Disproportionate prize pools in California Lottery

I'm working on a new page about the California Lottery. This will likely be followed by analyses of other state lotteries.

A peculiar thing about the California Lottery is a strong inclination towards pari mutual payoffs. You would think a state as big as California could afford to pay fair odds on games like the Daily 3 (a simple game of choosing 3 numbers from 0 to 9). I recall Maryland paid fair odds in similar games. However, California, being what it is, must do things differently.

In this game they calculate wins as follows:

1. Take the dot product of the number of each type of win and it's win share. Let's call this the total winning shares.
2. Divide the total win (50% of amount bet) by the total winning shares to determine the win per share.
3. Pay the players according to the winning share of whatever way they bet the game and the win per share.

There are three basic ways to play:

1. A straight bet (must match your chosen numbers in exact order).
2. A box bet (must match your chosen numbers in any order).
3. Straight/box (50/50 split between the above two)

Here are the shares by type of bet for types 1 and 2.

Straight 12.5
Box (three unique numbers): 2
Box (two duplicate numbers): 4

For a straight/box they give you half the share value for each half of the bet.

Here is the problem -- the straight share is too big in proportion to the box bets.

For example, if you do a box bet of three unique numbers, like 2-4-6, your chances of winning are 6/1000, for which your given 2 shares. Shares * probability of winning is 12/1,000.

Meanwhile, a straight bet has a 1/1,000 chance of winning but gets 12.5 shares. Shares * probability of winning is 12.5/1,000.

In other words, everything would be proportional if straight bets got only 12 shares. Why are these bets getting an extra half share? What is happening is the box bettors are subsidizing the straight bettors.

Am I right? I welcome all comments, questions, and especially corrections.

The question for the poll is how do you feel about this? (multiple votes allowed)

More information: California Lottery regulations (see pages 19-22)

p.s. I meant "Maybe screw-top wine isn't so bad after all."

I believe California law requires it to be pari mutuel.

Their Daily 4 is the same way: 12.5 for a straight when 12 would be proportional.

Quote: rsactuary

I believe California law requires it to be pari mutuel.

Yes a 1996 CA supreme court decision made it this way according to wiki.

https://en.m.wikipedia.org/wiki/California_State_Lottery

Quote: tringlomane

Yes a 1996 CA supreme court decision made it this way according to wiki.

https://en.m.wikipedia.org/wiki/California_State_Lottery

Thanks. For the benefit of others, the thinking is that the state should have no interest in the outcome of a lottery game and that players should only play against themselves and not the lottery itself.