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September 23, 2007 updated January 3, 2008

For the PGT Table sorted by Tile Number Selection Ascending, click here.

For the PGT Table sorted by Combinations Descending, click here.

For the PGT Table sorted by Point Total Ascending, click here.

For the PGT Table sorted by House Way Low-Hand Ascending, click here.

For the PGT Table sorted by House Way High-Hand Ascending, click here.

Q: Is it wrong to gamble in a casino?

A: Disregarding any moral considerations, it is wrong to gamble in a casino if and only if your attitude and gaming style is repeatedly geared towards beating the casino. Such a gaming style is inherently destructive since there is no way to beat the house in the long run.

Q: What kind of gambling could actually be beneficial to the player and is recommended under the right conditions?

A: Responsible Gaming is recreational and occurs when the follwoing conditions are met:

Player is aware that each and every bet he puts or leaves on the table has a negative EV and is further aware of the house edge for each specific game he is playing.

Player is NOT gambling with money he can not afford to lose.

* Cost of entertainment. Player is aware of how much he is expected to lose based on his "action" (the total money wagered over the course of the session) multiplied by the house edge. For example, if you are going to play blackjack according to Basic Strategy for one hour betting $25 per hand and you figure the dealer to get out 60 hands per hour, then your action will be $1,500. Multiplying that by the house edge of .04% your expected loss over the session is $1,500 x .04 = $60. Being aware of WHAT you are getting involved in so you know what the stakes are is extremely essential when it comes to gambling.

* Player is setting certain limits to how much he is willing to lose and is also setting goals for a win that is sufficient enough to call it a day. Remember that the longer you stay at the table the likelier it is that the math will catch up to you and you will be down by an amount equal to the abovementioned formula (action x house edge). Bear in mind that regardless of whether you are actually ahead or behind for that particular session, you are really always behind since you are always a mathematical underdog. And so when you are quitting, you are essentially cutting your losses and that is always a correct play, regardless of whether you are up or down for that particular session.

Under normal circumstances these stop-loss limits and goal-achieving wins can have other qualifications attached to them. The point here is that you don't try to chase your lost money by pumping more money in a game that you can't win. Also, since --regardless of what precisely defines your gambling satisfaction all players feel much better after a win than after a loss-- it is therefore natural that you should strive to have a winning session if possible. Thus if there is not much of a compelling reason to remain after playing several hours and getting lucky, you are probably best off psychologically to leave. (Note that in reality it's all one long session anyway and so you will inevitably give it back eventually but that doesn't concern me since for now you are experiencing the satisfaction of being a winner by quitting while ahead and winning is unltimately the goal of the gambler).

* Attitude. Player should always bear in mind that he is playing recreationally. Do not try to break the bank! Millions of of people have tried it and cintinue to do so as I write and they all unltimately fail miserably. Even if they get lucky once in a while and win, they are destined to lose it back on a later session unless they are quitting for good after only one lifetime gambling session and that rarely if ever happens.

It is extrememly tempting to see the dealer break hand after hand in blackjack and your neighbor who is betting a bunch of black chips is winning thousands of dollars. You are thinking to yourself: if only I took advantage of the my good luck and the dealer's bad luck I could have been up all this money too. Very Very wrong thinking!!! What is really happening is that your neighbor who is betting $300 a hand is losing $1.20 per hand whereas you who are betting the table minimum of $25 are only losing 10 cents per hand. After the shoe is done you and your friend both take inventory. Your friend reports being up $3,000 and you are up a measly $200 (10 bets). "Oh well..." you think "if only I took a shot..." Actually, your friend is not up $3000; it's an optical illusion, it only seems that way. He is really down $72 for the shoe (assuming 60 hands were dealt, and this does not include the expense of tipping which is surely appropriate for someone winning such a large amount) while you are down a measly $6. You both paid for the same service, the same entertainment. Your friend, however, is so addicted to gambling that $25 bets don't turn him on any longer and so he needs a more powerful drug to provide him the entertaining pleasure of gambling: $300 bets. Fortunately, you are able to derive that very same pleasure from $25 bets and so you are getting the same effect for a cheaper price. Think of it as buying the same drug your friend is buying for a significantly better price. You are saving a fortune while your friend needlessly pays much more for the same drug!!

* Playing right. The biggest mistake I see gamblers make in the casino is playing games that they don't know well and making all the wrong moves. After all, the goal of any game is to win. Even if there wasn't real money involved in the outcome of an event, why play like a moron when for a little effort you can learn to play smart and have a much better chance at beating your opponent!!?? The problem here is twofold: 1) player is making bad bets. A bad bet is a bet where the house has a large positive expectation such as the tie bet in baccarat (over 14%). 2) player does not know the optimnal play against each and every "move" his opponent makes. There should be no hunches in games of chance. Don't try to speculate "maybe the dealer has this so I will do this but I'm guessing that he has that so I'll do that". This is stupid and a waste of your brain power. The only thing that matters in the long run is the math behind the game. Computers have figured out that players are slightly better off hitting a 16 in blackjack against a dealer face card vs standing, if surrender is not an option. Therefore, if you play blackjack on a regular basis, don't guess!!! Your guessing will invariably lead you to lose more in the long run than you would by simply following the best mathematical advice which says: hit, if surrender is not allowed; otherwise surrender. If you are going to use your brain why not use it to learn the best mathematical strategy in every game you play rather than wasting it on stupid guesses.

