Maybe you saw my earlier article about teaching my kids blackjack? It helps them gain fluency with quickly adding small numbers. This is a critical building block in making them comfortable with playing with math.
Well, now that they are playing the game (with terrible strategy, I must add), I want to add a little more contemplation to it. Here are the questions we are working through. My answers below.
- What is the chance that the next card (or any unknown card) is a 10?
- When the dealer has a “soft 17”, what is the chance that the next card will help? (A “soft 17 is and Ace+6)
- What are the chances that a hit won’t hurt the “soft 17”?
- What are the chances that a hit will bust the “soft 17”?
- What about for a “soft 18”? Chance to help? Stay neutral? Bust?
- Why don’t you split Queens (or any hand with 2 tens?)
- Some casinos pay out 6:5 for a 21, some pay out 3:2. If you are betting $100 per hand and get 5 “blackjacks” over the course of an evening, what is the difference in the amount of money?
- Are your odds different when playing with a 6 card shoe (an object that holds 6 shuffled decks) vs a continuous shuffle machine (cards are constantly and randomly mixed back in? Are they different for the casino?
- Why are cards dealt face down in two-deck blackjack? Why are bets limited to be so low?
- What is the probability of getting a suited blackjack (Ace and Face card of the same suit). Many casinos will let you place a separate bet on this that pays out 10:1. Is it a good deal?
- 4/13 - about 32% (there are 16 10’s per deck of 52).
- 4/13 - about 32% (hand is made better by an A, 2, 3 or 4)
- 4/13 - about 32% (the total doesn’t change if a 10,J,Q,K is drawn)
- 0% - There is no card that can bust a soft 17.
- 3/13 - about 24%, 4/13 - about 32%, 0%.
- You are taking an almost always winning had (20) and turning it into two unknown hands. Ther is no such thing as a sure bet, but 2Q against the dealer is a very good one.
- At the first casino, you get $300 on $250 of money bet. At the second casino it’s $375 on $250 of money bet. A net difference of $75 between the institutions.
- Your odds change as the content of the shoe changes. They typically change in a random way and overall do not affect the odds of the game. So, in general, your odds are not different for a shoe versus a continuous shuffle. However, some people count the cards that come out and are able to calculate new probablilties of certain bets and strategies based on the cards left in the shoe. You can’t do that with a continuous shuffle. The casino benefits greatly from the impossibility of card counting; the average player does not
- It doesn’t take as much skill to card count with two decks. Keeping the card face down makes it much more difficult (you only see them for a second before they are cleared). Casinos have a lot of liability with two deck blackjack and offer it for novelty but not serious gambling (thus the low limits).
- I’m not sure. I dropped out of Discrete Math when I was in college, and I have forgotton how to calculate this. Put the answer in the comments, and I’ll pass on a $SBD of my appreciation!
Disagree? Have some better questions? I welcome the conversation!
BeriBeri Quite Contrary * Mathamatrix * Preschool Gambling Coach * Busywork Boss