Eight 30:1s in one shoe

What are the odds of eight 30:1s happening in a single shoe of Baccarat. For the sake of argument, let's say they were all on Player, giving the 30:1 the best chance of happening. Assume eight decks with a 16-card penetration.

Quote: Deucekies

What are the odds of eight 30:1s happening in a single shoe of Baccarat. For the sake of argument, let's say they were all on Player, giving the 30:1 the best chance of happening. Assume eight decks with a 16-card penetration.
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Is a "30:1" any 3 card 0 for the player vs any 3 card 1 for the banker, or are there other criteria that you are looking for?

Dieter,
A 30:1 is a dragon bonus. It can be and is equally paid on either side, B or P.

30:1 is any three card 9 versus the opposite side having a 0. Examples. Player returned a face/10 and bankers returned a 10/2. Players third card is a 9 bring the players to 9. Bankers third card is an 8. Players win 9 to 0. It will always have to be 3 cards on both sides.

The other dragon bonuses are:

10:1. One side winning by 8 points over the other. Has to be three cards both sides as well.
(The rest can be 2 cards or 3 cards both sides or 2 on one side and 3 on the other):
6:1. One side winning by 7 points over the other side.
4:1 One side winning by 6 points over the other side.
2:1 One side winning by 5 points over the other side.
1:1. One side winning by 4 points over the other side.

However some casinos also will do winning by 4 or 5 points pays out 2:1 and if they do that
they also do winning by 6 or 7 points pays out 4:1. Everything else the same.

Also, all naturals pay out 1:1
Also all natural ties the bonus hand will push.

As far as how many 30:1s in any shoe, it’s the same as trying to figure out how many fortune 7s. Personally I have seen anywhere from zero to a good half a dozen 30:1s in one shoe on. On a mean average there will be one or two in each shoe at the very best (as a mean norm).

I simulated 100 million shoes, and got this: (Note that this is counting both player and bank wins in a shoe)

8 wins: 1 / 9,090,909
7 wins: 1 / 729,927
6 wins: 1 / 51,733
5 wins: 1 / 4552
4 wins: 1 / 473.65
3 wins: 1 / 62.64
2 wins: 1 / 11.27
1 wins: 1 / 3.109

There are about 0.3 player 30-1s and 0.25 bank 30-1s per shoe.

Quote: Marcusclark66

Dieter,
A 30:1 is a dragon bonus. It can be and is equally paid on either side, B or P.
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Thanks for the clarification.

Quote: ThatDonGuy

I simulated 100 million shoes, and got this: (Note that this is counting both player and bank wins in a shoe)

8 wins: 1 / 9,090,909
7 wins: 1 / 729,927
6 wins: 1 / 51,733
5 wins: 1 / 4552
4 wins: 1 / 473.65
3 wins: 1 / 62.64
2 wins: 1 / 11.27
1 wins: 1 / 3.109

There are about 0.3 player 30-1s and 0.25 bank 30-1s per shoe.
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Thank you! That's exactly what I wanted to know, and you even went one step further by giving me the odds for eight 30:1s on either side.

Quote: Deucekies

What are the odds of eight 30:1s happening in a single shoe of Baccarat. For the sake of argument, let's say they were all on Player, giving the 30:1 the best chance of happening. Assume eight decks with a 16-card penetration.
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I'm assuming what you mean by a 30-1 is any 9-0 hand (where either side can have the 9), in which the Dragon Bonus pays 30 to 1.

The probability of a Player 9/Banker 0 is 0.003683066.
The probability of a Player 0/Banker 9 is 0.003079055
So, the probability of either is 0.006762121

For the sake of simplicity, let's say there are 81 hands per shoe, although the true number is closer to 80.884.

The probability of exactly eight 9-0 wins is 1 in 11,670,083.

The probability of eight or more 9-0 wins is 1 in 11,029,777.

The expected 9-0 wins per shoe is 0.547731813.

Compared to some other claims we've heard on this forum, this one is within the range of believability.

As a basis of comparison, this is like getting 10.4 yo's in a row.

Quote: Wizard

Quote: Deucekies

What are the odds of eight 30:1s happening in a single shoe of Baccarat. For the sake of argument, let's say they were all on Player, giving the 30:1 the best chance of happening. Assume eight decks with a 16-card penetration.
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I'm assuming what you mean by a 30-1 is any 9-0 hand (where either side can have the 9), in which the Dragon Bonus pays 30 to 1.

The probability of a Player 9/Banker 0 is 0.003683066.
The probability of a Player 0/Banker 9 is 0.003079055
So, the probability of either is 0.006762121

For the sake of simplicity, let's say there are 81 hands per shoe, although the true number is closer to 80.884.

The probability of exactly eight 9-0 wins is 1 in 11,670,083.

The probability of eight or more 9-0 wins is 1 in 11,029,777.

The expected 9-0 wins per shoe is 0.547731813.

Compared to some other claims we've heard on this forum, this one is within the range of believability.

As a basis of comparison, this is like getting 10.4 yo's in a row.
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I don’t believe any claim was made. I think Deucekies was just asking a question.

Quote: SOOPOO

I don’t believe any claim was made. I think Deucekies was just asking a question.
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Good point.

Don’t forget, you are not wagering only for a 30:1 to win to pay out, your one dragon bonus wager can and will be paid for 7 possible and all except for the 30:1 three card 9 against a zero, occurs quite often.

I heard third hand (at least) that this situation actually occurred in a cardroom in Washington with the strong accusation the shoe was rigged. Let me emphasize that this is just talk and to not believe everything you hear.

Quote: Wizard

I heard third hand (at least) that this situation actually occurred in a cardroom in Washington with the strong accusation the shoe was rigged. Let me emphasize that this is just talk and to not believe everything you hear.
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If the Wiz is referring to eight 30:1s, (3 card 9s players side over a bankers side of 0) in one shoe, I would 1,000,000 percent, it would very rarely happen.

I have seen 1, 2 and on occasion 3, 30:1s on one side in a shoe and another 1 or 2 at the most on the other side in the same shoe. Most shoes, 1 or 2. Sometimes zero as well.

But I was curious after thinking about this for a couple of days. I asked several of our multi-decade floor people working at our baccarat tables and every single one of them has said they never seen 8, 30:1s on one side in a baccarat shoe. About the highest number they can recall seeing was 5 maybe 6 and most importantly, not on one side.

Quote: Marcusclark66

I have seen 1, 2 and on occasion 3, 30:1s on one side in a shoe and another 1 or 2 at the most on the other side in the same shoe. Most shoes, 1 or 2. Sometimes zero as well.

But I was curious after thinking about this for a couple of days. I asked several of our multi-decade floor people working at our baccarat tables and every single one of them has said they never seen 8, 30:1s on one side in a baccarat shoe. About the highest number they can recall seeing was 5 maybe 6 and most importantly, not on one side.
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When I posed the question, I limited it to one side simply to make the math easier for whoever took it on. As it turns out, that wasn't necessary.

I was looking at your question from the live B&M casino reality aspect of it.