Q: Is it ever correct to make a large negative-EV bet in a casino?

A: Yes! It is possible for a person to be in a condition where his prncipal is not worth much to him since he cannot use for the purposes intended. If he can manage to double (or triple) the money it would then be much more usable.

For example, say you are looking to save up money to go to college. You need $20,000 to enroll and you can save 10k a year. You want to go to school in one year from now; two years from now is unacceptable. In other words, your options are 1) go to school in one year from now 2) not go to school at all. If the 10k of surplus money you make per year is not essential for any other of your needs then it makes sense to take a shot against the house with a negative-EV bet. What you are doing is paying the house for the chance they are giving you to double up EVEN IF this is a negative-EV chance. This is just like buying insurance. Insurance buyers are losers in the long run compared to non-insurance buyers since the insurance companies wind up making a profit. Yet, It is a wise decision for consumers in certain situations to buy insurance and PAY for the security of knowing that a loss will be covered by the insurance company. Likewise, we all know that the house always wins in the long. Yet, the house is willing to provide you a service: namely the possibility of doubling up and it is thus sensible under the right conditions (such as the one mentioned above) to pay the price and take the chance.

Q: If you are gambling under the abovementioned conditions what is your best bet?

A: Your goal is to double up fast, while giving the house as little theoretical edge over you as possible. If you make many small bets against the house hoping to be up 10k by the end of the day, you are giving the house too much action. Remember that they have a positive EV for every dollar you wager against them. You are better off making one large bet in a game where the house has the smallest edge. If you would play the banker in a baccarat game for a 1.06% house edge you are paying the house $106 for giving you a chance to go to school! What a great and noble cause for a reasonable price!! Go for it!

Note that even though blackjack offers a lower house edge in the long run, you don't know if any double-downs or splits will be in order and so you cannot bet all your bankroll on one hand. The same is true with craps (you must leave money for the odds bet) and many other games. Playing the banker in Baccarat is therefore your best choice.


Pai Gow Tile FAQ and Information

Q: Is it correct to take the bank on your turn in Pai Gow Tiles and Pai Gow Poker?

A: By all means!!! Not taking the bank is one of the biggest mistakes I see players make, especially when the action is heads up. On every hand there is a slight possibility of a copy hand and the banker wins all copies. Why give up this slight edge the house is offering you at no cost?

Q: What if there are many other players on the table?

A: Actually, the more players playing against you when you're banking the better off you are (per dollar wagered). In fact according to the "Wizard"'s calculations (WizardofOdds.com) you actually have a positive EV in Pai Gow Poker if you are banking against a full table.

However, it is unfortunate that most pai gow players --especially the Asians-- are extrememly superstitious and they will not play against a player-banker. Apparently they are convinced that they will win and they want to win the money from the house rather than from a fellow player. They are, however, gravely mistaken. Any bet placed against the house has a losing expectation and this is all the more compounded if you are not the banker. Therefore if you were going to make that negative-EV bet on a house-banker, why not make it on a plyer-banker so that you can give your fellow player a piece of the pie. By taking back your bet you are not doing the player a favor; you are doing the house a favor by saving your money so that you will lose it later to a house-banker copy hand rather than a fellow-player-banker's copy hand.

Therefore, if you are sitting at the pai gow table and are having a friendly game, you may disrupt that friendship by taking the bank on every other hand. Most players will elect to sit out when you bank and so will be inconvenienced. Those who do choose to play against you, will be thinking that you are unlucky and therefore making it a personal thing when it shouldn't be.

Q: What are the superstitions in Pai Gow?

A: 1) players taking the bank ONLY after they lost with a big hand or when the house is running hot. These idiots don't realise that if they take the bank all the time the house will have less of a chance of becoming hot in the first place. 2) players changing their bets on "no-rolls" (if the dice in the pai gow shaker don't settle properly thus requiring another roll). 3) players sitting out when another player is banking.

Q: Is the House Way in Pai gow the optimal way?

A: NO! House way is designed to be as simple as possible and thus easy for dealers to memorize. The house way is NOT the optimal way to play many of the hands. Yet, the House Way is good enough that the house figures to have a positive EV in the game due to the commission, EVEN IF the player outplays them.

This is why Pai Gow is such a beautiful game! It's a game of skill! The better you play the less your expected loss and you will sometimes face extremely close calls in which it is perhaps okay --if you insist-- to gamble and go with your feeling since the EV is extremely close. I faced such a hand yesterday with 55446QJ (I happened to have a $1,000 bet up on that hand and I was banking) The house way is split since I don't have a king or better. It turns out, however, that with a QJ (especially when I'm banking) it's a very close call. I finally decided to split them and wound up winning against a AQJ-high. If I had kept them together I still would have won since I was the banker.

Q: In Pai Gow Tiles how many different "number selections" are possible that do not contain a pair?

A: There are 441 different "number selections". Note that this is not the same as the overall number of tile combinations which is a lot higher. I am disregarding the particular tile that represents the given number. For example 8742 has 256 combinations but they are all counted as one "number selection" among the 441 total.

Q: How many different "number selections" are possible that do contain a pair?

A: There are 468 such "number selections". There are an additional 51 selections for two pair. The total "number selections" are 960.

Click Here to view the Pai Gow Tile 960-row Table created by the author Jacob Gluck. Copyright is reserved. However, you are encouraged to link to my table. If you wish to distribute it commercially or reproduce it on your own website without linking to my website, you need my permission in writing.