Ask The Wizard #222

Let's kick things off with the Joker Poker game at level 4 where I've pre-calculated the winnings by a factor of 8, reflecting the 8x multiplier applicable at this level. In the lower right cell, you can see a return of 8.36 times the wager for each level, indicating that reaching level 4 will reward you with 8.36 times your bet at that level.

The next table is for the Deuces Wild Moving to the game at level 3, the current winnings have been adjusted with a multiplier of 4, representative of the 4x multiplier for this level. The 'future levels' column indicates the benefit of progressing to level 4, while the 'total value' encompasses both current and future values. The return featured in the lower right cell shows 8.00 times your bet for each level, meaning if you reach level 3, the total game value (across levels 3 and 4) is 8 times your initial wager.

The next table is for the All American Now considering the game at level 2, the winnings in the column marked 'this level' have been doubled using the 2x multiplier from level 2. The 'future levels' column estimates the benefits of moving on to level 3, while the 'total value' combines both existing and future potential. The bottom right cell displays a return of 5.63 times the wager per level, implying that if you can attain level 2, you will gain a total value of 5.63 times your stake across levels 2 to 4.

The final table is for the Jacks or Better In the game of level 1, the 'future levels' column illustrates the potential value of progressing to level 2. The 'total win' reflects the total value you could accumulate, both now and in the future. The return noted in the lower right cell shows a multiplier of 3.60 times the wager for each level.

This game, assuming optimal play, stands to yield a return of 3.603417 units. However, the requirement to bet 4 coins to participate results in a return of 90.1%.

In my view, the two fundamental principles of gambling should be the prohibition of cheating and the respect for bets made. There shouldn’t be any time limits or justifications; an individual should honor their gambling commitments. You didn't specify how many points you achieved. Ideally, you should return the winnings solely if you had a 20, or refund both the winnings and your original wager if you had less. If they were unpleasant in their request, I wouldn't hold it against you for exiting the casino, but I still would have settled my debt. I've been asked similar questions before, suggesting this may be the norm.

It sounds like you are talking about Lucky Pairs This side bet rewards players whose initial two cards make a pair, with many baccarat tables also providing this option. As explained on my baccarat section, the house edge sits at 10.36%, assuming eight decks are in play. In both games, to have any advantage, you'd essentially have to eliminate an entire rank of cards. To achieve this, meticulous tracking with 13 distinct counts would be necessary. While this could be manageable in baccarat since players can take notes, extensive analysis indicates that such profitable situations are too rare to justify the effort.

There are combin When calculating this, I started with (50,5) to get 2,118,760 combinations for five cards chosen from the remaining 50 cards in the deck. Out of those, 42 cards rank from 2 to Q. Therefore, the number of combinations for 5 cards from this selection is combin(42,5)=850,668. Consequently, the probability of not drawing a king or ace is calculated as 850,668/2,118,760, translating to 40.15%. Therefore, the probability of drawing at least one ace or king is found by calculating 1-40.15%, which equals 59.85%.

Alternatively, one can compute it as 1 minus the probability that the first card in the flop isn't an ace or king, multiplied by that of the second card not being an ace or king, and so on until the fifth card: 1 - (42/50) × (41/49) × (40/48) × (39/47) × (38/46) results in the same figure of 59.85%.