Casino games and mathematics. part three

After one more year Thorp published a book (I mentioned it at the beginning of the article) in which he rather in details, in the form comprehensible to any even a slightly literate and sensible person, set the rules of formation of a winning strategy. But the publication of the book did not only cause a quick growth of those willing to enrich themselves at the cost of gambling houses' owners, as well as allowed the latter ones to understand the main reason of effectiveness of the developed by Thorp strategy. First of all, casinos' owners understood at last that it was necessary to introduce the following obligatory point into the rules of the game: cards are to be thoroughly shuffled after each game! If this rule is rigorously observed, then a winning strategy of Thorp cannot be applied, since the calculation of probabilities of extracting one or another card from a pack was based on the knowledge of the fact that some cards would already not appear in the game! But what does it mean to have "thoroughly shuffled" cards? Usually in gambling houses the process of "thoroughly shuffling" presupposes the process when a croupier, one of the gamblers or, that is still oftener seen of late, a special automatic device makes a certain number of more or less monotonous movements with a pack (the number of which varies from 10 to 20-25, as a rule). Each of these movements changes the arrangement of cards in a pack. As mathematicians say, as a result of each movement with cards a kind of "substitution" is made. But is it really so that as a result of such 10-25 movements a pack is thoroughly shuffled, and in particular, if there are 52 cards in a pack then a probability of the fact that, for instance, an upper card will appear to be a queen will be equal to 1/13? In other words, if we will, thus, for example, shuffle cards 130 times, then the quality of our shuffling will turn out to be more "thorough" if the number of times of the queen's appearance on top out of these 130 times will be closer to 10. Strictly mathematically it is possible to prove that in case our movements appear to be exactly similar (monotonous) then such a method of shuffling cards is not satisfactory. At this it is still worse if the so called "order of substitution" is less, i. e. less is the number of these movements (substitutions) after which the cards are located in the same order they were from the start of a pack shuffling. In fact, if this number equals to t, then repeating exactly similar movements any number of times we, for all our wish, can not get more different positioning of cards in a pack, or, using mathematical terms, not more t different combinations of cards. Certainly, in reality, shuffling of cards does not come down to recurrence of the same movements. But even if we assume that a shuffling person (or an automatic device) makes casual movements at which there can appear with a certain probability all possible arrangements of cards in a pack at each single movement, the question of "quality" of such mixing turns out to be far from simple. This question is especially interesting from the practical point of view that the majority of notorious crooked gamblers achieve phenomenal success using the circumstance, that seemingly "careful shuffling" of cards actually is not such! Mathematics helps to clear a situation with regard to this issue as well. In the work "Gambling and Probability Theory" A. Reni presents mathematical calculations allowing him to draw the following practical conclusion: "If all movements of a shuffling person are casual, so, basically, while shuffling a pack there can be any substitution of cards, and if the number of such movements is large enough, reasonably it is possible to consider a pack "carefully reshuffled". Analyzing these words, it is possible to notice, that, firstly, the conclusion about "quality" of shuffling has an essentially likelihood character ("reasonably"), and, secondly, that the number of movements should be rather large (A. Reni prefers not to consider a question of what is understood as "rather a large number"). It is clear, however, that the necessary number at least a sequence higher than those 10-25 movements usually applied in a real game situation. Besides, it is not that simple "to test" movements of a shuffling person (let alone the automatic device) for "accidence"! Summing it all up, let’s come back to a question which has been the headline of the article. Certainly, it would be reckless to think that knowledge of maths can help a gambler work out a winning strategy even in such an easy game like twenty-one. Thorp succeeded in doing it only by using imperfection (temporary!) of the then used rules. We can also point out that one shouldn't expect that maths will be able to provide a gambler at least with a nonlosing strategy. But on the other hand, understanding of mathematical aspects connected with gambling games will undoubtedly help a gambler to avoid the most unprofitable situations, in particular, not to become a victim of fraud as it takes place with the problem of "cards shuffling", for example. Apart from that, an impossibility of creation of a winning strategy for all "cases" not in the least prevents "a mathematically advanced" gambler to choose whenever possible "the best" decision in each particular game situation and within the bounds allowed by "Dame Fortune" not only to enjoy the very process of the Game, as well as its result.

