The Game Of Texas Hold’EmTexas Hold’Em in a CardroomTexas Hold’Em OnlineWinning pokerTacticsStrategiesPutting It all togetherPsychological ConsiderationsWhere to go from herePlaces to PlayAppendix I Hold’Em poker VariationsAppendix II Poker Tournaments 
MATHEMATICAL CONSIDERATIONSPast, Present and Future –Do Probabilities Change?Sid has a friend who has believed that if you were to toss a coin three times, and it would come up heads each time, a greater than even chance would exist for it to land tails on the fourth toss. If you were to question why she had believed the probability changes, her answer would be: ‘ Over the longrun the coin had to land heads as often as tails, so id a streak of heads were to occur, a tail would become more probable since even numbers of each had to be maintained.’ This fallacious belief that the coin’s past history would affect its future would be fun to explore with further questions. Examples: 1.Suppose Sid had flipped the coin three times and it had comes up three heads, then Sid had put it away. 2.The next day he had taken it out again. 3.Would the probability have still been greater that a tail would have occurred? 4.If the probability would be greater, what would have happened if he had waited a week or a month or a year? 5.If after some elapsed time interval (day, week, month), the probabilities would have reset to 5050, why would this have happened? 6.If there were no time interval that had reset the probabilities to 5050, how would he know it hadn’t due for three heads in a row? 7.After all, he may have just received the coin, so how would he know the previous owner hadn’t flipped it five times and gotten all tails? 8.How exactly would the probability have changed of a tail occurring after three heads in a row? 9.What would it have been if just one head had appeared, or after five heads in row? If his friend’s belief were true, all these questions should have had answers. The fact that all answers to these questions would have been nonsense shows the belief has been false.Of course, a more profitable exercise would have been to find a poker betting person who had believed that a past sequence of coin flips would affect the future. If this person would be willing to pay better than even money on the outcome of a fourth head each time three heads had appeared in a row, you would be assured of making money. Since past coin flips would have no affect on future ones, the probabilities would remain 5050. Anyone who would be willing to pay out better than even money on wagers against coin flips even selected coin flips that would occur after streaks will be losing over the longrun. Sid relates the story of his friend’s belief in coin flips even selected to see that the belief had been wrong. However, many gamblers have shared the same wrong belief and haven’t realized it. They would have behaved as if the past would affect the future. Examples of common behaviors: 1.You had just lost seven hands in a row at blackjack. 2You had decided to bet the table maximum on the eighth hand because it would have to be time for a win. 3.After all, how often had you lost eight hands in a row? 4.You had been receiving garbage poker hands for the last hour and had decide that no matter what, you would be betting heavily on the next hand because it would have to be time for a winning hand. 5.You had repeatedly played the same lottery numbers, believing that if those numbers haven’t won yet, their time must be coming. Each of these behaviors have resulted from believing that ‘I’m due.’ Claiming that ‘I’m due’would be just another way of claiming that the past would affect the future.There have been more subtle expressions of this wrong thinking, such as having believed that other poker players in the game had affected the probabilities. Examples: 1.Some poker players have believed that the more players there have been competing for a pot, the more likely it would have been that they would have been dealt threeofakind or better. It would have been easy to fall into this trap, since winning hands would tend to be higher when there would have been more players at the table. Three of a kind would have been much more likely to be the winning hand when seven poker players would compete, while with two players, a high pair would have been often enough to win. However, winning poker hands have been higher, only because more hands had been dealt, and to win, you would have to beat more people. Whatever the number of players, the probability of you, an individual, receiving threeofakind would always be the same. Present events, such as the number of players who had decided to fold early, would not after the fact affect the probabilities on the past event of the deal. Just as the past wouldn’t have affected the future, the present wouldn’t have affected the past. 2.Some poker players have believed in betting heavily during winning streaks and have advised not to leave the table. This may have been sound advice if the reasons for the winning streak have had to do with being at a table filled with bad poker players. However, if the reason had been a sudden streak of great cards, there would have been no reason to believe this would have had anything to do with the table, your seat, your opponents, the dealer, the day of the week, the color of your socks, or any factor, period.Good streaks would happen just like bad streaks.There has been no reason; that has just been the nature of a series of random events. You should make sure that your playing decisions are grounded in correct reasons. You should analyze the reasons for your decisions. If the reason would come down to believing that the past would affect the future, the reason would be wrong. 

