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December 23rd, 2018, 08:43 PM   #1
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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 02:34 PM.
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December 23rd, 2018, 10:07 PM   #2
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What does "probability of losing" mean?
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December 24th, 2018, 01:02 PM   #3
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$p_0 = P[\text{slot is our pick}] = \dfrac{1}{38}$

$p = P[\text{slot is one of our 3 picks}] = 3p_0 = \dfrac{3}{38}$

$P[\text{we win with 3 number street bet in 7 spins}] =

\sum \limits_{k=1}^7 (1-p)^{k-1}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.
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December 24th, 2018, 02:48 PM   #4
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For the 7 spins, how does that take into account the "or until win" stipulation?
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December 24th, 2018, 02:49 PM   #5
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Quote:
Originally Posted by skipjack View Post
For the 7 spins, how does that take into account the "or until win" stipulation?
I am interpreting that as I continue to spin until I win or I have spun a maximum of 7 times.
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December 24th, 2018, 05:44 PM   #6
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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 10:02 PM.
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December 24th, 2018, 10:08 PM   #7
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The house edge is the same, regardless of how you bet. Hence your best strategy is not to bet.
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December 24th, 2018, 11:33 PM   #8
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Quote:
Originally Posted by skipjack View Post
The house edge is the same, regardless of how you bet. Hence your best strategy is not to bet.
For some people, the correct strategy is to bet.

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 high-risk habits, just grant me that "enjoys gambling" is orthogonal to all other traits.

Therefore a data-driven 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.
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December 24th, 2018, 11:42 PM   #9
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Quote:
Originally Posted by skipjack View Post
The house edge is the same, regardless of how you bet. Hence your best strategy is not to bet.
It's perfectly rational to gamble. Many people derive pleasure and excitement from gambling. You have to factor that in. You go on vacation, perhaps to state like Nevada whose main industry is gambling. You stay in a hotel, you lounge by the pool, you have dinner, you go to the casino. You experience the thrill of putting your money at risk in a game of chance. The lights, the sounds, the free drinks. It's a hugely popular form of entertainment the world over as I'm sure you know.

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.
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January 3rd, 2019, 08:02 PM   #10
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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 08:18 PM.
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