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Ask the Wizard #26

Are these very fair rules:

  • The dealer deals from an infinite deck
  • Dealer stands on soft 17
  • No surrender allowed
  • Player can split any pair
  • Player can re-split, except for aces
  • Insurance offered only when player has two cards
  • Player can double down on any hand
  • Player can double after a split

These are the rules at 4 Aces casino, where I always seem to bust if I hit a 12 or 13 and the dealer wiped me out with a mind numbing over 40 21’s including twice 21’s four times in a row. They do allow late surrender even though it states otherwise in their rules. What is an infinite deck? If these are good rules could you point out a good strategy.

Douglas from Cumberland, Maryland

According to my blackjack house edge calculator, the house edge with these rules, assuming eight decks, is 0.45%. The effect of infinite decks, compared to eight, is 0.10% in the house's favor. So, the total house edge would be 0.45% + 0.10% = 0.55%.

You also seem to also imply that this casino is not dealing a fair game. Unless you provide some hard data I can't comment on that.

How do you read the odds on the board at the racetrack? For example what does 20-5 pay if you bet $20 to win?

Denise from Placerville, USA

I don’t think the board would say "20-5" but rather reduce the ratio to 4-1. That means that the bet will pay 4 to 1. So you will win 4 times your bet, plus get the original bet back, if you win. Thus a $20 wager at 4-1 would win $80. When you take the ticket to the window they will give you $100 ($80 winnings plus original $20 bet returned).

Here in Finland we have blackjack tables in some nightclubs and restaurants but these tables follow the following rules: six decks, ties push only on 21 and blackjack, ties on 17,18,19 and 20 the house wins!! No surrender, European no hole card rule, double 9-11, unlimited splits! I understand this is a bad deal for players but how bad is it? What is the house edge in this game?

Kim from Helsinki, Finland

I have actually seen these rules when I went to Helsinki in 1986. Without a doubt, the worst blackjack rules I have ever seen.

To answer your question, my blackjack house edge calculator says the house edge is 0.54%, before considering the rule that ties lose on 17-20. My list of rule variations says the effect of losing on 17-20 ties is 8.38% in the house's favor. So, the overall house edge would be 8.92% (ouch!).

I'm a little confused on what beats what in five- and seven-card poker. For example, flush beats a straight and so on. Can you please help me out and let know the full list of what hands beat what in poker. Thanks!

James from USA

Here are the hands from highest to lowest, for both five- and seven-card poker: straight flush, four of a kind, full house, flush, straight, three of a kind, two pair, pair.

Lets say you have a slot machine like sizzling sevens that pays a top prize of 60 coins for one coin played 500 for 2 coins and the progressive for the 3rd coin. Let's say the machine is played only by one coin players receiving only 60 coins max prize. In other words they excluded themselves from the progressive and 500 coin hits. How does a manufacturer program the machine to satisfy local gaming regulations if this machine will never pay out a jackpot higher than 60 coins. Obviously the machine doesn't return the same amount to one coin players as it does for three coin players. Doesn't this violate the minimum payout requirement or does the machine compensate for this?

Jim from USA

Unlike most slots, this game has different types of wins according to the number of coins bet. The first coin enables the player to win the small frequent "bar" wins, from 2 to 60. The second coin enables larger "seven" wins from 100 to 500. The third coin doubles the wins for sevens, except it also qualified the player for the progressive jackpot for three sizzling sevens.

The ways these games are programmed is to give the player a slightly higher return on each additional coin bet. For example, the first coin might have a return of 92%, the second 93%, and the third 94%. You seem to think the return for one coin would be very low, due to the small wins, but those wins happen more often than the wins for sevens.

In Nevada, regulations require slots to theoretically pay at least 75%. Even the games at the airport, which are very tight, still pay at least 85% or so. I'm quite sure that the return for any number of coins bet in Blazing Sevens conforms to industry norms.

With a 52-card deck, what are the odds of drawing a pair of Jacks?

Rick from Gardnerville, USA

Assuming you draw five cards, and count all hands with exactly two jacks, then the probability would be combin(4,2)*combin(48,3)/combin(52,5) = 6*17296/2598960 = 3.99%.

The www.ccc-casino.com has no-zero roulette, which they call Super Chance Roulette. Are there any systems that would be effective since there is no zero? Without the zero could one effectively play both black and red at the same time, since there is no fear of the zero?

Jon M. from Danville, New Hampshire

I played it in practice mode and it seems to be a legitimate no-zero roulette wheel. There is no system that can either beat or lose to this game in the long run. The more you play the more the ratio of the net win to the total amount bet will get closer to zero.

Update: This casino has since closed.

Some casinos offer "comps" for different levels of action. I was wondering if there was a way of approximating how much I would have to wager to earn these comps.

Steve from New York, USA

Your comp offers will depend on the product of your average bet, time played, hands per hour, house edge, and some "comp" constant, which is usually 33% to 40%. I indicate what one Vegas Strip casinos assumes for house edge and hands per hour in my house edge summary.

How can I convert your probabilities into the x to y format?

Ralph Harpster from Turlock, USA

Saying the odds of something happening are x to y means that the event in question will happen x times for every y times it doesn't happen. To make the conversion let p be the probability of some event. The odds could also be expressed as (1/p)-1 to 1. Lets look at an example. The probability of drawing a full house in five-card stud is 0.00144058. This could also be represented as 693.165 to 1.

I would like to know what the players edge would be in Let It Ride if he can see can see both the community cards and then if he can only see one of them? I was told that you could figure it out.

Jeff F. from Hammonton, USA

If you could see both the community cards, then your edge would be 42.06%. I don't know the advantage for one card, I'm afraid, but I am sure it would be high, especially if the second one were exposed.

The video poker machines at Casino Niagara have no progressive jackpots. According to Stanford Wong, if an 8/5 quarter video poker machine doesn't have at least a $2,200 jackpot with five quarters played, then don't play. What is your opinion on this.

Gordon Maska from Lewiston, New York

Assuming you played conventional 8/5 strategy the return in your example would be 99.68%. However, if you played optimal strategy for this jackpot the return would be 100.08%. So, Wong was not wrong.