Selecting the right online casino

Ah, online casino selection. Now there's a potential pain in the butt. It was one thing to select an online casino back in the late 90s, but today there are loads of online casinos and more seem to pop up daily. I've got three solid tips to help you stay safe and have fun by selecting that perfect online casino for you. Following these few quick tips can save you a world of hurt. Ready? Okay, let's jump right into it. Selection Tip One It starts with credibility. We want to find trustworthy online casinos. After all, if they are not trustworthy, then nothing else matters. This can be a bit tricky. I mean no online casino is going to tell you they aren't trustworthy on the front page. But, we can simplify this task. My favorite thing to do is visit Google-and I'll follow this up with MSN and Yahoo too. If you use the plus sign, you can single out pages that contain all of your search words. So, if we pair the online casinos name (or domain name) with hot words, such as scam, illegal, arrested, rip off and so forth. Here's a search example: Casino+name+scam Domain+scam Selection Tip Two So, we've done the searching and didn't find anything too alarming. It's now time to progress to step two-bonuses. There is absolutely no reason to play at an online casino that doesn't offer generous bonuses. That would be like going to a grocery store that just sold canned peas. Why? Going back to the search engines, we can type in things like “casino+name+bonus.” It's rare, but sometimes affiliates offer bonus items for joining through them-poker comes to mind. Once you've found a potentially trustworthy online casino with great deposit bonuses, contests and so forth, it's time to complete the process. Selection Tip Three Take a look at the deposit methods for the online casino you're interested in. Do they offer tons of choices? If all they offer is Western Union and checking account deposits, run away. Any solid online casino will offer multiple options and they should include 3rd party deposits too. I recommend using a 3rd party system if you plan on playing at multiple online casinos, because you want to limit how much of your financial data is out there. In the end, spending minutes to an hour of research can save you heartache and money loss. When in doubt, look for the biggest names. Sometimes they don't offer the best bonuses, but at least you know that your money is safe and that you'll be paid.

Rocks at the poker table

This article will focus on how to spot and defeat any rock at the poker table. First, I will define a “rock” as a poker player who plays very few starting hands, yet plays aggressive when he/she decides to play a pot. I was recently playing in a NL 5 – 10 poker game at a local club. After about an hour, I had a pretty decent read on everybody at the table. There was one player who really stood out to me. It was a young guy and he hardly played a hand. He sat there and as this article was created in my mind that night, so was an ultimate strategy against rock players. He was not only going to be my victim that night he was also going to be my guinea pig, my study guide for how the mind of a “rock” poker player works. I noticed many things about this guy that were sure signs for anyone who was paying attention, that this guy was a TIGHT PLAYER. The first thing you obviously notice is that they do not play a lot of starting hands. They usually fold, in fact almost always fold unless they are in the blinds or have a strong hand. The second thing I noticed is that this guy kept counting and rearranging his chips every 2 seconds like he was losing them or something. Like seriously man, you haven’t played a pot in half an hour why in the world are you still counting your chips – they haven’t moved! A third thing I found while studying this guy was that he slouched every hand… except for when he had a strong hand! In fact this guy was such a rock that I would call him a robot because he perked up everytime he found 10 10 or up. Now I have to admit, this was a pretty strong NL table and there were also a couple of drunks donating. With that being said, I had to laugh when even the drunk guys folded every time this rock tried to come in with a raise. That leads me into the next section of this article, how to easily handle any rock poker player once you have identified them. Now that you know what to look for in a rock we can proceed on how to handle them. Like I just mentioned, I could barely help myself from laughing at this guy every time he entered a pot. I knew he had something strong it was written all over his face. The fact is – when these rocks enter the pot, they have the goods. If you see high cards on the flop, you can be pretty sure they have got a piece of it or already have a high pocket pair. Just fold pre-flop. Yes I said it and since it is the drop dead only way to play against rocks I’ll say it again – Just fold pre-flop. Unless you have AA, AK-AQs, KK, or QQ you are most definitely beat. So just fold. The funniest thing about this particular guy was, that everyone knew it and folded pre-flop when ever he entered with a raise. It was truly amusing as this guy got peeved and started playing crap hands. But this is where I noticed a new tell of our friend the guinea pig, he would still erect his posture when holding strong hands but when he tried to limp in with crap to throw us off he remained hunched over the table and his drink. At this point you just play off of the rock’s tells. You’ve got to remember that tight poker players are usually tight because they don’t like losing money and they like poker to be a mechanical grind slowly increasing their bankroll. Throw them off one or two hands and a rock turns into something their not – a loose or just frustrated poker player – one that you can take advantage of the rest of the session. To sum up this strategy guide against rock poker players, firstly you have to identify the tight rocks at your table. This can be done by their appearance, the number of hands they play, how they play them, and even how they stack their chips or hold themselves. Once you have identified them and what kind of strong hands they play, you get out of their way unless you have a premium hand yourself. Proceed to play them like a puppet until they get off their game and take advantage of them the rest of the night.

