Ask the Wizard #199
Michael L. from West Mifflin, PA
For the benefit of other readers, the full set of rules is:
- Single deck.
- Dealer stands on soft 17.
- Winning blackjack pays even money.
- Player may double any first two cards.
- No double after split.
- Player may resplit to four hands, including aces.
- No draw to split aces.
- No surrender.
- Six-card Charlie (player unbusted six cards automatically wins).
- Cards shuffled after every hand.
- If game runs out of cards, all unbusted player hands automatically win.
The house edge using total-dependent basic strategy is 2.13%. I ran a 7-player simulation, using total-dependent basic strategy, and the average number of cards used per round was 21.65, with a standard deviation of 2.72. In almost 190 million rounds played, the most cards ever used was 42, which happened 7 times.
It is my educated opinion that even with computer perfect composition-dependent strategy the player would still realistically never see the last card. You could cut down the house edge much more using composition-dependent strategy, according to all the cards seen as you go along. However bucking 2.13% house edge to start with, you’ll never get anywhere near break-even, regardless of how hard you try.
Mary Jo from Calgary
Let’s assume 10.8 for the standard deviation, which I get from the Red, White, and Blue game described in my slot machine page. The standard deviation of the mean over n spins is standard deviation per bet divided by the square root of n. In this case, 10.8/10,0000.5 = 0.108. The difference between 93% and 91% over 10,000 spins is just 18.5% of one standard deviation. To get the standard deviation of the mean to just 2% you would need a sample size of 291,600 spins. The standard deviation in slots will vary substantially, so take these figures with a grain of salt.
Steve S. from Lake Grove, NY
To be honest with you, I don’t know that much about it. I would imagine you would have to file a complaint through the country in which the ship is registered, usually Panama, the Bahamas, or Liberia. Good luck getting any satisfaction that way. Your odds would probably be better writing to the corporate headquarters of the cruise line. As a last resort, I would suggest making a stink on as many forums about cruising as you can.
J.B. from Las Vegas
You’re welcome. I ran some random simulations in 9/6 Jacks or Better, to get at the answer to your question. The following table shows the covariance for 2 to 9 lines played, in 9/6 Jacks or Better. The variance would be the same as the base game played.
Covariance in 9/6 Jacks or Better Spin Poker
Let’s look at an example of 9-line 9/6 Jacks or Better. The variance of the base game is 19.52. The covariance is 33.46. So the total variance is 19.52 + 33.46 = 52.98. The standard deviation is 52.981/2 = 7.28.
Nick from London
They also have zero house edge baccarat and roulette, so that can’t be entirely the reason. My theory is that it is a way to get players through the door. Their main casino has many more games and higher bet limits. I’m sure some of the Zero Lounge players wander into the regular casino eventually.
Jack from Georgetown
Video Poker strategy charts are not an exact science. There is always a tradeoff between brevity and accuracy. There are also issues about the best way to express a rule. Unless there was a huge emphasis on simplicity, it is unlikely two writers would come up with the same strategy.
The probability of three pairs and six singletons in twelve spins is combin(38,3) × combin(35,6) × combin(12,2) × combin(10,2) × combin(8,2) × fact(6)/3812 = 9.04%. The math gets rather messy asking about the probability that this could happen in any 12-spin span over 20 total spins. Suffice it to say that it is significantly more than 9%, more likely than not, I would guess. So these seem like very normal results to me.