## The Game Of Texas Hold’Em## Texas Hold’Em in a Cardroom## Texas Hold’Em Online## Winning poker## Tactics## Strategies## Putting It all together## Psychological Considerations## Where to go from here## Places to Play## Appendix I Hold’Em poker Variations## Appendix II Poker Tournaments |
## MATHEMATICAL CONSIDERATIONS## Past, 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 long-run 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.
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 50-50, why would this have happened? 6.If there were no time interval that had reset the probabilities to 50-50, 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 50-50. 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 long-run. Sid relates the story of his friend’s belief in coin flips even selected to see that the belief had been wrong.
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
## 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 three-of-a-kind 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 ## 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 |
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