How to efficiently choose an online poker website

Online poker websites have become increasingly popular in the last five years or so. Due to the fact that online gambling is a popular form of entertainment, online poker websites have jumped on the proverbial bandwagon in order to make some money of their own with regard to this type of enjoyable pastime. With that said, there are a number of online poker websites out there boasting that they are the best ones to use and ones which will yield the biggest payouts for online poker players. The hard part in perusing all of this advertising is trying to find out which online poker website really is the best one to use when looking to have some fun and perhaps make a little money as a result of this fun. Search engines on the internet are a great way of finding out more information with regard to particular websites and, in this case, online poker websites. Researching various websites is a great way for you to find out what types of online poker websites are out there. By doing this type of independent research you are also able to check out all of the advantages and disadvantages that go along with the different online poker websites. You can utilize a search engine to find out pertinent information in the following manner. Think of what you are looking for in way of an online poker website and then come up with a phrase that best describes your thoughts relating to this type of website. For example, say that you are looking for an online poker website that has the best odds. In order to find out which websites claim to have the best odds or have been found by others to have the best odds, you would simply type in a phrase such as “online poker websites best odds” or “high winnings online poker websites”. This will pull up a number of results for you to scroll through. By doing this you will be able to effectively weed through the masses and come up with a select few that you would be interested in using to play your online poker games. Another way in which to efficiently and effectively find online poker websites, and more importantly, good online poker websites is by reading up on poker related issues. You can find out some good information related to online poker websites by going to your local library or bookstore. There are many authors out there today that focus the topics of their books not only on gambling or poker, but more specifically on the subject of online poker. By perusing these types of gambling-related texts you will undoubtedly come up with a number of recommended online poker websites in which you should take a look at. Since the individuals writing these books are widely familiar with poker card games and in some instances online poker, you will feel confident in knowing that they know the subject of which they speak. A third way to find out additional information relating to recommended online poker websites is to utilize the internet not by search engine tactics but by a specific search for a poker guru. If you go directly to a poker information website you will most likely be able to have all of your online poker-related questions answered in a few simple keystrokes. By entering a single specific search for a poker website you will be able to find one single website that answers all of your poker card game questions. One last way that you can search around for answers relating to which online poker website is the best choice for an online poker player is to ask your friends and family members for help. As online poker games are played by large quantities of people, you will most likely know of someone who has played online poker in the past or does so currently on a regular basis. As friends and family members are trustworthy sources to consult when it comes to a matter of this sort, you can be comforted by knowing that they will not purposely steer you in the wrong direction. They will be able to tell you all sorts of things relating to the online poker website that they recommend such as betting limits, odds, payout methods, convenience, etc. They should also be able to alleviate any fears that you may have regarding safety issues and gambling online. If they have utilized the particular online poker website and have had their financial information safeguarded, then you should be fine as well. I find that friends and family members are a great resource with regard to a lot of different things. This does not mean that you always have to abide by their advice because, face it, they are human and humans are sometimes wrong. However, simply take note of it and use it to your advantage should you feel that it would help you out in the long run. The aforementioned items relay just a few ways in which a prospective online poker player can effectively and efficiently choose an online poker website. To recap, in order to find a great online poker website consider doing a search engine type of search online, look at books in your local library and/or local bookstore, do a specific online search for a informational poker website or ask your friends and family members for recommendations (or all of the above). Do not feel as if you have to follow all suggestions mentioned above. These are just some things to consider when looking to find the perfect online poker website that meets your online gambling needs. Simply look through and if any of the suggestions listed above peak your interest and sound like they may work in your favor, then by all means, utilize them in any way that you see fit. Good luck in your future online gaming venture and enjoy yourself along the way!

