Bad blackjack players and royal flushes

1 May 2016

By John Grochowski

QUESTION: Playing blackjack, another player was really getting on my nerves. He kept hitting 12s. I know you guys say it’s right to hit 12 when the dealer shows a 2 or 3, but this guy hit 12 when the dealer had a 4. Not every time, just sometimes. I couldn’t believe it. Can’t players do anything to keep a guy from making hunch plays like that that wreck the game for others?

ANSWER: In blackjack, 12 vs. 4 is a close-call hand, one that card counters frequently hit. Even if you’re a non-counter, this one is so close that if there are more 10-value cards than 2s through 5s on the table for one hand, you’re slightly better off hitting than standing.

The player who was irritating you might have been making good, advanced plays all along.

Beyond that, I disagree that players making plays that are outside the basic strategy table ruin the game for others. He was betting his own money and has the right to make his own strategy decisions.

Besides that, another player’s strategy, even if it’s a mistake, is as likely to help you as to hurt you. Sometimes his play will be the reason the dealer draws 21 and you lose, but sometimes the card the other player draws will take the dealer once card deeper into the deck for a bust card.

We tend to remember the plays that hurt us more than the ones that help us, but they balance out over time. If you can convince yourself to ignore the play of others, that’s for the best. If you can’t, then when you find another’s play irritating, you probably should change tables.


QUESTION: I have seen the 40,000:1 figure thrown around a lot for the odds of hitting a royal flush in video poker. Do you know how this is derived?

ANSWER: The calculation assumes expert strategy for the game. It takes all possible starting hands, then assumes you play them out at expert level and calculates all possible outcomes. There are so many possible deals and draws that I can't walk you through the calculations here – I use WinPoker software to calculate such odds whenever I rate a new game.

The 1 in 40,000 figure varies somewhat depending on the game, because expert strategy differs a bit with each pay table. In 9/6 Jacks or Better, expert strategy brings us an average of one royal flush per 40,390 hands, while in “Not So Ugly” Deuces Wild, the royals come an average of once per 43,456 hands.

That’s due to a number of strategy differences between the games – in Jacks or Better, for instance, we’ll hold a single high card, giving us a long-shot chance to draw a royal around it, while in Deuces Wild we hold a single card only if it’s a 2.

There are differences even on different pay tables in the same game. If we’re playing expert level on 9/7 Double Bonus Poker, we draw a royal an average of once per 48,035 hands, while on the lower-paying 9/6 Double Bonus, we get more royals, an average of once per 40,864 hands.

That’s because the higher flush payback on 9/7 Double Bonus dictates that we hold three-card flushes. Dealt Jack-5-2 of diamonds, 9 of clubs, 7 of spades, we hold all three diamonds in the 9/7 version, but hold only the Jack in the 9/6 version. That means we have an outside chance at a royal in the 9/6 game, but we more than make up for it with extra flushes at 7-for-1 in the 9/7 game.