QUESTION--Playing Don't Four Set-Ups in Craps!

Dear forum members:

Here is my question to the distinguished members.

While playing the "Dont"--

If I wait for two fours to come up before a seven, is it true that the odds of a third Four coming up before a seven is only 3.7% (1/3 to the power of 3 = 1/27)?

If so, wouldnt I just wait for that set-up to occur and then go large with a "Dont Four" bet given these low odds of another four coming up before a seven?

Thank you in advance for your reply!

Eric

Depends when you're talking wanting to know the odds.

For arguments sake assume the shooter is just about to start his first roll and you ask what are the chances of (i) 4-4-7 or (ii) 4-4-4 (ignoring other numbers) then obviously P(4)=1/3 P(7)=2/3 so 4-4-7 = 1/3*1/3*2/3 and 4-4-4 = 1/3*1/3*1/3.

However if the question is given there have already been two fours (without a seven), i.e. "I have waited UNTIL two fours have happened", now what is the chance of 444 as opposed to 447 (given 44) - then the answer is 1/3. The next relevant number will either be a 4 or a 7.

Waiting for two fours, or anything else like the cocktail waitress bringing your coffee, doesn't affect the chances once YOU start to play - for YOU it is as if the shooter were making their first roll (other that you can't make a Pass or Don't Pass bet).

fwiw the same argument is used for asking whether after ten reds the chances of black increase - it doesn't (assuming a true wheel)!


As an aside - there is an argument if you suspect the dice are somehow loaded towards 4s (say there have been significantly more fours than expected) then there is a case for betting with 4s. However in casinos you can rest assured they check the dice quite thoroughly as they wouldn't want us to profit from any bias like that!

Classic gambler's fallacy argument. Please read The Truth about Betting Systems and be enlightened.

The chance of a four (or any other number) is exactly the same on every roll. Even if there were 10 fours in a row, the odds of another one being rolled would not change.

That being said, sometimes numbers hit more often than others but it isn't because there is any difference in the odds that one will be rolled...

Quote: emenke

Dear forum members:

Here is my question to the distinguished members.

While playing the "Dont"--

If I wait for two fours to come up before a seven, is it true that the odds of a third Four coming up before a seven is only 3.7% (1/3 to the power of 3 = 1/27)?

If so, wouldnt I just wait for that set-up to occur and then go large with a "Dont Four" bet given these low odds of another four coming up before a seven?

Thank you in advance for your reply!

Eric

Makes sense to me. I am gonna put a lot of money on this system next time I am in Las Vegas.

Thanks Charlie--Your answer is quite articulate and makes sense. Thank you.

Thanks Ron for your thoughts on this!