Wager Mage
Wager Mage
Photo: Ann H
The “21 + 3” blackjack side bet is based on examining the player's two cards and the dealer's up-card. If the three cards form a flush, straight, three-of-a-kind or straight flush, the player wins. In the original version, the payout for each of these was 9-to-1.
#12 is called the inside center and is a very hard and powerful runner on offense and loves to tackle. Inside centers are used for the short tough...
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This means a bet theoretically even in probability (for instance, a coin flip) is offered at -110, meaning bettors have to spend $110 to win $100....
Read More »The “21 + 3” blackjack side bet is based on examining the player’s two cards and the dealer’s up-card. If the three cards form a flush, straight, three-of-a-kind or straight flush, the player wins. In the original version, the payout for each of these was 9-to-1. With this pay table, the game has a house edge of 3.2386%. Recently, new pay tables have been introduced that have higher house edges and greater volatility. The point of attack I considered is to target flushes. Any strong imbalance in the suits favors the player. For example, consider a situation where there are 40 cards, 10 of each suit. Without going into the math, the number of ways of making a three-card flush is 480. Now, take those same 40 cards, and assume they are distributed 15, 10, 10, 5. Then the number of three-card flushes is 705. The more unbalanced the distribution of suits, the more the edge swings towards the player. To make use of this, it is necessary to keep track of the number of cards in each suit that remain in the shoe. This can be accomplished by a team of counters, each keeping track of one of the suits (or by a mentally gifted solo counter). The counters then compute the difference between the most abundant and least abundant suits. This difference is then turned into a true count, and if that true count is sufficiently large, the player has an edge. I created a simulation to model using this system on a six-deck shoe game dealt to 52 cards and simulated one hundred million (100,000,000) shoes. This work showed that a counter can gain an edge on approximately 3.5% of the hands dealt (1.75 hands per shoe). The counter should make the 21+3 wager whenever the true count is 8 or higher. The average edge when the wager is made will be just over 5%. If the table limit is $25, then a counter playing heads-up can earn about $2.20 per shoe. The new pay tables were not evaluated. As an experiment, I shuffled one hundred thousand (100,000) shoes and computed the edge at the point when there were 100 cards remaining in the shoe. The result of this simulation was an average house edge of 3.247%, which is close to the theoretical value of 3.239%. More interesting was that the standard deviation of the house edge was 3.57%. It follows that a player edge is 0.910 standard deviations above the mean. Therefore, the player will have an edge on about 18.14% of the shoes at that point. The trick is knowing which ones. My simulation gave a maximum player edge of 23.71% and a maximum house edge of 13.55%. There are two reasons that APs will not target 21+3 with this system. The first is its complexity, the second is the low return. However, there is another approach that may be significantly stronger.Consider a shuffle tracking approach where a slug of cards is identified that is either deficient in one suit or abundant in one suit. In this case, by tracking that slug through a weak shuffle, the AP will have a good opportunity. My knowledge of shuffle tracking is minimal. I cannot say if this is an approach that has been used in practice. Finally, I have not considered if the new pay tables have a similar vulnerability to the 9-to-1 pay table.
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Read More »Breeks is the Scots term for trousers or breeches. It is also used in Northumbrian English.
Breeks is the Scots term for trousers or breeches.[1] It is also used in Northumbrian English. From this it might be inferred that breeches and breeks relate to the Latin references to the braccae that were worn by the ancient Celts, but the Oxford English Dictionary (also online) gives the etymology as "Common Germanic", compare modern Dutch broek, meaning trouser. Outside Scotland the term breeks is often used to refer to breeches, a trouser similar to plus fours, especially when worn in Scotland and engaging in field sports such as deer stalking, and the activities of taking pheasant, duck, partridge and other game birds. Whilst breeks are a neater, trimmer fit, plus twos are slightly wider with an extra 2 inches of material to fold over the knee, and plus fours a further 4 inches of material (and a wider, baggier fit).
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