Where does the blackjack edge begin?

13 September 2018

By John Grochowski

QUESTION: At what point does the house edge in blackjack kick in?

I recall reading that a casino would never allow a person to make a one-time bet of a million because the house edge would not factor into a single transaction.

So the issue then is at what point does the edge kick in. Since it is a proven fact that the longer you play the more your results will approach the house edge, could it be that the shorter you play the more results will depart from house edge?

ANSWER: The house edge doesn't kick in after any given number of hands? It applies on every hand.

It's true that short-term results are more volatile than long-term results, but that works in both directions. At times, players win more than expected in the short term; at times they lose more.

The odds of the game will drive the overall outcome closer and closer to an expected norm the more hands are played.

Think of it this way. Instead of one player playing 10,000 hands, there are 200 players each playing 50 hands; some will win more than the average outcome, some will lose more than the average outcome, some will be about on average. But the casino is getting 10,000 hands, and it will collect something close to its expected percentage.

Casinos do make their money from relatively narrow house edges being applied over and over again. With pushes excluded, there's a better than 46% chance the house will lose big on a single million-dollar bet. If the money is divided into 200,000 $5 bets instead, the house is likely to grind out a profit.

However, it's overstating the case to say no casino would ever accept a one-time bet of $1 million. In the days when Benny Binion and son Jack were running the Horseshoe in downtown Las Vegas, the stated policy was that you could exceed posted table maximums, but if you did, your first bet was your max. A player on a roll couldn't turn around and exceed the max, but fresh money could.

I don't know if there were $1 million one-hand bets actually placed in blackjack, but it's known to have happened in craps.


QUESTION: I read that the strategy for Three Card Poker is to bet with queen-6-4 or better. I'm trying to figure out what that means. What about jack-10-8, where two of the three cards are better than in queen-6-4. What about queen-7-2, where the 7 is one higher but the 2 is two lower? Or queen-5-5, where the 5 is one lower and the other 5 is one higher?

ANSWER: You'd bet with queen-5-5 because it includes a pair. The queen-6-4 strategy is the dividing line on hands that don't include a pair, straight, flush, three of a kind or straight flush.

With that proviso, you evaluate the hand starting with the top card. The minimum high card for a basic strategy player to stay in the hand is a queen. If your highest card is a Jack or lower, with no pairs or better, then it's best to fold. With your example, Jack-10-8, you'd fold.

Next, you look at the second highest card. If your second-highest card is a 5 or lower, you fold. If it's 6 or higher, you then evaluate your low card.

Given a high card of queen of higher and a second-high card of 6 or higher, you bet of the low card is 4 or higher and fold if it's a 2 or 3. Your queen-7-2 is a folding hand.