Monday, October 11, 2010

Questions, questions, questions

Q. I have a question about video poker. The experts all tell you to discard the ace when holding three unsuited high cards to the ace. Why?

A. Discarding the Ace and keeping just an unsuited Queen-Jack, King-Queen or King-Jack is a question of balance and tradeoffs. Are we better off with the head start on straights and the greater chance of pairing a high card that holding three high cards gives us, or are we better off holding just two high cards and leaving open the possibility of four of a kind or a full house while increasing the possibility of three of a kind or two pair?

The key is that not all three-card starts to a straight are created equal. In a hand that includes an Ace and two other high cards, the only possible straights are Ace-high. King-Queen-Jack, it is possible to draw straights that are either Ace high or King high.

Starting with Ace-King-Queen, for example, you can draw straights only by drawing one of the four Jacks along with one of the four 10s. There are 16 possible Jack-10 draws. If you hold King-Queen-Jack, you can complete a straight either by drawing one of the four Aces along with one of the four 10s, or one of the four 10s along with one of the four 9s. That’s 32 possible draws.

That greater chance of drawing a straight with King-Queen-Jack makes it worth our while to eliminate all possibility of drawing four of a kind or a full house while also depressing chances of drawing three of a kind or two pair. When the hand includes an Ace, the balance tips the other way. Our chances of drawing a straight are much lower, so we’d rather keep intact our chances at other hands that pay more than our bet.

To use 9-6 Jacks or Better as an example, dealt a hand like Queen-Jack-Ace of mixed suits along with a 4 and a 7, your average return for a five-coin bet is 2.496 coins for holding Queen-Jack, and 2.280 for holding Ace-Queen-Jack.

Q. I was at a casino when one of the card shuffle machines was malfunctioning and the floor boss made the comment, “It’s missing some Kings.”

That got me thinking. Sometimes too much thinking is a dangerous thing, but in this case if the shuffle machine is identifying individual cards, what prevents this machine from stacking cards in such a way that in an eight-deck shoe the casino would get a significant advantage? I noticed this especially at a table in the high-roller room where they would deal horrible shoes for 5-6 hours or more. Taking into account the randomness induced by the cut of the deck could there be bias built in?

A. I don’t know that there was anything wrong at the game you were playing, but I would be really, really wary of continuing to play at a casino where I heard a supervisor say, “It’s missing some Kings.” If Kings, or any other 10-value cards, are being selectively removed from play, you get fewer blackjacks, and it diminishes your chances of drawing a 10-value on double downs. Obviously, that hurts.

That doesn’t mean I think the shuffler is doing the removing. Automatic shufflers aren’t equipped with card recognition capabilities. They have random number generators that select designated slots to move the cards, but they don’t know the value of the card being moved.

When casinos want to know the value of the cards being played --- whether it’s to insure correct payoffs, estimate the quality of the player for rewards purposes or to sniff out advantage players --- there are systems they can use to do it. All are expensive and not in common use at this point, but optical scanners as well as card-reading shoes that sense RFID chips embedded in the cards are available.

I would be more worried about casino personnel manually removing cards from the deck. This is rare, but not completely non-existent. If I’d observed bad shoe after bad shoe, then heard a comment about Kings missing, it wouldn’t prove cards were being removed, but it would tempt me to take my business elsewhere.

Q. There are times when I’m playing slots and I just keep on winning. Then the machine gets cold and you start losing. It’s like the machine is on a winning streak or losing streak.. I know it’s supposed to be all random but is there any kind of streaks?

I also have a friend who tells me that the amount you play per line changes the results. He’ll tell me that he will play a machine at three coins per line and he’s doing well, so goes up to five units per line and the machine stops paying out. Sso he’ll go back down to betting three units and he’ll start winning again.

He also says there have been times when a machine is not returning any money and he will cash out and put new money in and start winning. He swears this changes the machine’s rhythm or cycle.

A. Are there streaks? Sure, streaks are part of the normal odds and performance of any game. Can we predict them and make them happen? No. All streaks are historical --- that is, we only know there's been a streak after it's happened.

Are there programmed cycles? That’s a different question, and the answer is “No.”

Everything your friend is experiencing is coincidence. If you tracked over hundreds of thousands of spins, you’d find the same percentage of winners no matter how many coins were bet.

The random number generator that determines what you see on the reels or screen doesn't know how many coins you bet or whether you’ve cashed out or whether you’ve put in fresh money. Your wager or cashout patterns can't influence a program that doesn't know how much you bet or whether you’ve cashed out.