TV Game Shows
On the game show Let’s Make a Deal, there are three doors. For the sake of example, let’s say that two doors reveal a goat, and one reveals a new car. The host, Monty Hall, picks two contestants to pick a door. Every time Monty opens a door first that reveals a goat. Let’s say this time it belonged to the first contestant. Although Monty never actually did this, what if Monty offered the other contestant a chance to switch doors at this point, to the other unopened door. Should he switch?Yes! The key to this problem is that the host is predestined to open a door with a goat. He knows which door has the car, so regardless of which doors the players pick, he always can reveal a goat first. The question is known as the "Monty Hall Paradox." Much of the confussion about it is because often when the question is framed, it is incorrectly not made clear the host knows where the car is, and always reveals a goat first. I think put some of the blame on Marilyn Vos Savant, who framed the question badly in her column. Let’s assume that the prize is behind door 1. Following are what would happen if the player (the second contestant) had a strategy of not switching.
- Player picks door 1 --> player wins
- Player picks door 2 --> player loses
- Player picks door 3 --> player loses
Following are what would happen if the player had a strategy of switching.
- Player picks door 1 --> Host reveals goat behind door 2 or 3 --> player switches to other door --> player loses
- Player picks door 2 --> Host reveals goat behind door 3 --> player switches to door 1 --> player wins
- Player picks door 3 --> Host reveals goat behind door 2 --> player switches to door 1 --> player wins
So by not switching the player has 1/3 chance of winning. By switching the player has a 2/3 chance of winning. So the player should definitely switch.
For further reading on the Monty Hall paradox, I recommend the article at Wikipedia.
What is the best game to play?
It depends on the rules of the game and how well you play it. Limiting the answer to popular games, assuming you play the optimal strategy and stick to all the best bets when given a choice, I’d narrow down the best games to the four in the following list. (The percentage shown is the element of risk of those games, which is the ratio of how much you can expect to lose to how much you bet, which I think is a proper measurement of the value of a game.)
- blackjack (six decks, dealer stands on soft 17, double after split allowed, surrender allowed, re-splitting aces allowed) — 0.25%
- craps (3-4-5x odds, laying the maximum odds allowed) — 0.27%
- video poker (9-6 jacks or better) — 0.46%
- Ultimate Texas Hold 'Em — 0.53%
What is your favorite game?
My answer would be whichever game has the lowest element of risk at whatever casino I'm in. However, the answer to the question about which game I find the most fun to play is pai gow (tiles). I dislike volatility and tiles offers a slow game with lots of pushes. It’s also a challenging game to understand and play well. I find that other players are generally smart people and pleasant to play with.
What do you think of my betting system?All betting systems are equally worthless. Not only can't a betting system overcome the house edge, it can't even dent it. If a betting system makes gambling more fun, be my guest. Just don't delude yourself that it will help in the long run.
Which is your favorite casino in Las Vegas?The casino that I feel offers the best odds and overall value is South Point.
Casino (insert name here) is cheating. Can you please warn your readers about them? I know because (insert adjective-laden story about losing here).This kind of accusation rarely comes with any evidence behind it other than adjectives. What rare times I get some actual numbers, the loss could easily be explained as ordinary bad luck. Nevertheless, I have exposed cases of cheating at Internet casinos several times, starting with such accusations. So if you suspect a casino is cheating, please follow the scientific method before writing to me; in other words, make a hypothesis about how the casino cheating, gather evidence to confirm or deny the hypothesis, and finally analyze the evidence. I’m happy to help with step 3.
Why are you such a Debbie Downer when it comes to gambling? You take all the fun out of it with your mathematical strategies, which take away my free will.If you want to lose more by making mistakes, go ahead. I can only lead a horse to water. You don't have to drink it if you don't want to.
Do bad players, in particular in blackjack, cause everybody else to lose?No. While everyone remembers the time a bad player took the dealer's bust card and caused the whole table to lose, people tend to forget the times that a bad player saved the table. This practice of selective memory to support pre-existing beliefs is called “confirmation bias.” In the long run, bad players are just as likely to help you as hurt you, so leave them alone.
Why do you say not to take "even money" on a blackjack when the dealer has an ace up? It is a sure winner!There is a 69.1% chance the dealer doesn't have a blackjack and you'll win the full 3-2. (1.5 × 69.1% = 103.7%.) That’s more than the 100% you get by taking even money. You’ve already established the fact that you're a gambler by playing in the first place. Don't suddenly become risk-averse and give up that 3.7% because you don't want to take a chance.
In blackjack, sometimes the dealer unknowingly exposes the hole card. What is the player advantage when this happens?The player advantage is 10% +/- 0.5%, depending on the specific rules. Here is the strategy when the dealer exposes both cards. This is different than the double exposure strategy, where the player loses on ties.
What is your opinion on dice control?For the benefit of those who don't understand the question, books, videos, and lessons allege that it’s possible to beat the odds in craps with a careful toss that favors certain outcomes, namely lowering the probability of a total of seven to less than 1 in 6. I'm firmly in the skeptics camp on this one. I have yet to see any credible evidence leading me to believe that anyone can consistently influence the dice. There is much more money to be made selling books and lessons on how to do it than actually doing it.
Where do casinos put the loosest slots?As a rule of thumb, the location makes no difference.
If a ball landed in red the last 20 spins in roulette, what is the probability it will land in black the next spin?The same as red, 47.37% on a double-zero wheel, 18 black numbers divided by 38 total numbers.
I think you're wrong about the previous question. The odds of 21 reds in a row is (18/38)21 = 1 in 6,527,290. The odds must overwhelmingly favor black.That's true, but it doesn't matter. That’s the same probability of 20 reds followed by a black. The fact is the past doesn't matter in games of independent trials like roulette.
I've thought of a way to beat the casinos in roulette! Start with a small wager on any even-money bet, like red or black. If it loses, then double the bet on the same thing. Then keeping doubling until it wins. The winning outcome has to happen eventually and when it does I'll profit my original wager. Then repeat. What is your opinion? Also, please don't tell anybody.This is probably the most popular of all betting systems, known as the Martingale. Gamblers have been conceiving of it and using it since time immemorial. Like all betting systems, not only doesn't it beat the house advantage, it doesn't even dent it. The reason is the gambler will eventually have a bad losing streak where his bankroll isn't enough to make another double.
In your previous answer, you explained why the Martingale doesn't work. Then how about the opposite, doubling your bet after each win until a desired target is hit?This is known as the anti-Martingale and is equally worthless. The times your bankroll gets grinded down to nothing will outweigh the winnings when you hit your target. Regardless of what betting system you use, or none at all, the more you play, the more your ratio of money lost to money bet will approach 5.26% in double-zero roulette.