Lottery changes enacted

The state Lottery Commission has rolled out the new version of its flagship Texas Lotto game amid confusion over how to play and grumbles that it's even more of a ripoff than it used to be.

In the past, as I explained here, Texas Lotto was a simple game of picking six numbers out of 54, with odds of hitting the jackpot being one in 25,827,165. The new game has two sets of 44 numbers. You pick five numbers from the first set and one more from the "bonus" set (this is the basic style of Powerball games, which I talked about in February) in order to win. This makes the odds of winning one in 47,784,352. I've got the calculation of that under the More link if you're interested.

Though not mentioned in the online version of this story, the print version notes that lottery payouts will drop from 55% of revenue to 52%. The expectation is that the state will get an extra $50 million or so annually from Lotto as a result of this change. As always, I'll believe it when I see it.

UPDATE: Apparently, someone on the Lottery Commission was really sure this change was going to be enacted:

The Texas Lottery Commission paid $83,150 for two new drawing machines a month before the formal vote to adopt changes that made the game harder to win and increased the size of jackpots, the Austin American-Statesman reported Thursday.

That timing has many people -- including Gov. Rick Perry and several lawmakers -- concerned that the decision may have been made before the formal vote was taken, the newspaper reported.

[...]

On Tuesday, Deirdre Delisi, Perry's deputy chief of staff, called Lottery Commission Executive Director Reagan Greer "out of concern of the purchase of the equipment prior to the change in the game," according to Perry spokeswoman Kathy Walt.

The equipment was purchased Feb. 28. The game change was approved March 27.

Greer defended the purchase, which was set in motion by then Acting-Executive Director Gary Grief, as "by the book."

Greer said Grief acted on his own and not as a result of any direction from the three-member Texas Lottery Commission as to how it planned to vote on the game change.

State Rep. Jack Stick, R-Austin, has asked Attorney General Greg Abbott to review the purchases.

I just want to add that "Jack Stick" is one of the greatest names I've ever heard.

To calculate the odds of winning the jackpot in this new-and-maybe-improved Texas Lotto: There are 44 balls in the hopper, each with a number painted on it. Once a ball is taken from the hopper, it is not replaced, so the first ball is picked from 44, the second from 43, and so on. That means there are 130,320,960 possible combinations (that is, 44 x 43 x 42 x 41 x 40) of the five numbered balls.

Since order doesn't matter (i.e., 1-2-3-4-5 and 5-4-3-2-1 are the same thing here), you need to eliminate duplicates, so divide that by 120 (which is 5 x 4 x 3 x 2 x 1), which is the number of ways to arrange five numbers. That gives 1,086,008, which is the total number of ways to pick the five balls.

The "bonus ball" is then picked from another hopper, which has all 44 balls in it. Multiply 1,086,008 by 44 and you get 47,784,352. Clear? Leave me a question in the comments if not.

Posted by Charles Kuffner on May 08, 2003 to Jackpot! | TrackBack