Ask the Wizard! (No. 173)

The lottery is always a sucker bet! Briefly, the return of the Powerplay option is 49.28%. The return from a Powerball ticket alone is so much worse that it would be better to buy x/2 tickets with the Powerplay option than x without it. I added details about this option to my lottery section if you want more information.

Thanks for the compliment. There is a formula for questions like this, which I explain on my site www.mathproblems.info, see problem 116.

With a bankroll of b units, winning goal of g units, probability of winning p, and probability of losing q your probability of success is ((q/p)^b-1)/((q/p)^b+g-1). In this case b=20, p=18/37, q=19/37, and g=20, 50, and 100. So for a bankroll of $200 the probability is ((19/18)²⁰-1)/((19/18)⁴⁰-1) = 0.253252.

For a winning goal of $500 the probability is ((19/18)²⁰-1)/((19/18)⁷⁰-1) = 0.045293.

For a winning goal of $1,000 the probability is ((19/18)²⁰-1)/((19/18)¹²⁰-1) = 0.002969.

Thanks. To answer your question, no, I don’t think it is a good game. The house edge is too high. If you are looking for a big win you could play a progressive betting system in blackjack, pressing your bets as you win. Of course this comes at the cost of frequent smaller losses.

Thanks. Payout percentages such as this are historical. For example King Neptune’s casino posts their June 2006 report at www.kingneptunescasino.com/report567.php?bTag=knaff2287. The 96.78% for table games means that in June 2006 the ratio of money returned to money bet was 96.78%. In other words an actual house edge of 3.22%. Your own results will depend on the game rules, your skill (in games of decision making), and luck. In most games the odds are quantifiable so payout reports are not useful. It shouldn’t matter to you how badly other players have played or the mix of games they chose. Where these reports are very useful is in evaluating the slots. No casino that I know of volunteers how loose their slots are theoretically set, but such payout reports gives the user a good idea. If looking at other months you see that King Neptune’s pays about 96% in slots. I also think it is a good sign of a good operation to have return percentages independently verified. It shows the casino has nothing to hide.

Most redoubling situations tell you to double anyway. However, with a soft 15 to 17 against a 3, when the strategy says hit, you should actually redouble.

I asked my father this question since he has a Ph.D. in physics and also a solar panel on his house. Here is what he said,

It would help, but the economics might not justify it. Probably less than 25% of heat enters houses through the roof. The reflectivity of the mirrors would probably degrade to 60% or less as they age and get dirty. It makes a lot more sense to use that space for water heaters or solar electric panels. On a sunny day, my roof panels provide enough power to run both the A/C and the pool pump, which are my biggest power eaters. When one or both are off, my meter runs backwards. The pool heater panels had the pool temp up to 90 degrees last week. I had to cut back on the pumping time.

Thanks. Paying a 25-cent commission on a $3 bet amounts to an 8.33% commission. Assuming you only play as the player, you will win both bets 28.61% of the time. So the normal cost of the 5% commission rule is 0.2861×0.05=1.43%. The losing on copies rule costs the player 1.30%, for a total house edge of 1.43%+1.30% = 2.73% normally. In the case of this game, the cost of the commission is 0.2861×0.0833=2.38%. So the total house edge is 2.38%+1.30%=3.68%.

As my blackjack section shows, the 2 to 1 on blackjacks is worth 2.27% and doubling on 3 cards is worth 0.23%. Otherwise the rules look standard. All things considered, the house edge in the blackjack game has a player advantage of 2.1%. The probability of winning on a 4 or 10 in craps is (6/36)×(3/9) = 5.56%. Every time this happens you get an extra unit, so it is worth 5.56%. Normally the house edge on the come bet is 1.41%, so overall the player edge under this rule is 4.15%. So I agree that craps was the better game to play.

According to my poker source, “J.B”, a player should never be eliminated if he has any money on the table. In the situation where a player doesn’t have enough to post the small blind then he should go all-in with whatever he has. A sub-pot should be formed with 15 chips from each player who made or called the big blind. If the 15-chip player has the best hand then he should win that sub-pot. In the event nobody calls the big blind then the big blind would take out 25 chips from the pot and the best hand would win the 30 chips left in the pot. In the event there are only two players, the big blind would simply match the 15 chips and the best hand would win.

I forwarded your question to Brian, a former regulator and current casino manager. Here is what he said.

There are two types of changes. The first would involve completely swapping out the machine and the second would consist of simply changing the game, but keeping the existing cabinet. As you can imagine, changing the software is much cheaper which is why there is so much hype around downloadable games. How often games are swapped out depends on a casinos capital expenditures budget. Participation machines are turned over much more rapidly because the manufacturer has a vested interest in keeping the best product on the floor. In many instances, they will handle the scheduling for software and new machine replacements. Participation machines are those that are on lease to the property by the manufacturer. Usually, the manufacturer gets 20% of the revenue, less taxes. From an accounting perspective, the useful life of a slot machine is 5 years and then the asset is fully depreciated (no longer has a book value). The final consideration is popularity. How often do you go into a casino and see a section of slot machines that are the old IGT three reel Red White and Blue machines? If the machines are performing well, why spend $10,000+ to replace each unit?

Assuming six decks, the probability of a suited blackjack is 4×6×24/combin(312,2) = 1.19%. So the $25 bonus on that is worth $25×0.0119 = $0.2968 per hand. The probability of a suited 7-7-7 is 4 × combin(6,3)/combin(312,3) = 0.000015957. So the value of $100 on that is $0.0016. The probability of suited 6-7-8 is 4×6³/combin(312,3) = 0.00017234. So $100 on that is worth $0.0172. The probability of a suited ace and jack of spades is 6×6/combin(312,2) = 0.0007420. So $100 extra on that is worth $0.0928 (the player is already getting $25 for the suited blackjack). Adding this all up, the bonuses are worth 11.25 cents. So this is nowhere near enough to compensate for the 50-cent commission.