a gambler, who has relatively smaller resources, will eventually lose his entire bankroll to an opponent who has relatively greater resources. In context, the opponent is the House, which has in principle an infinite bankroll.

A simple example illustrates how a gambler’s conceit ultimately leads to ruin in a perfectly fair, even-bet game. Aaron has 100 pennies, while Ben has 12,800 pennies. Every time Aaron wins, Ben gives him one of his pennies, and vice versa.

So, Aaron and Ben begin to play. Because the game is entirely fair, each has a perfectly even chance of winning or losing each decision. However, because Ben has more pennies, the chance that Aaron will go bankrupt before Ben does is almost certain. In fact, Aaron has a greater than 99% chance of going broke before Ben does.

Look at it this way. There are only two possible outcomes for Aaron: 1) he will double his 100 pennies, or 2) he will lose all 100 of his pennies. Each possibility occurs with a 50% chance. So, Aaron’s outcomes are like a coin-toss in itself: heads, Aaron doubles his money; or tails, Aaron loses his bankroll. In order for Aaron to win all of Ben’s pennies, this “outcome coin” would need come up “heads” 7 times in a row, netting Aaron 200, 400, 800, 1600, 3200, 6400, and 12,800 pennies, to finally bankrupt Ben. But it only takes 1 “tails” at any time to bankrupt Aaron. The chance of getting 7 “heads” in a row is (0.50)^7 = 0.78%, which means his chance of ruin is more than 99%.

Ben’s chance of winning is higher simply because he has a larger bankroll and can survive more losses (“tails” of the “outcome coin”) than Aaron can.

If Aaron includes a stop-loss or profit-target for each game session, he only prolongs the inevitable and does not change his odds.

Aaron’s chance of success becomes even smaller when the game has a built-in mathematical advantage in Ben’s favor, and of course, when Ben has a practically infinite bankroll. Ben represents the House, and in the long run, its winning against Aaron is virtually guaranteed.

A gambler’s conceit that leads him to believe he can always stay one step ahead of the House is an example of irrational thinking, because in order for the gambler to stay ahead, he must continue playing, but because he continues playing, he increases the chances that he will meet his ruin. This is why the House generously lavishes enticing comps on the winning gambler to encourage him to keep coming back to play. The longer and more often he plays, the greater the chances he will lose it all back to the House. In fact, the chances he will ultimately be ruined rises exponentially the longer he plays.

Clearly, in order for a gambler to consistently stay ahead, he must win more often than he loses. But in a perfectly fair, coin-toss type of game, the best one can hope to achieve is 50% accuracy in the long term. To be consistently more than 50% accurate requires one to be able to see into the future or to alter the odds of the game in one’s favor, both presently impossible. A more sophisticated gambler might employ a betting progression to dig himself out of temporary holes, but eventually, all betting progressions require 1 more unit than is available in the bankroll, resulting in ruin.

[PS: I split the previous discussion into two different topics. You can follow it here: Regression toward the mean ]

Re: Gambler's Conceit
« Reply #2 on: November 20, 2014, 05:41:38 AM »
Bravo! Kav and Mike.  I really enjoyed reading this topic and I follow both of you completely. You make perfect sense. I am going to quote the book "Ten Days at Monte Carlo at the Banks Expense."

"The reason why the Bank wins with such regularity, is not because it has a great advantage over the players in the percentage, but because it is a machine, with a practically unlimited capital, playing mechanically against a host of players, most of whom possess no capital at all, and all of whom, at a critical moment, are liable to lose their tempers and their nerve.

The punter is also habitually greedy.  What player do you know who is content to go into the Casino, and make even 10% a day net profit on his capital?

Most of your gambling friends would laugh at the idea!  They all expect to double their capital, and most of them hope to make 400-500%.  And yet the Bank in a good year only makes about 1% a week. If the Bank expected to win in the same proportion as most of the players, its expectations would amount to the modest little sum of about 400 million sterling per annum.

The Bank certainly has a great advantage in the point of capital, it has the advantage of being a machine, and it also possess the advantage of the limit, but against all this you must remember that the player has two great pulls in his favor.  He can continue playing as long as he is a loser, and he can vary his stake according to whether his luck is good or bad. To put it in a vulgar parlance, "the Bank has to stand up to be shot at."

This being so, we must make as much use as possible of our advantages, and endeavor to reduce those of the Bank to a minimum.  In order to do this, we must fight them with their own weapons, so to speak, and attacking them with a large capital, be content to make a small percentage on our money.

We must play cautiously, and go very slow when luck is against us, and the moment the luck turns sufficiently to give us a small profit on the day, we must leave off at once and give the game a rest till the next day.

99% of all the systems ever invented fail for want of sufficient capital; the remaining 1% are defeated by the maximum. 

Therefore, the only way to hope for success, is to attack the Bank with a large capital, in such a way that the maximum will probably never be reached."

Keep up the wonderful philosophical perspective! I enjoy it very much and it helps us become not only well rounded and innovative players, but well rounded individuals.