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## Poll

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**11 members have voted**

As always, I welcome all questions, comments, and corrections.

The question for the poll is which of the 5 Treasures bets would you make?

Quote:SM777What is the house edge of Coverall? It pays 6-1 if any of them hit in a given hand.

Thanks. I didn't know that. I'm getting a house edge of 2.97%.

Quote:WizardThanks. I didn't know that. I'm getting a house edge of 2.97%.

Not bad. Very reasonable.

The others, not so much.

I guess I don't understand the difference between these two sidebets:

Fortune 7 — Wins if the Banker has winning 3-card total of 7. Pays 40 to 1.

Blazing 7s — Wins if the Player or Banker have a three-card total of 7. Pays 200 to 1 if both do and 50 to 1 if one does.

It seems that any time the Fortune 7 wins, the Blazing 7s would also win, since the dealer would have a 3-card 7, and in that case the F7 pays 40, while the B7 pays 50 (or 200 if the Player also has a 3-card 7). However, the B7 would ALSO win if only the Player has a 3-card 7. Given this, I expected the B7 to have a much lower house edge than the F7, but your numbers say otherwise.

What am I missing?

Also, the wording on your F7 return table, "Player or Banker both have 3-card 7s", is unclear.

Dog Hand

Quote:DogHandWiz,

I guess I don't understand the difference between these two sidebets:

Fortune 7 — Wins if the Banker has winning 3-card total of 7. Pays 40 to 1.

Blazing 7s — Wins if the Player or Banker have a three-card total of 7. Pays 200 to 1 if both do and 50 to 1 if one does.

It seems that any time the Fortune 7 wins, the Blazing 7s would also win, since the dealer would have a 3-card 7, and in that case the F7 pays 40, while the B7 pays 50 (or 200 if the Player also has a 3-card 7). However, the B7 would ALSO win if only the Player has a 3-card 7. Given this, I expected the B7 to have a much lower house edge than the F7, but your numbers say otherwise.

What am I missing?

Also, the wording on your F7 return table, "Player or Banker both have 3-card 7s", is unclear.

Dog Hand

With the Fortune 7 the Banker has to win with the three-card 7. In Blazing 7s, it doesn't matter if the 7 wins, loses, or ties.

I'll try to clarify that table title.

Quote:WizardWith the Fortune 7 the Banker has to win with the three-card 7. In Blazing 7s, it doesn't matter if the 7 wins, loses, or ties.

I'll try to clarify that table title.

Wiz,

If the Banker has a winning 3-card 7, then both the F7 bet and the B7 bet win, right? That's the only time the F7 wins, but the B7 also wins if the Banker has a losing 3-card 7, or if the Player has a 3-card 7... right? If that is so, explain how the F7 probability is LARGER than the B7 probability: your tables show the F7 prob as 0.022534, but the B7 prob as only 0.002312.

Dog Hand

Quote:DogHandIf the Banker has a winning 3-card 7, then both the F7 bet and the B7 bet win, right?

Yes.

Quote:That's the only time the F7 wins, but the B7 also wins if the Banker has a losing 3-card 7, or if the Player has a 3-card 7... right? If that is so, explain how the F7 probability is LARGER than the B7 probability: your tables show the F7 prob as 0.022534, but the B7 prob as only 0.002312.

The 0.002312 is the probability of the Player AND Banker having a 3-card 7. If only one side has it, with probability 0.008971, it pays less. The F7 probability is greater than the sum of 0.008971 and 0.002312.

Quote:WizardYes.

The 0.002312 is the probability of the Player AND Banker having a 3-card 7. If only one side has it, with probability 0.008971, it pays less. The F7 probability is greater than the sum of 0.008971 and 0.002312.

I think this is the point of confusion. The Blazing 7 pays more (50-1) for, what appears to be more possible winning states (Banker OR Player with 3 card total of 7; win not required) than the Fortune 7 that only pays 40-1 for a specific state (Banker 3 card win with total 7).

