Ask The Wizard #290

You're right that the value of the bonus is the same regardless of how many lines the player bets in the initiating spin. However, it takes five bonus symbols on an ACTIVE payline to trigger the bonus. So, the probability of triggering the bonus is directly proportional to the number of lines bet. Thus, the return to the player should be the same regardless of the number of lines bet.

Thank you for that information. I just updated my blackjack survey to reflect that rule change.

You're right that with this change the Alamo no longer has the honor of having the most liberal blackjack in Las Vegas. That honor now belongs to the single-deck game at the El Cortez. There are still a few legitimate (meaning paying 3-2 on a blackjack) games in Vegas, but the El Cortez is the only one that allows doubling on any two first cards. The other properties follow the northern Nevada rule of restricting doubling to totals of 10 and 11. The full El Cortez single-deck rules are:

• Single deck.
• Blackjack pays 3-2.
• Dealer hits soft 17.
• Double on any first two cards.
• No double after split.
• No surrender.
• No re-splitting aces.
• No cut card.

Assigning a house edge depends on specifically the dealer's behavior in deciding when to shuffle. The cut-card effect is important in a single-deck game, lowering the house edge by 0.11% if there is isn't one.

It is my understanding the dealer's shuffle after a certain number of rounds, according to the number of players at the table. Usually, the single-deck game at the El Cortez has at least four players, which equates to the dealer shuffling after two rounds. As long as the dealer deals exactly x rounds per deck, that is good for the player. Given this policy, and the usual crowded table, I put the "realistic" house edge at 0.19%, which is what the basic strategy player can expect.

So, congratulations and kudos to the El Cortez for the new best blackjack game in Vegas!

Yes! If anything, you should tip more because a greater amount of work is involved in creating a check than paying in cash.

This question is asked in discussed in my forum at Wizard of Vegas.

The Wizard says that website sounds like a lot of ranting and raving with no credible evidence whatsoever to justify the accusation. I'd be happy to expose any casino for using biased dice, if I had any evidence of it.

If anybody has legitimate evidence of biased dice, I'd be happy to examine it and publish my conclusions. Evidence I would like to see are either log files of rolls or, better yet, some actual alleged biased dice.

Furthermore, if the casinos really were using dice that produced more than the expected number of sevens, then why aren't these detectives privy to the conspiracy out there betting the don't pass and laying the odds?

No! Futures and betting favorites on the money line are two of the worst bets you can make when betting football. This sounds like a betting system, adding a sequence of negative bets and expecting the sum to be positive. However, I will probably need more than that to convince you, so let's look at the numbers.

First of all, the Panthers are only in the playoffs because they are the least bad team in an awful division (the NFC South). Their record is 7-8, and they have given up 35 more points than they have scored all season.

If they are so bad, why are they six point favorites against the Arizona Cardinals, you might ask? Arizona made the playoffs mostly on the efforts of Carson Palmer in the first six games. He was injured in the sixth game, but they still managed to squeak into the playoffs anyway. Plus, Carolina enjoys home field advantage.

Given that Carolina is a six-point favorite against Arizona, I show their probability of winning that game is 70.3%.

Assuming they win, they will mostly likely have to beat both Green Bay and Seattle to win the NFC. What are the odds of beating those two teams? Keep in mind, given the playoff rules, they will be the visiting team both times.

There is an easy way to get a close estimate of the point spread in any game. Here is my Wizard formula for the point spread on the home team:

(Net points per game of away team) - (Net points per game of home team) - 2.67.

Let's look at a hypothetical match-up between Arizona and Green Bay.

During the 2014 season, Carolina has -35 net points all season. For Green Bay, it is +138. Divide both numbers by 16, because there are 16 played games in the season, for an average margin of victory per game of:

Carolina: -2.1875
Green Bay: +8.6250

Using my formula, the home team, Green Bay, should have a spread of -2.1875 - 8.6250 - 2.67 = -13.4825.

So, Green Bay would be about a 13.5-point favorite against Carolina. I'll skip the math over this step, but I show the probability of Carolina winning as a 13.5-point underdog is 14.3%.

Seattle has just about as strong a record as Green Bay, with 140 net points all season. So Carolina would also have about a 14.3% chance of winning that game.

The odds of Carolina winning all three games are 70.3% × 14.3% × 14.3% = 1.44%. So, a fair futures bet at that probability is 68.6 to 1!

Yes, you could argue that Detroit or Dallas might get lucky and make the Conference Championship. You could also argue that the odds of Carolina beating Green Bay and Seattle are positively correlated. However, those are minor considerations against the fact that my rough fair line is 68.6 and you're getting only 18.

You also have to consider the expense of betting the favorites on the money line as you go. This is generally an awful bet. Square bettors love to bet big favorites on the money line, creating value in the other direction. It is roughly a fair bet to take underdogs of seven points or more on the money line, meaning that the favorite bettors are paying all the juice.

Let's be generous and assume you could get +250 on Arizona and lay 5 to 1 in the following two games. Let's also say you bet $100 on Carolina at 18 to 1.

First, you bet $40 on Arizona at +250 as a hedge. If they win you win $100 on that bet and lose $100 on the futures bet and break even.

If Carolina beats Arizona you bet $700 to win $140 on Seattle. If Seattle wins, which they should, you'll be up $140, which will recoup your losses on Arizona and the futures bet, so you'll be even.

If Carolina should upset Carolina you will have to bet $4,200 to win the $840 you will have lost betting on Arizona, Seattle, and the futures bet. If Carolina loses, you'll be even. If they win you'll be down $40+$700+$4,200=$4,940. The $1,800 you'll win on the futures bet will not be enough to recoup that.

In closing, your idea of taking Carolina to win the NFC and hedge along the way is highly ill-advised.

For the benefit of other readers, a "ten-card Charlie" rule means that if the player gets to ten cards, without busting, then it is an automatic winner.

According to my simulation, the probability of the player getting to at least ten cards is 1 in 60 million. So, it lowers the house edge by about 0.0000017%.