Texas hold em an overview

Hold’em Poker has, in a few short years, exploded into the most popular poker variation of the game and Texas Hold’em is a game that started some time in the early twentieth century. However, it is only in the last five or six years that Texas Hold’em has mesmerized poker players and taken over poker rooms just about everywhere poker is played. No-Limit Texas Hold’em is the mainstay of the World Series of Poker (WSOP) which is the highest profile event in the history of the game and is televised around the world. Texas Hold’em is the main game played in the World Poker Tour (WPT) that promotes worldwide poker tournaments. Celebrity tournaments particularly as held in Las Vegas, feature Texas Hold’em and are extremely popular with spectators. In fact, Texas Hold’em tournaments have become highly popular spectator sports and are televised to enthusiastic audiences. Assuming you are acquainted with traditional poker, here is the basic Texas Hold’em play: You are dealt two personal cards face down and five cards are placed face up in the center of the table for use by all the players. These are the community cards. You make the best five card hand using your two personal cards and any combination of the five community cards. There are four betting rounds. Unless you are in a no-limit game, the first two bets will have a set limit – for example, two dollars. The next two bets have a limit of four dollars. Betting or raising for each round cannot exceed the pre-set limits. The first two bets are called “blind” or “posted” bets. The first player to the left of the dealer places a “small blind” or minimum bet which is half the maximum – or $2. The next player to the left of the minimum blind poster places the “big blind”. The maximum allowed in this case is four dollars. No other bets are made. Once play begins, the deal rotates around the table and each player, in turn, will act as the small blind, big blind and eventually as dealer. The game starts with the first small blind player receiving the first card face down and the deal revolving around the table with the last card taken by the dealer. The deal revolves around the table again with each player receiving the second card face down. The first round of betting begins with the player to the left of the big blind either calling or raising within the pre-set game limits. Betting, calling or folding goes around the table until the small blind poster is reached. The small blind poster can call the bet since a blind was already posted. The big blind then has the option to raise or to “check”. Three community cards are then dealt face up in the center of the table. In Texas Hold’em terminology, this is known as “the flop”. Bets are placed. Next comes “the turn” or “fourth street”, which means the dealer places the fourth community card among the first three cards. Again, bets are placed. The fifth and final community card dealt is called “the river” or “fifth street”. To play Texas Hold’em well, basic strategies should be learned and practiced and for the serious player, extensive study of advanced game strategies is a must.

