How to calculate the house edge

Apr 16, 2002 3:58 AM

My wife Andrea and I were supposed to meet some friends, Dave and Dena, in Las Vegas for a marketing conference, but they arrived a day late. They were bringing their fifth wheel, but their trailer hitch broke in Baker and it was still there, waiting for repairs. We found a hotel for them, finished the conference, then took the next three days off for a mini-vacation and to play craps. We had a lot of fun playing and made a little money, too.

  At dinner on our last day in Las Vegas, Dave regaled us with some interesting trailer hitch stories, again, when Dena suddenly asked, “How do you really know the casino edge is say, 1.5% for the 6 & 8 bet?”

“Huh?” I asked, “How did we get to place bets from trailer hitches?”

Well, she told me, something reminded her of something else, and so on. It was very complicated, something only a woman could reproduce accurately on these pages.

“I’m not exactly sure about calculations,” I replied, “but I’m sure we can figure it out.”

The trailer hitch now forgotten, Dena got out her ever-present mini-calculator and a pen and paper.

“Now I’m ready,” she said, “Let’s figure out the edge!”

I took the pen and paper. “OK! Let’s just take one number, the six. In 36 rolls, how many times does it win?”

She knew this. “Five.”

“And how many times does it lose?”

“If you mean how many sevens in 36 rolls, there are six.”

“OK, so we have five wins and six losses, right?”

“Yes. A total of 11 wins or losses.”

“Now we’re getting somewhere! Let’s say we bet $6 on all 11 events, so we have a total investment of $66 (11 x $6). Of that, we will win $35 ($7 x 5) plus get our $6 back each time ($6 x 5 = $30) for a total of $65. So we invested $66, and after 36 rolls are left with $65, so we’re down only $1.”

Dena smiled. “Hey! Not a bad deal after all that playing, and the casino only gets a dollar!”

“Yes, but that’s how they make all their money, just a little bit from every winner and every loser. That one dollar is very important. It’s how they build their waterfalls, volcanoes, theme parks, and other things that are vitally important to us gamblers!”

She frowned. “Ha! But how does that sacred dollar relate to the casino edge?”

“Divide the casino’s win ($1) by the total investment ($66) and what do you get?”

“Well, I’ll be! 1.5% ”” the casino edge for the six or eight.”

“Want to try another number? How about the four?”

She smiled. “I can do this. The four (or ten) rolls three times in 36 rolls. There are, unfortunately, still six sevens, so we have a total of nine events. If I bet $5 on each bet, I get a total of $45 ($5 x 9). Of that, we win $27 ($9 x 3) ”” plus we get the $5 back each time ($5 x 3 = $15) so we have a total on hand of $42. So now the casino’s cut is $3 ($45-$42).”

“So far so good,” I replied. “Since the casino wins $3 on the 4 (or 10), and only $1 on the 6 or 8, you know the edge has to be higher than the 1.5% on the six or eight.”

Dena picked up the calculator again. “Uh, right. Let’s see now: $3 divided by the initial investment of $45 is 6.6%-the casino edge for the 4 or 10!”

We all stood up to go. “It’s a fitting end to our vacation. We had fun, made a little money, and found out something new about place bets. What a terrific vacation!”

“What about our trailer?” Dave asked, “That’s not so terrific.”

I smiled. “Well, at least your vacation went off without a hitch!”