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Ask the Wizard #47

Wiz, this is a spliting 8's against a dealer's 10 question. Splitting is the is the correct play on single hand basis. However, I believe for the typical blackjack player it is better to stand when considering you are doubling the amount of the bet. Why double your bet against such poor, way below average, odds? After all, the goal is to maximize your overall return (i.e, the weighted average of all your bets). Your thoughts please?

P.S. Your site's great and advertising like banner ads and sidebars is understandable but invasive advertising like pop up windows and question prompts that try to force you to another site gets to be a bit much IMO.

Miami from Baltimore, USA

Although this is a close play, standing is the third worst option. Using my blackjack appendix 9G we can find the following expected returns:

  • Stand -.536853
  • Hit -.535361
  • Split -.474733
  • Double -1.07022

Splitting is the best decision because it results in the lowest overall loss for the hand. The expected returns for doubling and splitting are based on the total return for that hand relative to the initial bet. For example, if your initial bet was $100, and you split the eights, the total expected loss, all things considered is $47.47, which is less than the expected loss of $53.69 by standing.

The Stratosphere advertises poker machines that pay over 100%. In an earlier column, you said that in full pay Jacks or Better the perfect strategy player will average one royal flush every 40,388 plays. Given this fact, does this mean a player needs to play this many hands perfectly before the advertised payout percentage is realized? I speak for the millions of video poker players who, like myself, watch a $20 become $0 in that "98%" machine.

Derek G from Vegas, baby!

No, it does not mean that. Contrary to popular myth, there is no cycle. Every hand is independent. It would take an infinite number of hands, played perfectly, to guarantee reaching the theoretical 99.54% return.

Here are some figures for you. Royals contribute 1.98% to the return in 9-6 jacks or better. That means you can expect the game to return 97.56% between royals. The standard deviation of one hand is 4.42. The standard deviation of the return of 40,391 hands, the average number between royals, is 2.20%. So, even after a complete royal cycle you can still be a long ways from a 99.54% return. Thee is a 95% chance you'll be somewhere in the range of 95.24% and 103.85%.

About the pop-ups, I hate them too. However, something has to put rice on the table. Consider them the cost of the information you're getting.

Where can I find a strategy for playing Pick 'em poker?


You can buy the video poker strategy master which can generate a very good strategy for this game, as well as most any other video poker variation.

What are the statistical odds of getting a flush in Texas hold ’em. Is it easier to get a flush in 7-card stud or in holdem as a player.

Kevin from Richmond, USA

You can refer to my section on probabilities in poker to see the probability is 3.03%. The odds are the same in both Texas hold ’em and 7-card stud.

Have you ever heard of the Ken Fuchs progression. If so, would you please e-mail me or post the details on your site.

John from Baltimore, USA

I’m not familiar with it. Ken Fuchs co-wrote Knock-Out Blackjack so he can’t be all bad. However I just hear the word progression and I’m immediately skeptical.

There is a new rule in Moscow casinos in Caribbean Stud Poker. Player can buy one more card after looking his initial cards by giving the same amount of ante. Other rules and pay outs are still the same except no bonus is paid if player buys a card. Can you please help me to calculate house edge and the probabilities of this game? Thanks for your time

Eralp from Moscow, Russia

You’re not the first to ask me about this. I’m afraid I haven’t worked out the odds for this variation. If this twist ever makes it to Vegas I’ll make it a higher priority.

p.s. (Feb 21, 2006) I now address this rule variation in my Caribbean Stud Poker section.