Ask the Wizard #188
Fred P. from New Orleans
The table below shows the average dealer score, assuming the dealer does not bust, and the dealer already checked for blackjack, according to various rules. Note how the average score increases with the number of decks. More importantly, note that the average score is 0.0405 higher when the dealer hits soft 17. The probability that the dealer will bust is only 0.00403 higher when the dealer hits a soft 17. That is 10.05 extra dealer points per dealer bust. This, hopefully, goes to show why it is bad for the player if the dealer hits a soft 17.
Average Dealer Total in Blackjack
|Decks||Stand Soft 17||Hit Soft 17|
To answer your second question, I used a brute force combinatorial program in C++ to cycle through all the possible combinations of dealer hands.
Tom from Cleveland, OH
Many casinos are indeed paying 6 to 5 on blackjack in their low-limit games, and it is getting worse quickly. However, there are still real blackjack games out there at a $5 minimum. The other rules likely will not be the best, in particular six decks with dealer hitting on soft 17, but at $5 you can’t be too picky. It sounds like you were in town on a very busy weekend, or just didn’t look very hard. Any downtown or off-Strip casino should have some real $5 blackjack tables. Those tables are usually the most crowded. On Strip you should be able to find some token $5 games, especially mid-week, at properties such as the Excalibur, Monte Carlo, Harrah’s, Flamingo, Circus Circus, Riviera, and the Sahara.
Danielle from Louisville
My new Bad Beat Jackpot section shows the probability of this kind of bad beat in a 10-player game to be 0.0000108, or about 1 in 93,000.
Doug P. from Colorado Springs, CO
Thanks. Normally the house edge in Texas Hold ’Em Bonus is 2.04% under the Vegas rules and 5.59% under the Atlantic City rules. You are indeed right that no single wager can be over $5 in Colorado. Under the Colorado version of the rules, you describe above, the house edge is 2.35%.
Larry C. from Daly City
My flashing blackjack dealer strategy shows what to do in any situation where the dealer accidentally exposes his hole card. However, most players don’t have that memorized, incluing me. In cases like this where the dealer’s two cards total nine or less you may use basic strategy, assuming the dealer’s up card is the sum of his two cards. Using that rule of thumb, all three players played correctly. Contrary to what the dealer said, the player has every right to use any information gleaned from dealer errors like this. Not only would I have ignored the dealer’s comment, I would have kept playing, hoping he would do it again.
Ryan from Silay
1-(5/6)10-10 × (1/6) × (5/6)9 = 51.55%.
George P. from Stevens Point, WI
The probability of a 7, 11, or 12 is (6+2+1)/36 = 9/36 = 1/4. See my section on dice probability basics for how I arrived at that figure. The probability of rolling anything else is 3/4. The probability of going five rolls without rolling a 7, 11, or 12 is (3/4)5 = 23.73%.
Matt N. from Ann Arbor
You’re welcome. For those readers who may not understand the question, a "Charlie" is a rule in which the player automatically wins if he hits to some number of cards, usually five to seven, without busting. The following table, for three or more cards, shows the basic strategy if the player is one or two cards away from such an automtic winner.
Eric from Boston, MA
Assuming the commission is always payable, then the house edge would be 4% at a $3 commission (3/75), compared to 5.33% at a $4 commission.