# Ask the Wizard #173

Powerplay multiplies non-grand prizes from 2x - 5x. The Powerball site has listed testimonials from it’s winner’s that say "powerplay is the only way to go". I’m thinking it’s a sucker’s bet.

John from Morrisville, NC

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.

If I have a $200 bankroll that I don’t mind losing, and keep playing $10 on one single number on European (single-zero) roulette, what are the probabilities of winning, $200, $500 or $1000? Assuming I’ll stop after reaching the target. Thanks, great site, you wanted me to keep this short :)

Andy from Amsterdam

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.

Hi Michael. Awesome website! You’ve answered a few questions similar to mine, but not exactly. Simply put: Do you think Caribbean Stud Poker is a "good" game to play? Of course the odds may not be as good as blackjack, but it seems to be a pretty solid game to play and possibly win money at. What are your thoughts?

Parham from Atlanta

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.

I am a part time blackjack player with a lot of success in land based casinos. I am thinking to start playing online but I have a few questions about this. Does a payout percentage of for example 98% mean that you lose 2% anyway regarding good or bad play. In European blackjack with no hole card, if you play last box isn't it better to leave the little card for the bank or must I hit anyway? sometimes i have my doubs about this. P.S. love your site THANKS

Andrew from Belgium

Thanks. Payout percentages such as this are historical. For example King Neptune's casino posts their June 2006 report on their web site. 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.

In variants of Spanish 21 where redoubling is allowed, but the only permitted plays after doubling are redouble or stand, what is the correct play where the strategy card says "hit"?

Nick from London

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.

What is the reason people don't put mirrors on flat roofs in Las Vegas. Wouldn't that cut down on the expense of air conditioning?

Anonymous

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. *

Love the site. Regarding Baccarat, what is the house edge if one bet’s less than $5.00 per hand on the Banker? Some mini-baccarat tables used to have a $3.00 minimum. The commission would be calculated as 5% of the nearest $5.00 (so, $0.25 on a $3.00 wager, rather than $0.15.) Thanks for your consideration.

Gary from Albuquerque

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%.

At a recent charity casino night (not real money) there were some unusual rules for both Blackjack and Craps, and I wasn’t sure which to play. In BJ, Dealer stand on Soft 17, Double after splitting alowed (except on aces), Doubling allowed on 3 cards, BJ pays 2:1, no insurance, no surrender. In craps, COME bets paid 2:1 on 4 and 10, but no odds allowed on COME bets. I played craps until the table just got so crowded it wasn’t any fun any more, but I suspect my pass line / always COME strategy was better odds than I got at the BJ table. Was I right?

Greg from Fairfax

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.

I have a question that has caused a lot of discussion in our group. It concerns players that do not have enough chips to post the small blind (or big) blinds. Example: In tournament play, with blinds of 20/40. The player in the small blind position only has 15 chip value. Should that player be eliminated because he is unable to meet the blind value; or should he be allowed to play (all-in) the chips he has?

Chris from Brandon, Canada

A player may call for less in that situation, but he may only win the amount of his call bet from each of the other players who posted the small blind. In the example above, 15 chips from each player posting the small blind would be put in the pot. All other money would be put in a side pot, which the short-stacked player would not be eligible to win.

My thanks to Ashley Adams for her help with this question.

How often do Las Vegas or Reno (Nevada as a whole if easier) change their slot machines? Better stated perhaps as what is the average life cycle of a slot machine before it is worn out, out of fashion, unsecure, etc.? How does that average compare to smaller markets such as Deadwood, South Dakota?

Justin from Rapid City

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? *

The Firelake Casino in Shawnee, Oklahoma charges a 50-cent commission on each $5 blackjack bet. The other rules are the standard, standing on all 17s. A promotion pays an extra $25 for each suited blackjack, $100 for suited 7-7-7 or 6-7-8, $125 for ace and jack of spades.

Jeff from Shawnee

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 4×6^{3}/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.