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Texas Two Step Odds

cope's avatar - usconstitution

Lets say I play every Bonus Ball number (35 tickets total).

 

Then, I QP the White Balls for all 35 tickets.

 

The Bonus Ball drawn is 21.

 

I have a ticket with the winning Bonus Ball, but I QP'd the White Balls.

 

So, what are the odds of having the four winning White Balls on the ticket with Bonus Ball 21?

 

Is it still 1:53,900?

 

Here is the chart:

 

 

I know I would lose money by playing that way, but I am just curious about the odds.

 

Thanks.

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In response to cope

After re-reading, I believe I know what you're asking.  The odds of having the four winning white ball numbers in the same line as the bonus ball number 21 are 1:1,832,600.  The odds of having the four winning white ball numbers in one line somewhere on your tickets would be 35:53,900 (assuming the machine didn't give you any duplicate lines).

The answer I think you're looking for is like this: If the bonus ball were drawn first, and it was 21, and you had one line with a 21 bonus ball number, then, after that, and before the drawing of the white balls, you would have a 1:53,900 chance of matching all of them.  This is simply the reverse of the actual conditions, wherein immediately after matching all four white balls you have a 1:35 chance of winning the jackpot.

johnph77's avatar - avatar

Or is the original poster questioning the actual odds published by the Texas Lottery, as I would? The math:

35x34x33x32 =1256640::1 -  four specific numbers from 1 to 35 drawn in exact order.

1256640/(1*2*3*4) = 52360::1 - four specific numbers from 1 to 35 drawn in any order. - This is slightly more generous than the 53,900::1 odds posted by the Texas Lottery and would be the answer to the original poster's query about a ticket with Bonus Ball 21, or, for that matter, any specific bonus ball from 1 to 35.

52360*35 = 1832600::1 - four specific numbers from 1 to 35 drawn in any order and one specific number from 1 to 35 - and these are the odds posted posted on the Texas Lottery website.

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In response to johnph77

I saw when I was writing that there was a small mathematical error, but I don't have a calculator that would make it easy to determine how many combinations of white ball numbers would exist.  Your post showed me that the simple way is to divide the jackpot odds by the number of bonus balls.

The odds of winning the second prize are 1:53,900.  This is a little bit harder than matching all four white ball numbers because you must match those numbers and also not match the bonus ball.  As you state, he odds of matching all the white ball numbers in one line are 1:52,360.

I realize now I didn't answer the actual question.  Cope asked: "So, what are the odds of having the four winning White Balls on the ticket with Bonus Ball 21?"  (I assume by "ticket" he's referring to a single line.)  The conditions given are that he has 35 lines, one with each bonus ball number, and all four numbers winning white ball numbers are in the one line.  In that case, the odds of the winning white ball numbers being in the same line any particular bonus ball are 1:35.  After we assume he beat the 1:52,360 odds with the first four numbers, he has a 1:35 chance of winning the jackpot, and those two numbers multiply to form the jackpot odds.

This is an interesting discussion.

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