Quote:AyecarumbaI think this is the point of confusion. The Blazing 7 pays more (50-1) for, what appears to be more possible winning states (Banker OR Player with 3 card total of 7; win not required) than the Fortune 7 that only pays 40-1 for a specific state (Banker 3 card win with total 7).

I just put the ANDs and ORs in the return tables in all caps, to hopefully make it more clear.

Quote:WizardQuote:AyecarumbaI think this is the point of confusion. The Blazing 7 pays more (50-1) for, what appears to be more possible winning states (Banker OR Player with 3 card total of 7; win not required) than the Fortune 7 that only pays 40-1 for a specific state (Banker 3 card win with total 7).

I just put the ANDs and ORs in the return tables in all caps, to hopefully make it more clear.

My suggestion is to clarify this condition in the Blazing 7's Return Table:

"Player OR Banker both have a 3-card total of 7"

Should it read, "Player OR Banker both have a 3-card total of 7"?

But what I'm not understanding is how what appears to be a rarer event, a Banker 3 card win with a total of 7 (the Fortune 7), pays less than what appears to be a more common event, Banker or Player with a 3 card total of 7 (no win required). Maybe a more detailed explanation would clear this up.

Ok, I fired up my Baccarat CA Excel Workbook and ran the numbers for the Fortune 7 and Blazing 7s sidebets:

Fortune 7 | |||
---|---|---|---|

Result | Pays | Prob | Return |

Banker Winning 3-Card 7 | 40 | 0.0225338208603795 | 0.901352834 |

Lose | -1 | 0.9774661791396210 | -0.977466179 |

-0.076113345 | |||

Blazing 7s | |||

Result | Pays | Prob | Return |

BOTH Player AND Banker have a 3-card total of 7 | 200 | 0.0023119431243010 | 0.462388625 |

EITHER Player OR Banker has a 3-card total of 7 | 50 | 0.0699803501386726 | 3.499017507 |

Lose | -1 | 0.9277077067370260 | -0.927707707 |

3.033698425 | |||

By the way, you were victimized once again by the 15-digit limitation in Excel: note that when you sum your "Combinations", you don't get the precise "Total": the last digit is off.

We are in agreement on the Fortune 7 sidebet.

In particular, I found these probabilities related to the Blazing 7s:

Player has 3-card 7 0.0387636398899887

Banker has 3-card 7 0.0335286533729849

Notice I changed the wording on the B7 table (to "BOTH Player AND Banker have a 3-card total of 7" and "EITHER Player OR Banker has a 3-card total of 7") to reflect my understanding of the payouts.

Clearly, I have misinterpreted the payouts for the Blazing 7s sidebet… or the company marketing it has erred tremendously. What did I do wrong?

Dog Hand

Do U know who the distributor/inventor for this side bet is? Do you have a picture of the layout?

Quote:DogHandWiz,

Ok, I fired up my Baccarat CA Excel Workbook and ran the numbers for the Fortune 7 and Blazing 7s sidebets:

Clearly, I have misinterpreted the payouts for the Blazing 7s sidebet… or the company marketing it has erred tremendously. What did I do wrong?

Dog Hand

I just don't agree with your probabilities for the Blazing 7's. There is no easy way to prove yours are wrong or mine are right, as it is a matter of cycling through millions of combinations.

Quote:WizardI just don't agree with your probabilities for the Blazing 7's. There is no easy way to prove yours are wrong or mine are right, as it is a matter of cycling through millions of combinations.

Wizard,

I see you have changed the wording on the B7 return table: I think the new wording is much clearer.

Let me try one more time to clarify my question about your numbers. On the F7 table, you list the probability that the Banker has a winning 3-card 7 as 0.022534: I agree with this value.

However, on the B7 table, you list the probability that the Banker or the Player has a 3-card 7 as only 0.008971.

How can the probability that "the Banker or the Player has a 3-card 7" be less than the probability that "the Banker has a winning 3-card 7"?

Dog Hand

P.S. Maybe some of our other posters can chime in this as well.

I have the long numbers somewhere but knocked up an infinite deck analysis. These figures are very close to those above.Quote:DogHand...

