Spanish 21 & Super 7 Bonus

[V-man]

Friend of mine was playing at a local casino, she played Spanish 21 and at one time she had 2 bets each $25 on the table and miracle happen: one of her hand got 3 suited 7 (diamond) and dealer shows a 7 spade! This is one of the very rare event in Spanish 21. Since she bet $25, she got the super 7 bonus $5000 and everyone at the table got each $50. How nice!

How rare is this event? I asked many dealers and all of them never seen this before!

 

[The Mayor]

In a shoe game (at blackjack):

first 7 (any): 24/312
second 7 (same suit): 5/311
third 7 (same suit): 4/310
dealer 7 (any): 21/309

The probability of this event is: (24*5*4*21)/(312*311*310*309) = .00000108449

Thus, this event is 922,091 to 1.

--Mayor

 

[Ed Tice]

Here is a quick calculation (somebodz will correct me if I get it wrong, Im sure).

Assuming six deck shoe, first deal (of course the chance changes as you deal into the deck)

1/13 chance of getting a 7 on the first card. After that chance is 5/311 of getting a second suited seven. After that a chance of 4/310 of getting the third suited seven.

So I dont have a calculator here, but estimating we hae 1/10 x 1/60 x 1/75 = 1/45000.

If I made an arithmetic mistake someobdy will point it out to me.

1/45000 is not so rare when you consider that 5 hands are dealt on average at once equals one out of every 9000 deals. So if you are getting 100 deals per hour, it would be everz 90 hours. So a dealer ought to see it once every two weeks!

That actually seems too often to me, so check my numbers. I may have shifted a decimal somewhere.

Ed

 

[Sonny]

Re: You're right, just keep going!

> That actually seems too often to me, so check my numbers. I may have
> shifted a decimal somewhere.

Your numbers are right (thus far), but as you can see from the Mayor's post you simply forgot to include the probability of the dealer getting a 7 as well. In either case, your numbers for calculating the player's hand are still accurate.

-Sonny-

 

[V-man]

Actually the probability of this happening is alittle more due to the fact that Spanish 21 is dealt out of a deck without 10s.

Following your numbers:
first 7 (any): 24/288
second 7 (same suit): 5/287
third 7 (same suit): 4/286
dealer 7 (any): 21/285

one hand out of: (288*287*286*285)/(24*5*4*21) = 668382

For 8 decks, I got: (384*383*382*381)/(32*7*6*29) = 549188

Actually, the number is a little better than I thought. My local casino has 2 Spanish tables 8 decks, if dealing about 50 hands per hour (slow because table always crowded and many ploppies betting 'match the dealer' and dealer busy
handling this side bet). Assuming 2 tables, each 50 hands per hour, all 7 spots occupied, 20 hours a day (compensating for slow hours, table not full), 2*50*7*20 = 14000 hands per day. For the 8 decks, they should see this event every 549188/14000 = 39 days. This is happening more often than I thought (actually a lot more than I thought, but why no dealers ever seen this?)

Any other reason why?

 

[The Mayor]

I know I gave the numbers for BJ and not Spanish, because I thought more would be interested in the BJ numbers.

By the way, there is a count to beat the 7's bet on the BJ table -- but you need to be able to put down $25 on it (not $1 -- as in most places this is the limit).

It has been years since I ran this sim, but I think this is it...

In a shoe:
Count each non-7 as +1
Count each 7 as -12.

Make the $25 bet when the TC > 6

(roughly 32 non-7's dealt out off the top makes it an even bet).

--Mayor

 

[Ed Tice]

Re: You're right, just keep going!

You are correct so multiplying by the 21/309 ~ 1/15 a dealer should still see this at his/her table once every 30 weeks! Assuming that (s)he would be aware of it if it happened at an adjacent table that makes once every 10 weeks. Hardly something the delaer never saw unless (s)he was a newbie. Sounds like the dealer is told to say "I never saw that before" and think "...this month".

Ed