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The standard deviation of the final result over n bets is the product of the standard deviation for one bet see table and the square root of the number of initial bets made in the session.
This assumes that all bets made are of equal size. The probability that the session outcome will be within one standard deviation is The probability that the session outcome will be within two standard deviations is The probability that the session outcome will be within three standard deviations is The following table shows the probability that a session outcome will come within various numbers of standard deviations.
I realize that this explanation may not make much sense to someone who is not well versed in the basics of statistics. If this is the case I would recommend enriching yourself with a good introductory statistics book.
Although I do not mention hold percentages on my site the term is worth defining because it comes up a lot. The hold percentage is the ratio of chips the casino keeps to the total chips sold.
This is generally measured over an entire shift. A mathematician alone can not determine the hold because it depends on how long the player will sit at the table and the same money circulates back and forth.
There is a lot of confusion between the house edge and hold, especially among casino personnel.
The following table shows the average hands per hour and the house edge for comp purposes various games.
The house edge figures are higher than those above, because the above figures assume optimal strategy, and those below reflect player errors and average type of bet made.
This table was given to me anonymously by an executive with a major Strip casino and is used for rating players. A Spanish translation of this page is available at www.
The Wizard of Odds. House Edge of casino games compared. On This Page Notes: Standard Deviation Number Probability 0. Don't show this again.
Liberal Vegas Strip rules: Dealer stands on soft 17, player may double on any two cards, player may double after splitting, resplit aces, late surrender.
Counting cards is the best known advantage gambling technique used in blackjack, but there are several other ways of getting an edge over the house.
Counting cards is easier than you think, too. This site has an extensive series of pages about how to count cards in blackjack.
We even have pages about other advantage blackjack techniques like shuffle tracking. Video poker games resemble slot machines, but they offer players much better odds of winning.
And getting better odds of winning is something everyone should be interested in. Finally, video poker is a game that rewards skilled play. This is just too much pressure for some players.
That means if you need an ace to fill your straight, you can calculate the odds of getting that card. There are 4 aces in the deck—no more, no less.
With a slot machine, you have NO way of knowing what the likelihood of getting a particular symbol on a particular reel is. A cherry might be programmed to come up once every 10 spins, or it might be programmed to come up once every spins.
You have no way to know. As a result, the payback percentage for a video poker machine can be calculated.
The payback percentage for a slot machine can be calculated, too. But not by you. Even video poker games with less than ideal pay tables pay more than slots.
In fact, for players with my temperament, learning strategy is fun. Craps might be the most intimidating game in the casino.
You have lots of people standing around the table, the bets all have funny names, and you even need an entire crew of people just to run a single game.
This is a game with a lot moving parts, but at the end of the day, it all boils down to someone shooting dice and hoping to get certain numbers.
Another drawback is that the game is as streaky as a casino game can be. You can easily lose hundreds of dollars at the craps table in a matter of moments.
Finally, some of the bets at the craps table offer some of the worst odds in the casino. There are only 2 dice in use, and there is only one shooter at a time.
Her goal then changes. She now wants to roll the point before rolling a 7. The simplest bet at the table is a bet on whether or not the shooter is going to succeed or fail.
But the game also offers the only bet in the casino which has a 0 house edge. This is called an odds bet. This bet is a multiple of your original bet, and the maximum amount you can bet on this option is pre-determined by the casino.
This hedges your risk in a dramatic way. The more money the casino lets you place on the odds bet, the better your odds become.
Just stick with the simple bets on the table and avoid the ones that seem complicated. That puts this game on a par with blackjack.
The only strategy for this game is to avoid the bets which have a high house edge and focus on the bets with a low house edge.
Craps is also one of the most social games in any casino. People are jumping up and down, yelling, and giving each other high fives constantly.
I mentioned earlier that the game is, by its nature, streaky. Few gambling experiences are more exciting than getting involved with a craps table with a hot shooter.
And if you think the game is too intimidating, look for the casino game class schedule at the casino. Almost all casinos offer these in the mornings and in the afternoons.
It has advantages and disadvantages over other card games in the casino, but one of the biggest advantages the game offers is its relatively low house edge.
Baccarat is a simple guessing game. The dealer gets a hand and the player gets a hand. This game is perfect for high rollers, as the stakes are generally available.
I probably sounded pretty down on slot machines when I wrote about video poker earlier, but the reality is that for the right type gambler, slot machines are an excellent choice.
But not all slot machine games are created equally. You put your money in, you spin the reels, and you accept your luck.
The best slot machines are the ones played at the higher denominations. If you get in over your head financially, it can be disastrous, and that can happen really quickly.
Another consideration is how complicated the game is. The general rule of thumb is that the payback percentage on the simpler games is higher than for the more complicated games.
A 3 reel slot machine almost always has a better payout percentage than that of a 5 reel slot machine.
A slot machine with a flat top jackpot almost always has a better payout percentage than that of a progressive jackpot machine.
Just stay within your budget and stick with the simpler, more traditional games. In general, roulette gets a bad rap among so-called sophisticated gamblers.
They cite the lack of a skill element and the high house edge for the game. But somehow roulette has managed to remain popular for centuries.
One reason is because the relatively high house edge is mitigated by the pace at which it is played. European roulette, which only has a single 0, has a house edge of 2.
Remember we said that it had the same house edge, too? American roulette is going to make my list of worst casino games. The game simply has worse odds for the player.
Not all casinos have European roulette. My recommendation is to just skip roulette if the only version you can find is American roulette.
There are other options with much better odds which suit similar temperaments—baccarat is one choice that might work well for you.
If enough gamblers start ignoring the American roulette wheels, the casinos might start putting in more European wheels.
I love Pai Gow Poker for multiple reasons, but the main reasons have to do with the pacing. In that respect, it resembles roulette or baccarat.
But the game also presents opportunities for pushes on a consistent basis, which lowers your expected hourly loss even further. Like craps, though, Pai Gow Poker can be intimidating for beginners.
Pai Gow Poker is played with a 53 card deck—it includes a joker as a wild card. The gimmick is that each player gets a 7 card hand.
The dealer has to do the same, but the dealer has to do so in a prescribed way. This is another similarity to blackjack.
Other outcomes result in a push, which happens more often than you probably think.