December 23rd, 2018, 07:43 PM  #1 
Newbie Joined: Dec 2018 From: IL Posts: 4 Thanks: 0  Probability in roulette for street bet
What is probability of winning in American roulette betting 3 numbers/street bet for 7 spins (or until win) vs betting one time on 21 numbers or 7 street bets at once? Please explain math behind your calculations. Thank you.
Last edited by skipjack; December 24th, 2018 at 01:34 PM. 
December 23rd, 2018, 09:07 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,747 Thanks: 2133 
What does "probability of losing" mean?

December 24th, 2018, 12:02 PM  #3 
Senior Member Joined: Sep 2015 From: USA Posts: 2,463 Thanks: 1340 
$p_0 = P[\text{slot is our pick}] = \dfrac{1}{38}$ $p = P[\text{slot is one of our 3 picks}] = 3p_0 = \dfrac{3}{38}$ $P[\text{we win with 3 number street bet in 7 spins}] = \sum \limits_{k=1}^7 (1p)^{k1}p = \dfrac{50076285717}{114415582592}\approx 0.43767$ $P[\text{we win with 21 number street bet on 1 spin}] = \dfrac{21}{38} \approx 0.552632$ Both these number match sim I think the moral of the story is to give the house the fewest opportunities to use their inherent advantage. 
December 24th, 2018, 01:48 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,747 Thanks: 2133 
For the 7 spins, how does that take into account the "or until win" stipulation?

December 24th, 2018, 01:49 PM  #5 
Senior Member Joined: Sep 2015 From: USA Posts: 2,463 Thanks: 1340  
December 24th, 2018, 04:44 PM  #6 
Newbie Joined: Dec 2018 From: IL Posts: 4 Thanks: 0 
Thank you guys. It looks like betting 7 times on street has less chances to win than betting on 7 streets at once. But what will happen if I continue to bet on single street after win? I can win more then once. I can win even 7 times in a row. How percentage will change? I’ve been told that betting on street 7 times is equals betting on 7 streets at once bet. And it seems logical since 3/38+3/38+3/38+3/38+3/38+3/38+3/38=21/38. But it is not the case here. I am far from mathematics so please for stupid questions. Last edited by skipjack; December 24th, 2018 at 09:02 PM. 
December 24th, 2018, 09:08 PM  #7 
Global Moderator Joined: Dec 2006 Posts: 20,747 Thanks: 2133 
The house edge is the same, regardless of how you bet. Hence your best strategy is not to bet.

December 24th, 2018, 10:33 PM  #8  
Senior Member Joined: Aug 2012 Posts: 2,326 Thanks: 717  Quote:
You have to factor in the free drinks, the entertainment, the feeling of wild abandon you get risking your money on a game of chance. You're on vacation, maybe you're in a state full of casinos, maybe your entire purpose of the trip is to gamble. As long as the individuals are using discretionary income, not the rent money, it's perfectly rational to gamble; even though the mathematical expectation is negative. If a computer wanted to decide whether it was rational for a given individual to gamble, could it do so? The computer could know everything about a person ... but it would not know whether this person is someone who enjoys gambling. And ... stay with me here ... enjoying gambling isn't correlated with anything else. [That point can be argued but I don't want to get sidetracked so grant me this]. In other words maybe you'd think people who like to drive cars fast (observable by speeding tickets) or have other highrisk habits, just grant me that "enjoys gambling" is orthogonal to all other traits. Therefore a datadriven machine learning algorithm could not find any statistical pattern to assign a probability that this person enjoys gambling. It's entirely subjective. I've been thinking lately about arguments that we are not computations and this is an interesting example.  
December 24th, 2018, 10:42 PM  #9  
Senior Member Joined: Aug 2012 Posts: 2,326 Thanks: 717  Quote:
So it's true that the mathematical expectation of casino gambling is negative. But it's perfectly rational to play; and for some people, it's the correct strategy.  
January 3rd, 2019, 07:02 PM  #10 
Newbie Joined: Dec 2018 From: IL Posts: 4 Thanks: 0 
Can anybody do math how the percentage will change if I will bet 7 times total? I mean to bet after a win.
Last edited by skipjack; January 3rd, 2019 at 07:18 PM. 

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bet, probability, roulette, street 
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