In particular, I found these probabilities related to the Blazing 7s:

Player has 3-card 7 0.0387636398899887

Banker has 3-card 7 0.0335286533729849

I got 14385/371293 (0.038743) for the chances of the Player getting a 3-card 7.

As to the Dealer, I get 161805 of 371293 hands the dealer will take a 3rd card. Since the chances of a getting the correct card to get to a total of 7 are 1/13 then the probability the Dealer gets a 3-card 7 = 161805/371293/13 = 0.033522.

I get the times the dealer is drawing a 3rd card when the player has a 3C7 is 11169 of 371293, thus P(both 3C7) = 11169/371293/13 = 0.002314.

Similarly (by spreadsheet) the times either party get a 3C7 is 337641/4826809 = 0.069951.

Thus I get if the top payout is 200/1, a possible low payout could be 5/1 (or 6/1). Personaly I prefer 100/1 and 10/1 which gives a reasonable House Edge and is easy to remember.

When I first read the wizard page I saw that the chances of either party getting a 3C7 was likely to be larger than one particular party winning with a 3C7; so also tend to agree with the above interpretation.

Quote:DogHandWizard,

I see you have changed the wording on the B7 return table: I think the new wording is much clearer.

Let me try one more time to clarify my question about your numbers. On the F7 table, you list the probability that the Banker has a winning 3-card 7 as 0.022534: I agree with this value.

However, on the B7 table, you list the probability that the Banker or the Player has a 3-card 7 as only 0.008971.

How can the probability that "the Banker or the Player has a 3-card 7" be less than the probability that "the Banker has a winning 3-card 7"?

Dog Hand

You're absolutely right. My math was right, but I was lazy in the write-up of the page, my least favorite part of the job. It should have said that the big win is if both the player have 3-card totals of 7, and the small win is if they both have a 2-card total of seven. Thank you for the correction.

Quote:WizardYou're absolutely right. My math was right, but I was lazy in the write-up of the page, my least favorite part of the job. It should have said that the big win is if both the player have 3-card totals of 7, and the small win is if they both have a 2-card total of seven. Thank you for the correction.

Wizard,

Ok, I get the same values as you have on the B7 sidebet.

Let me make two small recommendations for your webpage.

First, you wrote: "Blazing 7s — Wins if the Player or Banker both have a three-card total of 7 composed of the same number of cards. Pays 200 to 1 if both hands are composed of three cards and 50 to 1 if both hands are composed of two cards." I would suggest deleting the phrase "three-card" from the first sentence.

Second, check the Combination numbers: they don't quite add up, probably due to Excel giving only 15 significant figures on integers. For example, on the Fortune 7 table, the Combinations for winning (112,633,011,329,024) and losing (4,885,765,264,174,340) don't add up to the total of 4,998,398,275,503,360. The problem is that the losing Combinations should be 4,885,765,264,174,336, with 16 significant figures.

Hope this helps!

Dog Hand

Quote:DogHandFirst, you wrote: "Blazing 7s — Wins if the Player or Banker both have a three-card total of 7 composed of the same number of cards. Pays 200 to 1 if both hands are composed of three cards and 50 to 1 if both hands are composed of two cards." I would suggest deleting the phrase "three-card" from the first sentence.

You're absolutely right, just did.

Quote:Second, check the Combination numbers: they don't quite add up, probably due to Excel giving only 15 significant figures on integers. For example, on the Fortune 7 table, the Combinations for winning (112,633,011,329,024) and losing (4,885,765,264,174,340) don't add up to the total of 4,998,398,275,503,360. The problem is that the losing Combinations should be 4,885,765,264,174,336, with 16 significant figures.

I updated that losing combinations number, but you can find this problem all over the site in hundreds of games. Not much I can do about it until Excel can support more significant digits.

Quote:Wizard<snip>I updated that losing combinations number, but you can find this problem all over the site in hundreds of games. Not much I can do about it until Excel can support more significant digits.

