# Ask the Wizard #176

Steve from KC

There are two significant rules changes to the Microgaming pontoon game. First, the dealer stands on soft 17, which is worth 0.47% to the player. Second, there is no drawing to or resplitting of aces, which is worth 0.49% to the dealer. So these two rules almost offset each other. Overall the house edge is 0.39%, with correct strategy, which is indicated in my Microgaming section.

Rich from Greenwood, IN

Measured in terms of the house edge, the number of other players doesn’t matter. Yes, they will eat up cards when the count is good, but they will also do so when the count is bad. In the long run it doesn’t matter. However, in terms of expected wins per hour, when you have an advantage, it helps to have fewer players, because you will play more hands in the same amount of time.

Chuck from Spring, TX

Thanks. My program is not very user friendly. I would recommend you use the blackjack calculator at gamblingtools.net, which will give you perfect advice for any situation and deck composition.

Nathan S. from New Plymouth

For those not familiar with the hold 'em terminology, you are asking for the probability of at least a pair in six cards, given that the first two are (the hole cards) of different ranks. I hope you'll forgive me if I just do the probability of getting exactly a pair, including hands that also form a straight or flush.

The number of ways to pair one of your hole cards is six (2 hole cards * 3 suits remaining). The other three cards must all be of different ranks from the 11 left. There are combin(11,3)=165 ways to choose 3 ranks out of 11. For each of these there are four suits to choose from. So the number of ways to pair one of your hole cards is 6*165*4^{3}=63,360.

Now let's look at the number of ways to get a pair outside of the two hole cards. There are 11 ranks to choose from for the pair. Once the pair is chosen there are combin(4,2)=6 ways to choose 2 suits out of 4. For the other two cards there are combin(10,2)=45 ways to choose 2 ranks out of the 10 fully intact ranks left. For both of those ranks there are 4 possible suits. So the total combinations for a pair, not including the hole cards, is 11*6*45*4^{2}=47,520.

The total number of ways to choose 4 cards out of the 50 left in the deck is combin(50,4)=230,300. So the probability of getting exactly a pair in six cards is (63,360+47,520)/230,300 = 48.15%.

Edward from Baltimore, MD

A straddle, often called a “live straddle”, is when the player after the big blind makes a raise before looking at his cards. For example in a $3/$6 game the large blind would be $3 so the straddle would be $6. I asked my friend Jason about the reason for this. He said, “The reason some people do this is to stimulate action in a "tight" game. The person who straddles also has the option to raise after the big blind acts. Card rooms like this and allow it because is almost assures a larger pot and therefore more rake.”

There are two uses of the term "props" in poker. First, a Prop Player is one who is paid by the poker room an hourly wage to play. The reason for this is to keep a certain minimum number of players at each table. For more information this questions is answered in much more depth on poker-babes.com. Second, a Prop Bet is a side bet made among the players, often on the flop.

Dan and co workers at maple island from Forest Lake

The probability of a five-of-a-kind on one throw is 6*(1/6)^{5} = 1/1,296. This is because there are six different five-of-a-kinds (one to six) and the probability each die will be that number is (1/6). The probability of not getting a five-of-a-kind is 1-(1/1,296)=1,295/1,296. The probability of going three attempts without a three of a kind is (1,295/1,296)^{3}=99.77%. So the probability of getting at least one five-of-a-kind in three tries is 100%-99.77% = 0.23%.

Kevin from Toronto

Keeping all the tens in the deck is worth 1.89% to the player. The house edge under those rules is normally 0.40%. So with all the tens in the shoe, the player edge would be 1.89%-0.40% = 1.49%.

"Anonymous" .

Follow up: In the February 1, 2006 column, a reader was mad because of the short expiration dates on slot machine tickets. I took her side, saying they shouldn’t expire at all. Many readers took me to task, saying that casinos routinly honor expired tickets. So I then did an experiment in which I collected $2 tickets up and down the Strip. After they expired I went to cash them in all of them were honored. So I have amended my answer and I offer my apologies to the casinos for my earlier harsh words.