Betting Systems - General Questions
I have read a couple of articles about "Parrando's Paradox." Is there a way that you could explain what is going on as it is extremely counter-intuitive that two losing games played in a certain sequence could add up to a winner. I thought I understood the mathematics of gambling / probability! I can see that there is a subtle link between games A & B as game B is dependent on capital that is affected by game A; I am unable to carry the logic any further. Does Parrando's Paradox have any implications for negative expectation casino gamblers? I doubt it but would love to hear it from someone with a greater understanding.
Parrando's Paradox states that two sub-optimal games of chance can show a long-term gain if played alternately. However the games can not be independent of each other, which eliminates any comparison to casino games.
I’ve been a dealer in Vancouver, Canada for over six years. Having dealt all casino games (except craps) I’ve decided that a person’s best betting strategy would be to bet all their bankroll on a one-shot bet, preferably in bacarrat, and on Banker. My decision is based on the observation that the longer a player gambles, the more likely that the odds will get the best of them, and the more likely it is that they will lose everything. The one-shot method may not be entertaining, but surely it’d be more profitable (or I should say, "less damaging")
You’re absolutely right. The fewer bets actually made the better the odds are of actually winning. The expected loss is also a function of the total amount bet. If the player keeps circulating money back and forth between himself and the dealer the house edge will gradually grind the player down. However maximizing the odds of winning should not be the only objective to gambling. Having fun is also important. Plopping an entire bankroll on the table in one bet may not be as fun as playing it out gradually. It may also may have a greater chance at a large loss depending on how much play is involved in the alternative. If one really wants to cut down the house edge the best thing to do is put your money in the machine marked "change."
You take a lot of your time or space on your web site to explain that no system can beat the house edge. I'd like to know what drives you to continue to play casino games if you know that you will loose in the end?
The rare times that I play a negative expectation game it is for entertainment. pai gow (tiles) is the only game I find enjoyable enough to play without an advantage.
First of all, I really enjoy your site. I thought I had the ultimate system until I did the math that your site provided me. My question is this, the casino is stationary, the gambler is mobile. If everyone went to the casino and promptly left after winning just one unit would there be any casinos? What I mean by one unit, lets say playing blackjack is a five-dollar chip, I show up with $50 and leave after winning $5. Is there a ratio that I should use if this is the strategy I want to play ($50 to $5 = 10%)? And most importantly can this work?
The casinos would still win. Most players would indeed walk away with their one unit but some would lose their entire stake, whatever it may be. If you consider only even money games with a probability of winning of p then the probability of winning 1 unit before losing x units is (((1-p)/p)x- 1) / (((1-p)/p)x+1 - 1). In the case of double-zero roulette, with a bankroll of ten units, the probability of winning one unit is 85.4268%. For every one of these players the casino will profit 10*(1-0.854268)- 0.854268 = 0.603056 units.
Also, changing casinos after a one-win doesn't make any difference in the odds compared to staying at the same casino and table.
Hi wiz, Let’s suppose I conjure up a sports betting system which requires $1K bets to return $80K per year. In order to produce this return approximately 250-300 bets per year are needed. Would the sports books eventually bar me in a similar fashion to the way the casinos bar card counters? Can you become a successful sports bettor openly, or do you have to sneak around like a card counter?
First, I’m skeptical that anyone could make 80K with 1K bets and a bankroll of only 250-300. And don’t even get me started about the word "system." To answer your question, for the most part the best sports bettors may practice openly. Even if a sports book did forbid a professional’s action or 86 them from the property it would be easy to get someone else to do the betting. Then again I once went to a Super Bowl proposition bet seminar by Fezzik, a professional gambler, and he gave his presentation in a Halloween mask.
Why do people insist on believing in betting systems and beating house odds when they know better? There are plenty of folks who are unaware of either rules or probabilities, but some of us know both well and still insist that through a betting system, timing, or some other fallacious method that the house can be beat. I know that your degree is in math, not psychology, but by your experience you also must have some insight into the gambler’s mind that gives you an idea about what motivates this line of thinking... right?
Good question. I have run across numerous system believers and the one thing they all seem to have is a lot of conceit. Despite the fact that they never seem to have gone much past algebra, if they made it that far, they all think they know better than greatest names in mathematics. This inability to consider contradicting evidence or other points of view is certainly not confined to betting system chasers. The more ridiculous a belief is the more tenaciously it tends to be held, and there is no shortage of ridiculous things for weak-minded people to believe in.
What do you think of the Bible Code?
I would put those behind it on the same level as those selling get rich quick gambling schemes. The mathematically ignorant taking advantage of the mathematically ignorant.
Hi, Wizard. Let’s say I have $300 to gamble with, and can accept a 25% risk of ruin. What should I do to maximize my upside? Thanks!
I would make the banker bet in baccarat. My betting advice would be to do what is known as a two-step progression. First, bet 1/3 of your bankroll. If that wins, walk away. If that loses, then bet the other 2/3. Again, if you win, walk. With any tie, just bet again until the bet is resolved. Here are the probabilities in baccarat:
Banker: 45.86%
Player: 44.62%
Tie: 9.52%
The probability of a banker win, given that the bet is resolved is 45.86%/(45.86%+44.62%) = 50.68%. The probability of losing both steps of the progression is (1-0.5068)2 = 24.32%. The banker bet pays 19 to 20, so you will have a 75.68% chance of winning $95 or $90 (depending on whether you win on the first or second bet), and a 24.32% chance of losing $300.
I think I have a winning betting system. However, I need more than the 3,000 baccarat shoes that you have on your baccarat page to test it. Can you make more?
I hope you're happy; I just created a quarter million of them. Better to find out your system will fail eventually, which they all do, for free than with real money in the casino.
This question is discussed in my forum at Wizard of Vegas.
You have now analyzed the Oscar's Grind, Labouchere and Fibonacci betting systems. Which offers the overall highest probability of achieving your winning goal?
Let's assume that we are basing each system on the Player bet in baccarat. Let's also assume that we have a bankroll equal to 50x our bankroll with Oscar's Grind and the Labouchere. Let's make it 53x for the Fibonacci, which is the sum of the Fibonacci numbers 1,2,3,5,8,13, and 21.
Here is the probability of success of each:
- Labouchere: 97.53%
- Oscar's Grind: 97.69%
- Fibonacci: 97.93%
You may wonder why they are different if I keep saying that "all betting systems are equally worthless." The reason is that I qualify that statement with "Measured by total money lost to total money bet." The Fibonacci has the greatest probability of success because the player bets less, on average. The other two involve a greater average amout bet, which is more opportunity to grind down the player's bankroll. The Labouchere, with the lowest probability of success, has the highest amount bet, which let's the player enjoy the experience longer. Overall, here is the ratio of the average amount bet to winning goal of each:
- Labouchere: 20.95
- Oscar's Grind: 14.56
- Fibonacci: 9.59
All things considered, your choice of betting system should depend on why you're playing. If you want to maximize your probability of success, the Fibonacci is bet. If you want to play longer and bet more, the Lobouchere is best.
Since they are all based on the same bet, the ratio of money lost to money bet will always get closer to 1.235%, the house edge on the Player bet, the more you play, regardless of what system you may use.