keno side game

There is a side game based on keno numbers, called keno racing, that I would like to know the chances/odds for.

The game is based on (see rules below).
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. 'h' and 'h's' means horse and horses respectively
. 20 numbers 'drawn' from a pool of 80
. 12 h's total in a 'race'
. h 1 to h 8 are allocated 7 keno numbers, eg h 1 are keno numbers 1 to 7
. h 9 to h 12 are allocated 6 keno numbers, eg h 12 are keno numbers 75 to 80
. h with the most numbers drawn wins ***

*** there are no ties in this game, so the way to break ties is as follows:
h 1 beats all ties, h 2 loses a tie against h 1 only and wins against all other h's, all the way to h 12 which loses all ties.
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Odds are as follows:

h 1: $4.70 win (finish 1st) / $1.80 place (1st, 2nd or 3rd)
h 2: $5.50 / $2.00
h 3: $6.50 / $2.30
h 4: $7.50 / $2.70
h 5: $8.50 / $3.00
h 6: $9.50 / $3.20
h 7: $10.70 / $3.50
h 8: $12 / $3.60
h 9: $24 / $5.50
h 10: $26 / $5.70
h 11: $28 / $5.90
h 12: $30 / $6.20

'book' %'s are below:

win : ~123.06%
place : ~ 375.81% (or ~125.27% scaled back to a '1 outcome market')

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other info that may be helpful

see website below and then scroll down to pick 6 and pick 7, for the base probabilities, if needed.

https://wizardofodds.com/games/keno/

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I doubt it is beatable based on such a high 'house edge', but I would still like to know which is the 'best bet' and what the odds/chances for each outcome are.

thanks in advance, if you need anymore information to solve this i will try to provide it if i can

More info that may help with working out odds (maths hasn't been checked, so correct me if I am wrong):

Below is the maximum number of ties, but also includes ties that don't pay/matter***:

*** Ties that don't pay/matter are: ties that place a horse 4th or worse, according to the above post's rules.

nb: 'catch' = ball, which may be easier to understand, if you have never heard of catch before in terms of keno (like me, before these couple of posts)

7 Catch = 2 horse tie (from a possible 8 different horses)

6 Catch = 3 horse tie, (nb: 6 catch to 0 catch ties are possible for all 12 horses)

5 Catch = 4 horse tie (1 doesn't pay)

4 Catch = 5 horse tie (2 don't pay)

3 Catch = 6 horse tie (3 don't pay)

2 Catch^^^ = 10 horse tie (7 don't pay)

^^^: this is the minimum number needed to come 1st and 2nd via the above posts 'tie-break' rules

1 Catch### = 10 horse tie (9 don't pay)

###: this is the minimum number to come 3rd via the above post 'tie-break' rules

0 Catch = 9 horse tie (9 don't pay)

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sorry, after spending all this time typing it up I am not sure if this extra post was very helpful for anyone to work out the odds/chances for the original post, even if the above 'tie information' was correct (because I am not even certain if it is correct)

Okay, if I understand this properly.....

Horse 1 is spots #1-7
Horse 2 is #8-14
Horse 3 is #15-21
Horse 4 is #22-28
Horse 5 is #29-35
Horse 6 is #36-42
Horse 7 is #43-49
Horse 8 is #50-56

Horse 9 is #57-62
Horse 10 is #63-68
Horse 11 is #69-74
Horse 12 is #75-80

Is that so far correct?

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Like regular Keno, there are 80 possible numbers, and 20 balls are drawn. Yes?

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In order to determine which horse comes in first place, second place, third place, etc.......

Whichever horse (group segment, ie: 1-7 or 8-14 or 15-21 etc.) has the most hits is the winner. Whichever has the second most hits comes in second. Whichever has the third most amounts of hits is third....etc. Is this correct?

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In the event of a tie, the horse with a lower number (ie: Horse #1 is lowest) wins the tie.

Horse #1 beats Horse #2-12 in the event of a tie.
Horse #2 LOSES to Horse #1, but beats horses #3-12.
Horse #3 LOSES to Horse #1 & Horse #2, but beats horses #4-12.
....
Horse #11 LOSES to Horses #1-10, but beats Horse #12.

That is all in event of a tie.

So far correct? Okay, good.

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As far as payouts / how the game works.....how does it actually work? It looks like it's based on $1 bets...is this correct? Are your options either to bet on a horse to WIN (1st place only) and the other option is to bet a horse will PLACE (come in 1st, 2nd, or 3rd)?

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I'm really confused as to what this means:

Quote:

win : ~123.06%
place : ~ 375.81% (or ~125.27% scaled back to a '1 outcome market')

Can you explain that a bit more?

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Is this a progressive or something? If it's just a regular slot / keno machine.....I very highly doubt any of the bets will be +EV (why would they do that?). Not that it hasn't ever happened before, where a casino puts in a game with messed up math / paytables on it.....but that just seems kind of odd....

Long response got eaten. "Place" is 1st or 2nd, not 1-2-3. In horse racing, anyway.

Quote: beachbumbabs

Long response got eaten. "Place" is 1st or 2nd, not 1-2-3. In horse racing, anyway.

Yes and no.

In some markets a horse "Placing" is determined by the number of horses running and could be 1st, 2nd, 3rd, or 4th depending on the size of the field. We tend to Americanize everything.

BTW, going on my annual trip to Del Mar for the races next week. I always expect to lose because my only handicapping knowledge comes from Sigma Derby.

The best bet is for Horse 4 to Win at 82.686% return.
The worst bet is for Horse 2 to Show at 78.630% return.

In short: don't play.

Quote: CrystalMath

The best bet is for Horse 4 to Win at 82.686% return.
The worst bet is for Horse 2 to Show at 78.630% return.

In short: don't play.

How'd you figure it out?

I wrote a program which went through all possible number of catches on each horse and calculated the probability of each event.

Sorry for the really long wait for my reply, thanks everyone for your posts.

I get sick a lot and I haven't been on this site for about 3+ months.

Reply to RS

"As far as payouts / how the game works.....how does it actually work? It looks like it's based on $1 bets...is this correct? Are your options either to bet on a horse to WIN (1st place only) and the other option is to bet a horse will PLACE (come in 1st, 2nd, or 3rd)"

Yes, it is based on a $1.00 bet

Yes, you can bet on the Win or the Place at the same time, or you can bet on just one of them.

There are other options like Exotics, but they don't tell you the payouts for those, or if they did, it was just a range of Odds, eg it may have been $50*** to $100,000*** for Trifecta's.

***: This was just the odds that I made up for illustrative purposes, so they are probably not the correct ones for the Exotic bets (like Trifecta's)

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" I'm really confused as to what this means:
Quote:
win : ~123.06%
place : ~ 375.81% (or ~125.27% scaled back to a '1 outcome market')"

This is similar to 'house edge' or 'EV', when it is greater than 100% it is in the houses favour, and when it is less than 100% it is in the players favour.

so for the win ,123% means, on average every $123 a player invests, he/she would expect to lose $23

and for the place, 375% means, on average every $375 a player invests, he/she would expect to lose $75

since there are 3 combinations that can place, you divide 375% by 3, to get the 'Easier' house edge, which is about 125% (so every $125 a player invests they should expect to lose $25)

NB: 375/300 = 125/100 = 125%

I just realised that the way I had written 'scaled back to a 1 outcome market' may have been a bit confusing, I should have written ' scaled to a 100% market'.

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All the other queries you asked and answered yourself seem to be correct.

Would be great if you can give us more details about that keno game. Right now the only keno that I know is the average keno that you can see on some casino. I just caught my attention when you mentioned keno racing.