Wizard,

If you don't mind using User Defined Functions (UDF's), the following website describes how you can perform Large Number Arithmetic in Excel:

http://www.tushar-mehta.com/misc_tutorials/project_euler/LargeNumberArithmetic.htm

Tushar's method will permit you to use integers in the range of +/-79,228,162,514,264,337,593,543,950,335 which should be sufficient ;-)

Two drawbacks:

1. These large numbers are represented as text, so if you try to use the large numbers directly in calculations, Excel automatically reverts to its 15-significant-figure limit (though, honestly, I doubt you'd notice the difference when calculating Probabilities between dividing by 4,885,765,264,174,340 as opposed to 4,885,765,264,174,336). If you REALLY want to use all the digits, you have to use the UDF's.

2. He doesn't give a division algorithm UDF.

Hope this helps!

Dog Hand

Quote:WizardWith the Fortune 7 the Banker has to win with the three-card 7. In Blazing 7s, it doesn't matter if the 7 wins, loses, or ties.

I'll try to clarify that table title.

"Blazing 7s — Wins if the Player or Banker have a three-card total of 7. Pays 200 to 1 if both do and 50 to 1 if one does."

Then Blazing 7s is much better than Fortune 7 simply because have higher pay( 1 pay 50) and yet it can be either BANKER or PLAYER. Am I missing something ?

a) P(T,3) vs B(T,7), PLAYER draw a 4, so final hand is P(T,3,4) vs B(T,7) 1 pay 200 or 1 pay 50 ?

b) P(T,T) vs B(T,7), PLAYER draw a 8, so final hand is P(T,T,8) vs B(T,7) loss 1 unit ?

c) P(T,T) vs B(T,2), PLAYER draw a 7 and BANKER draw a 5, so final hand is P(T,T,7) vs B(T,2,5) 1 pay 200 ?

d) P(T,2) vs B(T,2), PLAYER draw a 6 and BANKER draw a 5, so final hand is P(T,2,6) vs B(T,2,5), 1 pay 50 ?

Quote:ssho88Quote:WizardWith the Fortune 7 the Banker has to win with the three-card 7. In Blazing 7s, it doesn't matter if the 7 wins, loses, or ties.

I'll try to clarify that table title.

"Blazing 7s — Wins if the Player or Banker have a three-card total of 7. Pays 200 to 1 if both do and 50 to 1 if one does."

Then Blazing 7s is much better than Fortune 7 simply because have higher pay( 1 pay 50) and yet it can be either BANKER or PLAYER. Am I missing something ?

a) P(T,3) vs B(T,7), PLAYER draw a 4, so final hand is P(T,3,4) vs B(T,7) 1 pay 200 or 1 pay 50 ?

b) P(T,T) vs B(T,7), PLAYER draw a 8, so final hand is P(T,T,8) vs B(T,7) loss 1 unit ?

c) P(T,T) vs B(T,2), PLAYER draw a 7 and BANKER draw a 5, so final hand is P(T,T,7) vs B(T,2,5) 1 pay 200 ?

d) P(T,2) vs B(T,2), PLAYER draw a 6 and BANKER draw a 5, so final hand is P(T,2,6) vs B(T,2,5), 1 pay 50 ?

My understanding of the game is on the Blazing Sevens is, if both sides have a three card 7 then it's 200 to 1. If both sides have a 2 card 7 then it will pay 50 to 1. What is important to remember both sides have to have three cards or both sides have to have two cards. Not two on one and three on the other.

Either way it will always have to be a tie.

The confusion is coming from the "or" it's not either or but both must have a total of 7 (or a tie) 200 for three cards on both dealer and player hand, 50 for two cards on both player and dealer hand.

Quote:KINGBACC"Blazing 7s — Wins if the Player or Banker have a three-card total of 7. Pays 200 to 1 if both do and 50 to 1 if one does."

The confusion is coming from the "or" it's not either or but both must have a total of 7 (or a tie) 200 for three cards on both dealer and player hand, 50 for two cards on both player and dealer hand.

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I don't understand the question.