Differences between a professional bettor and an amateur bettor

Most casual bettors don’t make a profit from their sports-betting hobby. This includes bettors who are relatively sharp as well as those who couldn’t pick a winner if their lives depended on it. That’s not a horrible thing, either. If every bettor won, sportsbooks would be going belly up far more often than they do, and bettors would run out of places to play. And many bettors really don’t care very much about earning a long-term profit. They like to have some action on games as a form of recreation or excitement, not as an investment decision. Many of these types of bettors are far more interested in TV games than anything else, and they tend to bet more on bigger games, like the Super Bowl or the NCAA Tournament. Much of the industry considers money management as important as picking winners, and rightfully so. But throwing around buzzwords like ‘money management’ and describing esoteric concepts like ‘isolate a percentage of bankroll’ and ‘positive expectation bets’ really doesn’t help the fortunes of most recreational bettors. If you are content with betting solely for entertainment purposes, then this essay will serve little purpose. But if you wish to be a successful sports bettor and earn a profit from your betting through an extended period of time, here are some tips that should help in that quest. 1) Don’t bet into bad numbers Professional handicappers recognize the value of the half point. On the average college-basketball card for a Saturday, for example, there are at least six games that are won or lost against the spread by a point or less. A pro bettor will be on the right side of just about every one of those decisions. A professional will either getting the push when others lost, or the bettor will get the win when others pushed. The pro will take the extra time to shop around for the best number at multiple sportsbooks. The pro will have accounts that are funded in enough places to ensure that a bet can be made at the right place and at the right line. The pro will have an idea of which direction the line is likely to move, which will help in capitalizing on an advantageous number. A professional will take these calculated steps, and as a result, a pro will win these close games more often than not. If a pro bettor a modest 20 bets a week (which equals out to roughly 1,000 a year, a number that is on the low side for most professionals), it is not unusual to gain an extra 10 or 15 victories a year and another 10 or 15 pushes just by betting at good numbers. Assuming the bettor is betting a modest two percent of his bankroll on any given play, those 20 or 30 favorable decisions translates into a 40-60 percent swing in the return on a sports-betting investment. That is a profile on how to earn profits one half-point at a time. 2) Make more straight bets and fewer parlays Professional bettors make the vast majority of their bets as straight bets, not as parlays. For amateurs, the number is closer to 50/50, and there are many, many amateurs who rarely straight bet at all. But the straight bet is the pro’s bread and butter. Professionals are satisfied with the return on investment from a 3-2 day or a 12-8 week. They are in it for the long haul and not always the quick score that parlays provide. Amateurs are often lured by the big paydays that winning parlays provide, conveniently forgetting that a slow and steady winning approach will yield more profits. Straight bettors are pleased with taking more victories than losses because it will produce a profit every time. Parlay bettors would not be satisfied by this outcome. There’s a reason that every sportsbook in Las Vegas has their parlay cards prominently displayed. Frankly, parlays pay the bills at most joints in Las Vegas. That’s not to say pro bettors never go for the long shot score. But when they do, they do it for a considerably lesser percentage of their bankroll, and they do it in conjunction with their straight bets, not in lieu of them. 3) Concentrate more on box scores and less on final scores It’s easy to look at the final score of a game and make all kinds of false assumptions. But without reading game recaps and looking at box scores, you really have no idea of what took place and the current form of the participating teams. It’s key to handicap games again after the games are over. Ask yourself some questions: What happened that you expected to happen, and what was a surprise? Which things are likely to repeat themselves, and which are something of an anomaly? Here’s a fictitious example: The Pistons play the Bulls at home as nine-point favorites, but win by only 97-90. However, after looking at the box score, it’s clear that Detroit dominated for most of the game. The Pistons won the rebounding battle and forced the Bulls into turnovers. They led by double digits at halftime and after three quarters. But the Bulls hit some late shots in garbage time and closed the gap late. On that same night, the Raptors are nine-point favorites to the Nuggets and win by that same 97-90 margin. But the box score here indicates a whole different story. The Raptors trailed throughout this game, but got hot in the fourth quarter to steal the victory. Toronto made an uncharacteristic 27 of its 30 free-throw attempts and hit 10 3-pointers. Denver shot just 4-for-19 in the fourth quarter. By examining the box scores, you can recognize that the Pistons are in better form than the Raptors and/or the Nuggets are in better form than the Bulls. This sort of deduction can make your future wagers involving those teams more likely to be successful, even though the final scores of the two games were exactly the same. 4) Take advantage of value Linesmakers have a pretty good idea of which way the money is going to flow once they hang their opening numbers. Amateur bettors are a big part of this, falling in love with ‘public’ teams and betting them over and over again. Public teams usually refer to the team with the most media attention. In college sports, these teams are usually in the top-25 and from a major conference. In pro sports, these teams are the hottest teams or teams at the top of their respective divisions or conferences. The professional bettor will recognize this public bias, notice that the lines are inflated for many of the best teams in the country and either bet against many of the good teams or pass on their games entirely. The pro bettors concentrate much more on backing the teams that have fallen underneath the public’s collective radar, as well as fading some of the mediocre squads that are in poor current form. The pros bet against top-25 clubs far more often than they back them. Because the teams are the most recognized, a bettor will catch six points on the underdog instead of four. It’s equally important to recognize when the linesmakers have priced you out of a play. When a team is flourishing, it becomes more and more risky to side with them. A team's value dwindles as their success grows, and a professional bettor will always be able to spot this trend and stay away from supporting these teams. 5) Be smart when betting your streaks It’s one of the most common mistakes that amateurs make, and it’s quite possibly the most costly. They press their losses, raising the stakes to get back to even off a losing streak. Pro bettors know that there will be times when you lose more than you win. Hopefully, those times are few and far between, but inevitably, they will happen to everybody. Rather than raising the stakes during those times when you are having a bad run, the pro lowers his stakes, conserving bankroll while waiting for things to turn around. A professional bettor will avoid a perilous approach. Conversely, the pro knows that winning streaks are the time to press your bets, not the time to pull back with a conservative approach. When a pro bettor is in good form and good rhythm, the professional will not be afraid to raise the stakes a bit, making larger plays when the percentages are favorable (positive expectation wagers). It sounds so basic – don’t chase losses and ride your winning streaks. But few amateur bettors have the discipline.