In simulating different conditions of a Baccarat shoe, the following instances were observed: Wager refers to the wager type studied – Pairs, Wins on Natural 9s (WN9) and Wins on Natural 8s (WN8). Win % Probability indicates the percentage probability of that result occurring. Expectation, based on 11:1 for Pairs and 8:1 for Wins on Natural 8s and 9s, shows the expectation (player’s edge) of the respective wagers with the state of the shoe on the right. 1 – K indicates how many cards of that value have been dealt. Wager Win % Probability Expectation 1 2 3 4 5 6 7 8 9 0 J Q K Pairs 8.66% 3.9% 5 23 23 23 23 23 23 23 23 23 23 23 23 Pairs 25.02% 200.2% 5 5 30 30 30 30 30 30 30 30 30 30 30 WN9 14.27% 28.4% 25 25 25 25 25 25 25 25 5 5 5 5 5 WN8 13.21% 18.9% 25
Why does a Banker win on 6 pay half? If you have ever wondered about this, you are not alone. This table shows the Probability and House Edge for Baccarat (where Banker wins pay 0.95:1). Notice the House Edge on Banker (in bold): Wager Permutations Probability Break-Even House Edge Player 2,230,518,282,592,260 0.4462466093 1.02768 0.012351 Banker 2,292,252,566,437,890 0.4585974226 0.97307 0.010579 Tie 475,627,426,473,216 0.09516 9.50906 0.143596 Total 4,998,398,275,503,360 The House Edge means, theoretically in the long-term, for every dollar wagered, a player is expected to lose 1.05 cents. This is a table with the House Edge on Baccarat, comparing what the House Edge would be if Banker were paid half on wins of 1 to 9: Banker Win On: Permutations Probability Banker Win on Any Other Result Player Win Difference House Edge 1 24,291,119,898,624 0.004859781 2,267,961,446,539,260 2,230,518,282,592,260 – 49,588,723,896,320.0 -0.009920923 2 44,681,581,871,104 0.00893918 2,247,570,984,566,780
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This analysis spreadsheet is meant for Baccarat. This spreadsheet computes all the possible permutations of a Player, Banker, Tie or
This analysis spreadsheet is meant for Single-Zero and Double-Zero Roulette. By entering in the results at a table, the spreadsheet will indicate the numbers and areas where results have occurred most often. Do understand that Roulette is a random game of chance – the results of previous games have no implication on the results of subsequent games. The spreadsheet will show if there is a bias in the wheel, a dealer with a regular spin or some flaw at the table which causes the game to be not as random as it should. Use this system at your own risk. Purchase the spreadsheet below – the spreadsheet will be sent to your e-mail address. Good luck.
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In the past months, I have had ample time to sample some of the many forms of video games. Most games feature some form of simulation of real life, from racing to squad combat. AND for some of us, we spend way too much time in these environments. The real reason, which we may not realise at first, is the sense of accomplishment it provides. That extra level up, that unique weapon or that opponent defeated; video games offer a sense of gratification for effort expended. So great is this feeling that we look forward to the end of our work days so we can get back to gaming. Video games have a lot to teach us in the corporate world, in terms of how we look at work, our ways of recognising and rewarding effort and even the structures of our corporate environment. Video games always contain inherent traits, much of which can be applied to the real world:
Theoretical win and the standard deviations of expected value have been widely covered in numerous articles. Unfortunately for me, the discussion on the topic has seldom been comprehensive enough to be understood by the layperson (meaning me). This post attempts to explain the issue in the simplest possible way. Why is this important? Theoretical win is derived from the probabilities built into any casino game. As all casino games are designed (in theory) to guarantee a return to the casino, the theoretical win (winnings for the player) is always negative while the expected value, also known as expectation (winnings for the casino) is always positive. However, like with all probabilities, an element of randomness exists. The standard deviation of theoretical win thus provides a threshold for casino managers to decide if play has passed the limit where it becomes suspect. Theoretical Win and Expected Value The average of results is determined by the theoretical win formula. Hence, 50% of all
Programming is essentially an exercise in concentration. After several months learning this from the ground-up, I have come to 3 conclusions. The best solutions to problems are always simple and elegant. Attack problems with a clear mind. You can solve a problem in 5 minutes well rested, while 10 hours with a tired mind will yield nothing. Take a step back when you come to a road block. The solution you need requires you to take a different angle. And that’s it.