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Independent Trial
 

Another implication of the independence of gambling events Is that the player should not fall in love with a particular balance. When the prudent amount of action has been reached, it is time to move on, no matter what the balance. If a bonus run has been highly successful and has doubled the deposit, the strong impulse is to continue riding the streak. But this is a mistake, since future results are totally independent of the previous wins. Similarly, if a player loses $300 of a $500 deposit, there is a strong tendency to keep playing in order to try to get it back from the place that took it. This fixation on beating a particular villain is also a mistake. In the long run, your bankroll doesn't care where it gets played. Whether 100 bets are made at one place, or ten bets at ten places, it is all the same. Whether you are behind $400 at casino A, or ahead $500 at casino B, it makes no difference. All bets are part of the long term. The decision to move on should be based on one consideration only: the perception of the house auditors. It is important to play enough to look like a gambler, so there is often benefit in appearing to chase losses or ride streaks.

Although the probability of winning or losing the next hand does not change from casino to casino (this is all assuming the same games), there is an opportunity cost. If you ride a win at one place long after qualifying for the bonus, then you are wasting time that could be spent on a new reward. When you figure the bonus in, you are playing with a large edge until you qualify for it. Once they are ready to cut the bonus loose, your edge ends, and the house's edge begins.

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Hand Strengths
 
The rows list ranks of hands from royal flush to king high. The second column is the percentage rank of each hand (specifically, the percentage rank of the lowest hand within each type), which can be defined as the percentage of hands that are of the same or higher rank. For example, roughly 50 percent of all randomly dealt five-card hands will be better than a pair of two's, while only 3 percent of all randomly dealt five-card hands will beat a three of a kind. The third column is the chance of the hand beating one other opponent with a random hand, which is approximately equal to 100 percent minus its percentage rank. If you have three of a kind and you are against one random opponent, there is only about a 3 percent chance that his hand is better than yours is, so your chance of winning is 97 percent.
 
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