How advanced mathematics and gaming theory can help you as a trader
Okay, so I thought I'd contribute a little bit of wisdom or at least food for thought.
What would you say, if I told you that you can make money on a mutually exclusive, binomial event such as flipping a coin (50% probability)?
It blows most peoples minds when I tell them this. Here are the conditions......A) You must have control over the wager amount, B) You must have a significant starting capital (say 100x the initial wager amount) and C) You must adhere to a strict diet of progressive betting strategy.
Here's how it works: Progressive betting requires that it be truly mutually exclusive and also requires inherent "strings" be present over a given sample of n events.
Take for instance, our coin flip example. If you have a data sampling of say 10,000 flips. Over the course of that entire data set, you will experience both positive and negative strings. The distribution will follow an exponential decay (i.e. there will be a very small number of long strings and there will be a very large number of short strings.) A typical distribution for strings might look like this......10 strings 1, 9 strings 3, 8 strings 7, 7 strings 15, etc.
Ever wonder why typical profit analysis tools show strings? Here's how to make it work.
If the event is truly mutually exclusive and binomial, over large samplings, you'd expect the number of winning strings to be similar (negligibly identical) to losing strings.
So, you bet initally 10 units. If the outcome is a win, you take 50% of the profit and leave the other half out as an additional wager increase. If the next outcome is positive, you do the same, take 50% and leave the rest, again upping your wager. When you lose, you restart the wager sequence back to the original wager/lowest increment.
So over a string of 5 wins (10 unit start bet)....it would yield 65.9375 units of profit and the same losing string would yield a loss of 50 units.
The key to progressive betting is inherent strings. The system fails and you actually lose money if there are no strings and it's simply a binary oscillator (i.e. win, loss, win, loss, win, loss, etc).
This is exactly how successful blackjack betting strategies are employed.
The second part of this segment is second order effects and how even with a 50% probability and a "player" using progressive betting will still end up losing.
The following 15 users say Thank You to RM99 for this post:
Until now, I too thought that we can exploit the benefits of strings even in case of non-correlated bets, and thought that what @RM99 said in his opening post of this thread makes sense.
Then I have read the #62 post of @worldwary and realized that it doesn’t work in that way.
Thank you worldwary for your thoughts.
And also let me express my appreciation to @Fat Tails for his efforts to try to convince us and tell us the point in such an untiring way.
The point is in the quoted part above, read it again!
You find clear and valuable reasoning in Fat Tails’ posts, namely in #68, #72, #80.
Last edited by Arpad; April 27th, 2011 at 06:45 AM.
So the casinos are basically a license to print money. They have several strategies for reducing already less than 50/50 odds. (there's NO game in a casino with an equal or higher than 50/50 odds.....blackjack, when isolated and taking advantage of the double down, betting feature can yield 51/49 odds in your favor, but that's a topic for a different session).
Here's how the casinos REALLY make their money.
Second order effects ensure your doom (in the long run).
Basically, the house is an infinite and unlimited bank. This is a good assumption for all but the most rich "whales" who walk through the door. The casino knows, that even if you have "even" odds, all they have to do is get you to play long enough and they'll get you on a negative string long enough to send you back to the atm. The house on the other hand, can endure virtually limitless strings of positive gain on your behalf. This is exactly why they treat whales and high rollers differently. Those players have a much higher ratio with respect to bankroll to the house, so they can go on a positive run and really hurt the casino. This is why they do everything they can to get the player to continue playing and dump it all back.
So as stated above, a condition for success in progressive betting is having a significant starting capital to significantly reduce the second order bankroll-bankroll advantage the house may enjoy. (i.e., there's a very good chance you'll get felted if you start out with 3 units, vs, if you start out with 1000 units).
But alas, the casinos know that all of this takes a lot of confluence to work in the patrons favor. It's virtually impossible to isolate the odds properly and it takes an immense amount of discipline to execute the system. Throw in alcohol, breakdowns in discipline, the houses bankroll advantage and it's usually only a matter of time before they bust you out.
This type of analysis can be incorporated into strategies that feature long strings. The longer the average string, the more plentiful the longer strings, the more profitable a progressive betting strategy will be.
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Advanced mathematics can certainly be used to show that this is nonsense. You cannot make money by betting on an event that follows a binomial distribution, such as flipping a coin.
Please have a look at: Richard A. Epstein, Theory of Gambling and Statistical Logic
If a gambler risks a finite capital over a large number of plays in a game with constant single-trial probability of winning, losing, and tying, then any and all betting systems ultimately lead to the same value of mathematical expectation of gain per unit amount wagered.
Progressive betting systems can only be used, if there is a positive or negative (auto)correlation between successive bets. For Black Jack betting systems the notion of strings makes sense, as the winning probability after a losing game is slightly increased.
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Ummmm, no. This doesn't address the string nature. It's true, that when any single event is considered by itself, the probability is the same. But when strings of events are considered and approached as such, the odds of strings are substantially different than individual events.
Simply put, the odds of the next single event are 50%, but the odds of 2 stringed events together are 25% and so forth and so on. When the system approaches it from a set of events, rather than a single event....varying bet amounts has an effect on the outcome.
It's exactly why string analysis is featured in most profit analytics. A strategy that features long strings can be made to take advantage of varying bet strategies.
If a whale engages in playing roulette, he has the same negative expectancy as the sardine. When using a progressive betting system, such as a Martingale, the whale will indeed have longer positive runs (that is a higher winning percentage), but in the end the single loss that he will suffer will be much larger than the loss experienced by the sardine.
There is an analogy with trading: If your profit target is 1 tick and your stop-loss is 20 ticks, you will certainly have more winning trades than losing trades. But the average loss, you will experience offsets your advantage coming from the high winning percentage.
It is true that you need a considerable starting capital and an immense amount of discipline, to exploit any edge. However, if there is no edge (positive expectancy), discipline and capital will not help you a lot. In the long term you will lose.
The second-best strategy, if you do not have an edge (negative expectancy) is to put all your gaming capital on a single bet. If you win, just leave the casino. The best strategy is not to engage in any bets.
One last recommendation here for those who are interested: Well known Gambler and Hedge Fund Manager Edward O.Thorp has written a book on "The Mathematics of Gambling". You may download your personal (legal) copy here.
If you have a binomial distribution, this indicates that the single events are stochastically independent, or otherwise put uncorrelated. In this case there is no progressive betting strategy, which will give you an edge.
Progressive betting strategies only make sense, if subsequent events are correlated. This is not the case with a coin flip. Your example is simply false. Sorry for my lack of diplomacy.
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Agreed and that's how some of the negative progressives work. You simply keep increasing your wager to cover all previous losses until you end up winning, hoping that the house doesn't go on an infinite run. But as you said, you simply need a large bankroll to and an iron stomach to weather the swings, which mount quickly.
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I do some (gambling) counselling work with some people who have firm convictions about their ability to consistently make money from Roulette and other Casino games where they have no edge. Mostly they have devised some variable bet or Martingale type of money management approach based on capitalising on strings which they have had some winning experiences with. I work many of with these people in prison, not all. I have done quite a bit of spreadsheet simulation and research into this so as to be clear in my own conviction about it. Agree with FatTails on this one. But RM99 I am interested to see more of your mathematical explanation for your belief.