# Keno odds question **URL:** \ **Category:** Factual Questions\ **Created:** [July 18, 2003, 5:23am UTC](https://boards.straightdope.com/t/keno-odds-question/189335 "2003-07-18T05:23:12Z")\ **Posts on this page:** 9\ **Page:** 1
**Author:** ![bubinski](https://avatars.discourse-cdn.com/v4/letter/b/4af34b/32.png) [@bubinski](https://boards.straightdope.com/u/bubinski)\ **Post date:** [July 18, 2003, 5:23am UTC](https://boards.straightdope.com/t/keno-odds-question/189335/1 "2003-07-18T05:23:12Z")
This is my first thread on this board, so I hope I have the correct forum, and my question is not inappropriate (sp?). Everyone probably is familar with Keno. My wife and I have an ongoing argument about the odds I hope someone can answer. Say out of 80 numbers you can pick a max of 10. The game draws 20 at random. If you pick 10 numbers, you must hit 4 out of 10 for a minumum win. If you pick only 7 numbers, you only need 3 hits for a minimum win. I say that picking 7 and hitting 3 out of 7 is better odds than picking 10 and hitting 4 out of 10. Remember, 80 numbers, 20 drawn. Whos is correct? My wife or myself ? Thanks, bubinski. ---
**Author:** ![ccwaterback](https://avatars.discourse-cdn.com/v4/letter/c/df705f/32.png) [@ccwaterback](https://boards.straightdope.com/u/ccwaterback)\ **Post date:** [July 18, 2003, 7:52am UTC](https://boards.straightdope.com/t/keno-odds-question/189335/2 "2003-07-18T07:52:06Z")
Without doing all the higher math, I would say whichever bet pays more has the least likely chance of winning. ---
**Author:** ![dnooman](https://avatars.discourse-cdn.com/v4/letter/d/839c29/32.png) [@dnooman](https://boards.straightdope.com/u/dnooman)\ **Post date:** [July 18, 2003, 8:24am UTC](https://boards.straightdope.com/t/keno-odds-question/189335/3 "2003-07-18T08:24:46Z")
You just said that you’re gambling, if there was a science to it then it wouldn’t be a game of chance. Slots have always been the “sucker’s bet” in Vegas, but last time I went there the only advice I ever got was “don’t play Keno, ever, It’s a sucker’s bet”. This is certainly not meant to cast aspersions on your game of choice, but I have to agree with the fact that if there’s NO playing involved, then you must be at the house’s mercy…otherwise that game would be banned from their casino. ---
**Author:** ![The\_Great\_Unwashed](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/the_great_unwashed/32/4791_2.png) [@The\_Great\_Unwashed](https://boards.straightdope.com/u/The_Great_Unwashed)\ **Post date:** [July 18, 2003, 11:00am UTC](https://boards.straightdope.com/t/keno-odds-question/189335/4 "2003-07-18T11:00:14Z")
Firstly, welcome to the boards, **bubinski**. Secondly, _Keno_ is certainly _not_ familiar to everyone on these boards, but [_Google_](http://www.google.com) should be. _Googling_ for _keno odds_, the [first hit](http://conjelco.com/faq/keno-odds.html) gives the probabilities as: P(3 from 7) = 0.1750 P(4 from 10) = 0.1473 so, I guess you were right. ---
**Author:** ![ltfire](https://avatars.discourse-cdn.com/v4/letter/l/7ea924/32.png) [@ltfire](https://boards.straightdope.com/u/ltfire)\ **Post date:** [July 18, 2003, 11:46pm UTC](https://boards.straightdope.com/t/keno-odds-question/189335/5 "2003-07-18T23:46:47Z")
Why would you bet on any game where the house knows your numbers going in, but you don’t know their numbers until they are drawn? :confused ---
**Author:** ![hobbes730](https://avatars.discourse-cdn.com/v4/letter/h/97f17d/32.png) [@hobbes730](https://boards.straightdope.com/u/hobbes730)\ **Post date:** [July 19, 2003, 12:26am UTC](https://boards.straightdope.com/t/keno-odds-question/189335/6 "2003-07-19T00:26:48Z")
AFAIK, no one has _ever_ hit the jackpot in the history of Keno. Supposedly, you’re more likely to die by rolling out of bed and breaking your neck some 20 times in a row than to hit the jackpot in Keno. How you die 20 times in a row is beyond me, but that’s what I’m told 🙂 ---
**Author:** ![yabob](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/yabob/32/2821_2.png) [@yabob](https://boards.straightdope.com/u/yabob)\ **Post date:** [July 19, 2003, 1:22am UTC](https://boards.straightdope.com/t/keno-odds-question/189335/7 "2003-07-19T01:22:32Z")
Once upon a time, when I was a grad assistant teaching freshman classes, I allowed them to figure the expected return on the keno games in the local bars as an extra credit assignment (I believe I made the payoff schedule for one popular watering hole available to students who did not want to conduct their research first hand). I was rather surprised at just how bad they turned out to be - the best choice card (I don’t remember how many spots) returned about $0.50 on the dollar. Some of them returned about $0.20. Gambling games do not need to be that terrible to make good money for the business running the game. They could have returned about $0.80 on the dollar and done just fine. But then again, people were fool enough to play the game with the payoff schedules as they were. Background - it’s an exercise in computing hypergeometrics, which is the reason I used it as an assignment. The obvious way to think about it is that the probability of drawing W winners from choosing S spots on the card when K numbers are drawn out of N is: C(K,W)\*C(N-K,S-W)/C(N,S) Where C(n,k) is the “combinations of k things chosen from n” = n!/(k!\*(n-k)!). N = 80, K = 20, S = 7 or 10, and W = 3 or 4 in the OP’s original problem. You’ll get the numbers given in TGU’s link. If they thought about what they were calculating, they could reduce their effort a good bit - for instance, treating the spots as the “distinguished” objects rather than the drawn numbers leads to a constant denominator (C(N,K)) for all of the cards. That actually occurred to a couple of them. That they could iteratively compute the P(0), P(1), P(2) answers by multiplying the previous result by a fraction computed from 4 values occurred to none of them. ---
**Author:** ![ccwaterback](https://avatars.discourse-cdn.com/v4/letter/c/df705f/32.png) [@ccwaterback](https://boards.straightdope.com/u/ccwaterback)\ **Post date:** [July 19, 2003, 1:34am UTC](https://boards.straightdope.com/t/keno-odds-question/189335/8 "2003-07-19T01:34:48Z")
[Hijack] I have heard blackjack has the best odds of any casino game. But after watching people hit an 18 when the dealer holds 16 (has to hit), I have to conclude: It’s not so much the odds of winning as how you play the game. [/Hijack] ---
**Author:** ![whatami](https://avatars.discourse-cdn.com/v4/letter/w/85f322/32.png) [@whatami](https://boards.straightdope.com/u/whatami)\ **Post date:** [July 19, 2003, 4:57am UTC](https://boards.straightdope.com/t/keno-odds-question/189335/9 "2003-07-19T04:57:03Z")
> [@](#): > > \*Originally posted by ccwaterback \* > \*\*[Hijack] > I have heard blackjack has the best odds of any casino game. But after watching people hit an 18 when the dealer holds 16 (has to hit), I have to conclude: It’s not so much the odds of winning as how you play the game. > [/Hijack] \*\* I was just in Vegas a couple of weeks ago and watched a guy split 2 10s against the dealers 19. I got up and left after that…