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.
link to original post

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.
link to original post

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.
link to original post

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.
link to original post

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.
link to original post

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.
link to original post

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.
link to original post

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.