What is Casino War: Rules, Strategy, and Tips to Win. Casino War Strategy. Important.

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A State should only go to war if it has a reasonable chance of winning. Going to war for a hopeless cause may be a noble act, but it is an unethical one.

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First round. In the first round the player must beat the dealer. The dealer's card is excluded, leaving possible cards for the player.

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A State should only go to war if it has a reasonable chance of winning. Going to war for a hopeless cause may be a noble act, but it is an unethical one.

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Where the edge comes from is when there is a war you either win one unit The following table shows the probability of winning and expected.

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However, in the case that the winning card goes to the bottom of the winning assuming arbitrary initial state, you are absorbed with probability ONE If And Onlyβ.

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A State should only go to war if it has a reasonable chance of winning. Going to war for a hopeless cause may be a noble act, but it is an unethical one.

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First round. In the first round the player must beat the dealer. The dealer's card is excluded, leaving possible cards for the player.

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βSun Tzu The card game of war is typically considered a children's game, as it properties of the initial state that are indicative of a victory probability. Although on average a player will win and lose an equal number of.

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This game is also called Everlasting , due to its duration. The graph backs up our hypothesis that the more kings you have, the better chance you have of winning the hand. An example of a data file follows:. This is close to the E X of 0. This may enable a player to capture an opposing ace when he has none of his own. We thought that if you have more Kings than your opponent, then you will fair better in the end. This percentage should decrease as you look at smaller valued cards like having four queens compared to four kings , though we didn't test that theory. The graph obviously has a normal distribution, peaking at around. The value for R2 on the graph is 0. Each is dealt twenty-six cards face down, and each turns his top card face up. This continues indefinitely, until one player has won all the other's cards. Our third question looked at the total number of points in a players hand, and tried to decide whether the player was more likely to win or lose. The Java random number generator is unique from other generators in that it always generates a different number, and does not need to be seeded. Nevertheless, the results show that our hypothesis was correct, and that you have a better chance of winning if you have more kings in your hand. We can predict a winner, but only with a low probability.{/INSERTKEYS}{/PARAGRAPH} Questions First, how many games can player one expect to win over player two if they both play the game a certain number of times? Running it once simulates one hand played. Both have very good linear fits based on their R 2 values, so it is a difficult choice. We wrote a Monte Carlo simulation in Java, and ran some large-scale simulations to generate data. If two cards happen to be tied - as two tens - they are laid aside and go to the winner of the next turnup. Mean 0. So, the error bars for the 0 and 4 king cases are going to be much larger, since they have a much smaller n. Which of the two starting conditions of kings vs. The final piece of data is how many points are in player one's hand at the beginning of the hand, and which player won the hand. Analysis We ran separate trials to get different values of X bar. The resulting graph shows that as your hand total increases, so does your chances of winning the game. This gives values for X bar. Not only does having kings in your hand seem to better your chances for winning, but also having a larger point total than your opponent to begin each game seems to bring more victories. Our only conclusion is that it is all random. The validity of the line is strengthened by the high R 2 value of 0. This file had to be modified a little bit by hand so that MATLAB could parse it correctly and come up with values for the probability of winning with 0 kings, or 1 king, and so on. In addition, the deck is randomly shuffled before each game is played. If two are tied for high, any player turning up a lower card is included in the in the tie and has a chance of winning them all with the next turnup. We then looped it so 50 games were played, which constituted a "trial". {PARAGRAPH}{INSERTKEYS}War is a easy game, in fact almost embarrassingly simple, so we thought that analysis would be a breeze. Then we ran the program through 50 and 1, trials, and sent the results to a file. Here is a line fit from the data obtained by running trials of 50 games. This also means that the Java code seems to be working. In this case, we were interested in who won and who lost. The error sum of squares SSE is quite low, so we would conclude that the line fit is accurate. A player drops out when his cards are gone, and others continue until one player wins. As an added rule, after a tie, each player lays a card face down before turning up another; and these cards also go to the winner of the next turnup. Excel calculated an expected X bar value E X bar of 0. To a statistician, this suggests a binomial distribution. This is a flaw we should fix in the future. However, we only wanted the salient data to be sent to a file for processing. Ideally, this value should have a normal distribution. First of all, there were a lot more games played where each player had 2 kings than those where one player had them all. In theory, X will have a binomial distribution with a mean value of 0. The player who gathers in all the cards wins the game. Our correlation of the probability of winning vs. The histogram shows the number of times that a particular X bar appeared. Even if you have a high point total hand, the way the deck was shuffled has an large impact on the outcome of the game. If you have any questions or comments, feel free to email the authors:. The minimum point value possible is 98, and the maximum is However, since the hands were shuffled randomly, it was nearly impossible to ever generated that hand. We achieved the following results:. This paper will never win any awards though it did get an "A" , but it was a good introductory project. Data The data was collected by running our War simulator many times. For the second part of our experiment, we needed to keep track of not only which player won, but how many kings that player had in their hand. The higher value takes the lower and the cards are placed face down beneath the winner's packet. In order to tackle this question, we chose to use the King as the card to watch for, because the it has the highest point value of all the cards in the deck. Overall, this was a fun project, and the game demonstrated some interesting statistics. As in the previous experiments, we looked at trials of 50 games each. The kings had a slightly better fit, but counting the total number of points intuitively contains more information about the hand. The game can be played with three of more players, each on his own utilizing a double pack if desired. Since R 2 is relatively close to 1, it is safe to say that the percentage of winning has a linear relationship with the total number of points in a hand. Can you always win a game by having one or more of a certain high card? Here is a more mathematical way of representing the situation: Allow n games of War be played where X denotes the number of times that player one wins a certain hand and Y denotes the number of times player two wins instead. Primarily a two-player game, preferably for juveniles, with a fifty-two-card pack ranking A, K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, 2 with suits disregarded. The file looked like this. Our hypothesis was that player one and player two should win approximately the same number of games, since the game is symmetric.