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Ask the Wizard #209

What is the standard deviation of the difference between the final point differential between the two teams in an NFL game and the pointspread of that game?

Don from New York

For the benefit of other readers, let’s look at an example from the last Super Bowl, to illustrate what you are asking. The Patriots were a 12-point favorite, but lost by 3. So the game finished 15 points away from the point spread. If I understand the question correctly, you are asking about the standard deviation of this difference. The mean difference was close to zero for each league studied. Here is what I get for the standard deviation:


NFL 13.31 (based on 2000 to 2007 seasons)
College Football 15.72 (based on 1993 to 2007 seasons)
NBA 11.39 (based on 1987 to 2003 seasons)
So, the 2008 Super Bowl finished 15/13.31 = 1.13 standard deviations away from expectations. I’m ignoring the adjustment factor for a discrete distribution, to keep things as simple as possible. The probability of being 1.13 standard deviations or more from expectations, in either direction is 25.85%. This can be found in Excel, using the formula 2 × normsdist(-1.13).

In Pai Gow Poker, the high hand must be greater than the low. I didn’t notice a similar rule for tiles, though your Java game enforces one. Are players (not banking) allowed to set hands foul, and then forfeit, as in pai gow poker? Do you know what happens in tile tournaments? Can a player request "house way" in a tournament?

Tabby Cat from Huntington Beach

In pai gow tiles, it is always obvious which hand is higher. You don’t need to know where to place the high hand. Just make any two stacks of two tiles each, and the dealer will figure it out. I have never once heard of a pai gow tiles tournament. However, the Las Vegas Hilton has an annual pai gow poker tournament. I’m not certain whether you can request the house way, but I would bet against it. It is a very strict rule in most tournaments that the dealer can not give advice of any kind.

Hi, Wizard. Let’s say I have $300 to gamble with, and can accept a 25% risk of ruin. What should I do to maximize my upside? Thanks!

Jerry T. from Hertford

I would make the banker bet in baccarat. My betting advice would be to do what is known as a two-step progression. First, bet 1/3 of your bankroll. If that wins, walk away. If that loses, then bet the other 2/3. Again, if you win, walk. With any tie, just bet again until the bet is resolved. Here are the probabilities in baccarat:

Banker: 45.86%
Player: 44.62%
Tie: 9.52%

The probability of a banker win, given that the bet is resolved is 45.86%/(45.86%+44.62%) = 50.68%. The probability of losing both steps of the progression is (1-0.5068)2 = 24.32%. The banker bet pays 19 to 20, so you will have a 75.68% chance of winning $95 or $90 (depending on whether you win on the first or second bet), and a 24.32% chance of losing $300.

Dear Wizard, are there any online casino games that offer a positive edge to a player using an optimal strategy, and if so where can I find them? Many thanks and keep up the good work!

Bill from London, UK

Sadly, I can't think of any. Global Player used to have video poker over 100%, and some Boss Media casinos had a blackjack game with a player advantage. However, all such casinos either closed their doors, or removed the good games. If anybody else knows of any new straight up advantage games online, I'm all ears.

If the local casino offers me $10 in free play and then requires that I add a dollar to activate it, then how much is the offer worth theoretically? This is an offer I got on a postcard from Sunset Station Casino.

Mike F. from Henderson, NV

The value of that offer is $10.77, because the Sunset Station has full pay deuces wild, at a return of 100.76% (source: VPfree.com). The money you have to put in first is called "seed money." You don't need to actually play it. When you press "deal" the amount you bet will be deducted from the $10 in free play. If you get something back, it will be added to your real money balance. If you bet through the $10 exactly, you can cash out the real money balance, without ever actually betting the seed money. Personally, I find the seed money requirement annoying. If you are planning to do the free play only, it is an extra nuisance. At the Wynn and Venetian, no seed money is required when collecting free play.