Concepts

On 22 Jun 2021, Canada’s Interprovincial Lottery Corporation awarded its largest ever Lotto Max prize pool in the amount of $140 million ($70 million for the grand prize and 70 $1 million MaxMillion prizes). It thus seems timely to have a look at the math behind lotteries. The website states that the odds of winning the Lotto Max are 1 in 33,294,800. This is correct to a point, but misleading. Let’s have a look at the rules of the Lotto Max: Players choose 7 numbers out of 50 Numbers cannot be repeated Numbers are automatically sorted into ascending order Each play buys 3 lines Each play costs $5 Seeing that players choose 7 out of 50 numbers that are non-repeating, the equation for the total number of possible combinations (this is different from permutations where the order in which the numbers appear is significant) when playing the Lotto Max is: 50! / (7! x 43!) The ! sign is a

read more Concepts: The Math Behind The Lotto Max

There is something to be said about card counting in Baccarat. The immense number of permutations often makes it difficult to card count in this game without some form of assistance. The fact that different card values have different effects on probability in this game and that these effects are not always consistent, is another puzzling aspect. The following table shows the expectations of several side wagers using various permutations of card values with between 5 to 25 cards being drawn for each. This is done to show that the advantage can be obtained from card counting and that one does not need to go very far into the shoe for it. Note that a positive expectation here indicates that the player would have the advantage in the following coup on that wager. Now, some of these situations seem very specific and they are. This data is not meant to show that card counting is viable, but that it is

read more Baccarat – An Analysis on Side Wagers

Hi friends, This topic follows the study on the most beneficial cards to the Player, Banker and Tie wagers in Baccarat. The 3 tables below show the effect on the probabilities of the Player, Banker and Tie as 1, 2 and 3 cards are removed in isolation from each card value. Do take note of the changes in probability as each card is removed and their relationship to the respective wager. Player Card Value: Permutations Player Win % Compared to Other Wagers Player Win % by Card Value Effect of 1 Card Removed Effect of 2 Cards Removed Effect of 3 Cards Removed 4    1,036,330,148,130,820 44.9220% 7.7436% –                   0.0000435175 –                     0.0000870460 –                     0.0001305855 0    1,035,362,791,243,780 44.8801% 7.7363% –                   0.0000373810 –                     0.0000749287 –                     0.0001126377 J    1,035,362,791,243,780 44.8801% 7.7363% –                   0.0000373810 –                     0.0000749287 –                     0.0001126377 Q    1,035,362,791,243,780 44.8801% 7.7363% –                   0.0000373810 –                     0.0000749287 –                     0.0001126377 K    1,035,362,791,243,780 44.8801% 7.7363% –                   0.0000373810 –                     0.0000749287 –                     0.0001126377 1   

read more Concepts 16: Baccarat – Effects of Card Removal

Friends, The following 3 tables show the most beneficial cards for each wager. This was calculated by observing the number of times the presence of cards of these values led to a Player, Banker or Tie result. They are sorted in descending order of effect by card value. Some of the results are intuitive, others may surprise. Column 3: Player Win % Compared to Other Wagers compares the effect the card value has on a wager as compared to the other wagers, in this instance, Banker and Tie. Column 4: Player Win % by Card Value compares that card value’s effect as compared to all other card values for that particular wager. Player Card Value: Permutations Player Win % Compared to Other Wagers Player Win % by Card Value 4    1,036,330,148,130,820 44.9220% 7.7436% 0    1,035,362,791,243,780 44.8801% 7.7363% J    1,035,362,791,243,780 44.8801% 7.7363% Q    1,035,362,791,243,780 44.8801% 7.7363% K    1,035,362,791,243,780 44.8801% 7.7363% 1    1,034,132,990,550,020 44.8268% 7.7272% 3    1,032,891,882,528,770

read more Concepts 15: Most Beneficial Cards for Each Wager

All right folks. First off, please understand that having a 1st-card advantage means that the player has somehow found out what the first card of the as-yet undealed coup is. This is at worst cheating or at best, if the dealer or procedures are weak, advantage play. 1st-card advantage is essentially a study of all the possible card permutations that start with Ace through to King that result in a Player, Banker or Tie result from the remaining cards in the shoe. The 2 tables below show that knowing that the 1st card is a 1-5 or 10-K, would give a small advantage on the Banker wager. Knowledge of the 1st card being 6-9 would give an increasing advantage on the Player wager, with knowing a 1st card as being 9 giving a 21% advantage on the Player wager. Below is a table that shows the probabilities before the start of the shoe: Card Value: Player Win Banker Win Tie

read more Concepts 14: Baccarat 1st Card Advantage

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

read more Baccarat: Conditions for Positive Expectation on Side Wagers

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:

read more What video games can teach companies