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something odd with the odds

Published:

Last Edited: December 17, 2004, 7:36 pm

The odds in a 5/39 game are 1:575,757 right? Well I surfed over to West Virginia's official lottery website last night and noticed their odds were 1:607,744 for matching 5of5 in the Hot Lotto game. 5/39 with 19 bonus balls. Those odds excluded the bonus ball. I went back tonight just to make sure. Are the odds in WV computed different than in other states:-? Someone please tell me cause it don't compute to me.
Entry #2

Comments

1.
johnph77Comment by johnph77 - December 18, 2004, 12:51 am
Your figures are correct. No idea where WV got theirs.
2.
ayenowitallComment by ayenowitall - December 18, 2004, 9:08 am
Your odds for a 5/39 game are correct, BUT the 5/39 matrix of the Hot Lotto game cannot be viewed in isolation from the fact that it is linked to a 1/19 matrix. You have to account for the fact that there is a 1 in 19 (18 to 1) chance that a player will also have the bonus ball if he matches 5 of 5. Those odds of matching the bonus ball are working against matching just 5 of 5. 18 to 1 odds = 0.0555555555555555555555555555555556 . Multiply that times the 5/39 odds of 575,757 and you get 31,986.5 (the increase in the odds against matching 5 of 5) . Add the 31,986.5 to 575,757 and you get 607,743.5 . PRESTO!!! That's the 607,744 odds rounded up, and those are the correct odds of matching 5 of 5 in the Hot Lotto game. You can check the Hot Lotto page of the Multi State Lottery Association and the pages of all the other Hot Lotto states. They're the same odds on all of them. I hope this helps you understand what seems odd about the odds.
3.
waynrComment by waynr - December 18, 2004, 11:31 am
No ayenowitall it still doesn't make sense to me. Guess I'd have to see the actual draw to figure out how separate ball sets affect each others' odds. It's really not that important though. I thought it was odd enough to mention. Thanks for trying to clear it up. Looks good on paper, but when they(WV) exclude the bonus ball from the stated odds don't know any way but to view it in isolation.
4.
waynrComment by waynr - December 18, 2004, 1:28 pm
Okay I've thought about it a little more now. It looks like a mix of tangible and intangible odds. In other words I can buy all 575,757 combinations and say 5of5 guaranteed pre draw. I can't buy 607,744 pre draw and say 5of5 guaranteed. Funny.
5.
ayenowitallComment by ayenowitall - December 18, 2004, 9:46 pm
It's simply a matter of accounting for the possibility that you'll have 5 of 5 WITH a bonus ball as opposed to having ONLY 5 of 5 WITHOUT matching the bonus ball. I know it seems weird because the first time I noticed something like that about a dual matrix game, it didn't seem right to me either. Did you happen to notice that the odds of having just the bonus ball from the 1/19 matrix are about 1:39 instead of 1:19? It's the same thing at work because you have to account for the fact that you might also match some numbers from the 5/39 matrix. Again, it's a matter of the difference in matching ONLY the bonus ball as opposed to matching the bonus ball WITH OR WITHOUT any number(s) from the 5/39 matrix.
This would have been a good topic to raise in the Mathematics forum. It's something that most people don't understand about the odds in a dual matrix game. Thanks for giving me a chance to refresh my own memory and thinking about this.
6.
waynrComment by waynr - December 19, 2004, 12:53 am
It is a bit of a math twister to figure out. I've got a better grip on it now, but don't yet see any practical use far as playing goes. Actually to guarantee ONLY a 5of5 match the same number of combinations would have to be played as those needed to guarantee a 5of5 with the bonus ball. What threw me on this was the 31,987 extra combos. What are they? So basically the whole field of 575,757 with bonus ball #1 assigned to each combo would represent the 607,744 figure, but only after the draw IF #1 were not the bonus ball. Feel free to go to the math forum with it. Think I'll just fool around with this blog thing and see what happens.
7.
ayenowitallComment by ayenowitall - December 19, 2004, 3:58 am
waynr, while there are 575,757 combinations in the 5/39 matrix, the 31,987 (actually 31,986.5) represents the increase in the odds effected by the 1/19 matrix rather than an absolute number of additional combinations.
8.
waynrComment by waynr - December 19, 2004, 11:09 am
Thanks johnph77 for your comment and ayenowitall for the update on the math. I skipped the bonus ball games without even a glance when I chunked Lotto and went to a strictly 5 ball game. Never even considered how two ballsets would interact oddswise. May be a sorry excuse for ignorance, but I try to stay focused on what I think I can win that is closest to reality.

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