Zcore13
Joined: Nov 30, 2009
• Posts: 3649
May 1st, 2015 at 1:03:48 PM permalink
I was recently told by a game inventor that the chances of winning at least something (maybe not a net profit, but something back from original wagers) on a game was 70+%. I can't figure out how to figure out the math on it. Some people will win bet 1 but not 2 or 3. Some will win bet 3 but not 1 or 2. I don't think you add the three percentages and divide by 3.

So if the following is true:

Bet 1 - 48.93% hit frequency
Bet 2 - 24.79% hit frequency
Bet 3 - 19.72% hit frequency

Is there an answer to this with just this limited information??

ZCore13
I am an employee of a Casino. Former Table Games Director,, current Pit Supervisor. All the personal opinions I post are my own and do not represent the opinions of the Casino or Tribe that I work for.
ThatDonGuy

Joined: Jun 22, 2011
• Posts: 4744
May 1st, 2015 at 2:57:02 PM permalink
There's no way of knowing without knowing exactly how the three bets work.

How is it possible for some people to win bet 3 but not 1 or 2, and some people to win bet 1 but not 2 or 3?
Are these two groups of people involved in two entirely different bets?
Is it possible to win more than one bet at a time?

If the three bets are entirely different things - i.e. there is no chance to win two or three bets at the same time - then the probability of winning "something" is the sum of the three, or 93.44%.

The easiest way to explain it: suppose you're playing a 4-digit daily lottery, where you choose one of the 10,000 numbers from 0000 to 9999.
"Bet 1" wins if the winning number is anywhere from 0001 to 4893 - a 48.93% chance.
"Bet 2" wins if the winning number is anywhere from 4894 to 7372 - a 24.79% chance.
"Bet 3" wins if the winning number is anywhere from 7393 to 9344 - a 19.72% chance.
You win one of the three bets if the number is anywhere from 0001 to 9344 - a 93.44% chance.

Your question about winning "at least something" reminds me of a mass mailing scam that I haven't seen in a while, where you are guaranteed one of four prizes - usually something like a new car, \$5000 cash, a trip to somewhere in Europe, and a \$250 gift certificate which turns out to be good only on cheap knockoff luggage which you can probably find for \$10 if you look hard enough, but the scam lists as "normally \$400, but it's only \$150 after you apply your gift certificate".
One company figured that everybody got wise to this, so they put a spin on it, and the postcards started saying that you won TWO prizes from the list.
It didn't say that you would win two different prizes; pretty much everybody ended up with two gift certificates. At least they were honest about the odds; California law says that they have to put the odds of winning each prize on the postcard, and it said that the odds of winning the gift certificate were "2 in 1".
Zcore13
Joined: Nov 30, 2009
• Posts: 3649
May 1st, 2015 at 3:12:59 PM permalink
Yeah, I didn't think just the hit frequencies were enough. Players can win any combination of the three bets. None, one of any of them, two out of three or all. The three bets are independent of each other, but all three are mandatory.

ZCore13
I am an employee of a Casino. Former Table Games Director,, current Pit Supervisor. All the personal opinions I post are my own and do not represent the opinions of the Casino or Tribe that I work for.
charliepatrick
Joined: Jun 17, 2011
• Posts: 2362
May 1st, 2015 at 3:44:41 PM permalink
Some UK fruit machines have a reasonable chance of something back, but they do this by having (say) a bet of 50p and offering prizes of 5p, 10p etc. In the US they can do a similar idea by having multiple lines (say on a three reel machine, playing middle line, top/bottom line, each cross line).

If your case I'm guessing it could be Bet 1 is same colour, Bet 2 is same suit, Bet 3 (not sure as 1/5th!).
or (I haven't done the maths but think Three-Card poker, winner takes all)
Bet 1 - suppose you were playing a simple game where the dealer has a slight advantage and wins if you beat the dealer (assuming there is a tie break mechanism or low chance of a tie).
Bet 2 is your first card matches the dealer's upcard (or something similar such as three cards the same colour where p~=1/4).
Bet 3 is (no idea) but might be pair plus like concept.

This is why people like 3-card - although the pair-plus has a relation to the basic game, the prime (colours match) doesn't (except flush=colours match).
ThatDonGuy

Joined: Jun 22, 2011
• Posts: 4744
May 1st, 2015 at 8:24:37 PM permalink
Quote: Zcore13

Yeah, I didn't think just the hit frequencies were enough. Players can win any combination of the three bets. None, one of any of them, two out of three or all. The three bets are independent of each other, but all three are mandatory.

Actually, if they are independent, then you can.

Bet 1 has a 51.07% chance of losing
Bet 2 has a 75.21% chance of losing
Bet 3 has a 80.28% chance of losing
If they are independent, then the chance of all three losing is 0.5107 x 0.7521 x 0.8028 = about 0.3084, or 30.84% and the chance of winning at least one of them is 100% - 30.84% = 69.16%
Zcore13
Joined: Nov 30, 2009
• Posts: 3649
May 2nd, 2015 at 12:22:14 AM permalink
Quote: ThatDonGuy

Actually, if they are independent, then you can.

Bet 1 has a 51.07% chance of losing
Bet 2 has a 75.21% chance of losing
Bet 3 has a 80.28% chance of losing
If they are independent, then the chance of all three losing is 0.5107 x 0.7521 x 0.8028 = about 0.3084, or 30.84% and the chance of winning at least one of them is 100% - 30.84% = 69.16%

Well then maybe the guy was right. He said 70% chance of winning at least one.

ZCore13
I am an employee of a Casino. Former Table Games Director,, current Pit Supervisor. All the personal opinions I post are my own and do not represent the opinions of the Casino or Tribe that I work for.
beachbumbabs
Joined: May 21, 2013
• Posts: 14232
May 2nd, 2015 at 12:33:14 AM permalink
I just did a game where you could win any 1 of three bets, any 2, or all 3, and the overall hit rate for at least a partial was 64%. So it can be done.
If the House lost every hand, they wouldn't deal the game.
Joined: Feb 24, 2011
• Posts: 2225
May 9th, 2015 at 7:45:06 AM permalink
Z, do you think from a player's perspective, winning something, but still net losing on a hand is a good design feature? I would think that it would be more difficult to record a "net win" for any one seesion in a game designed that way. Wouldn't players would walk away a loser at the game more often than a 42% hit rate type game.....but I would have to have a brighter math mind than me determine that distribution.

Maybe that is OK as regular players expect to lose, but I would be turned off from a game I never felt I could win at, net. In fact I have started to avoid UTH and play more BJ just based on my recent negative volatility at UTH.....I just can't seem to get up at that game anymore, but BJ has been delivering some winning sessions.
MathExtremist
Joined: Aug 31, 2010
• Posts: 6526
May 9th, 2015 at 7:49:08 AM permalink

Z, do you think from a player's perspective, winning something, but still net losing on a hand is a good design feature?

Roulette has worked this way for hundreds of years...
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
EvenBob
Joined: Jul 18, 2010
• Posts: 24834
May 9th, 2015 at 12:44:03 PM permalink
Quote: MathExtremist

Roulette has worked this way for hundreds of years...

Yup. People spread \$40 around the board
and win \$25 and act like they've
accomplished something.
"It's not enough to succeed, your friends must fail." Gore Vidal