Ask The Wizard #103

If I put a $100 bill in a 98% return video poker machine and play until I go broke then how much on average will I bet in total?


There is a simple formula for this answer. It the initial investment divided by the house edge. In this case the answer is $100/0.02 = $5000. However due to the volatility of video poker, most of the time the $100 won’t last this long.

First I want to say many thanks for what I consider to be the best gambling related site on the web. I’m a frequent player at Foxwoods and mostly play Black Jack, Craps, and some Video Poker. However when I look at your House Edge Chart, I see that Catch A Wave has a lower edge than Craps and even Baccarat. This makes me wonder why I only observe $ 5.00 bettors playing the Wave. It seems to me that this would be an excellent game for bigger bettors. Am I missing something?


Thanks. As good as my site it I would doubt if 1 gambler in 1000 has visited it. So the vast majority of players don’t know what a good bet Catch a Wave is, if played correctly.

To the fellow who asked the question about order statistics (column #100), I have two quibbles: one small and one large. Your method failed to make a finite population correction, which I grant is trivial with 5000 employees, but it certainly wouldn’t have been had there been 20 employees!

More importantly, however, you implicitly assume that managers have no effect on their employees. Suppose good managers, through judicious hiring and firing, or through above-average motivational skills, raise the average level of their employees. Without accounting for this effect we will either upward- or downward-bias the resulting probabilities. I’m sure you knew this, but I am sensitized to it because I do a lot of calculations like this in discrimination cases and failure to adjust for things we can adjust for (in this case a group-specific effect) can often lead people astray.


Thank you for those good points. However the alternative to no control over the distribution of job performance ratings is rating inflation. The manager will be put in a position of giving out bloated ratings to keep his staff happy. As a government worker for ten years I speak with some experience on this. When I taught at UNLV there was no average class GPA standard but there were certain expectations about what a grading curve should look like at the end of the semester. At least in a college setting I thought that made for a reasonable policy. Perhaps in a business environment some sort of common sense medium would also be best.

There is a story today about a British man who will bet his life savings on one roulette roll. My friend and I have been debating about what the best casino bet is for this type of wager. If you can only place one bet, and you wish to maximize your odds, what is the best game to play and what is the best bet?


First, let me say this guy was a fool. He bet $138,000 on a normal American roulette wheel which has two zeros and a house edge of 5.26%. This amounted to an expected loss of $7,263. However had he taken a 10 minute ride to the Bellagio, Mirage, or Aladdin he could have made the bet on a single zero wheel which follows the European rule of giving half an even money bet back if the ball lands in zero. He planned to make an even money bet anyway. So, at these wheels with full European rules his house edge would have been only 1.35%, for an expected loss of only $1865.

To answer your question, if forced to make just one even money type bet I would have chosen the banker bet in baccarat with a house edge of 1.06%.

What is your opinion of Card Craps as played by many of the casinos in the San Diego area?


In California dice alone can not be used to determine the outcome of a game. To get around this law many casinos use a hybrid of cards and dice, or cards only. My crap section now addresses some of the ways this is done.

I have reviewed your blackjack site and FAQ, and I have a question about your Blackjack House Edge Calculator. From your description of methodology: "The program played each hand according to the correct basic strategy for those rules without regard to composition dependent exceptions." Can you explain how you determined total-dependent strategy (e.g., that which maximizes expected value)?


First, to those who don’t know, composition dependent strategy considers each and ever card in the player’s hand. Total dependent strategy only cares about the total, whether the hand is soft or hard, and whether it is a pair. So the basic strategy is total dependent. However the analysis of blackjack is generally composition dependent. The way derive the basic strategy charts is to take every composition of an initial two card hand and weight the expected value of each play by the probability of the composition. Let’s look at the case where the dealer stands on a soft 17 and the player has a 13 against a 2. The following table shows the composition dependent expected return of standing and hitting of all ways to compose a 2-card 13. The final column is the conditional probability of each compostion.

Expected values of 13 agaisnt 2

Player Cards Stand EV Hit EV Conditional Probability
7,6 -0.265046 -0.331966 0.142857
8,5 -0.264895 -0.331281 0.142857
9,4 -0.285726 -0.293008 0.142857
10,3 -0.31239 -0.304215 0.571429

If we take the weighted average of standing and hitting we get the following expected values:

Stand: -0.29503
Hit: -0.31045

Although hitting 10,3 is the better play overall standing has the greater expected value and is thus the better play.