Chances of a number appearing over a series
April 14th, 2018 at 10:24:38 PM
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Hello all,
I was hoping someone could tell me what the chance of a number appearing is over a series of results. For example, think of a roulette wheel without a zero. The chance of any particular number appearing is 1/35, right? So what is the chance a particular number will appear in 2 spins, or 10? I just would like to know how to calculate that.
Thanks for any help.
I was hoping someone could tell me what the chance of a number appearing is over a series of results. For example, think of a roulette wheel without a zero. The chance of any particular number appearing is 1/35, right? So what is the chance a particular number will appear in 2 spins, or 10? I just would like to know how to calculate that.
Thanks for any help.
April 14th, 2018 at 10:41:26 PM
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It's 1 in 36. There are 36 numbers on the roulette wheel. The probability of the number not being selected is 35/36.
The probability a number will appear in 2 spins is:
1-prob(not showing up) = 1 - (35/36)^2 = 5.48%
The probability a number will appear in 10 spins is:
1- (35/36)^10 = 24.55%
With double zero roulette, the probability of the number not being selected is 37/38.
number shows up in 2 spins:
1-(37/38)^2=5.19%
number shows up in 10 spins:
1-(37/38)^10=23.41%
The probability a number will appear in 2 spins is:
1-prob(not showing up) = 1 - (35/36)^2 = 5.48%
The probability a number will appear in 10 spins is:
1- (35/36)^10 = 24.55%
With double zero roulette, the probability of the number not being selected is 37/38.
number shows up in 2 spins:
1-(37/38)^2=5.19%
number shows up in 10 spins:
1-(37/38)^10=23.41%
April 14th, 2018 at 10:52:54 PM
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Thank you so much! There's a new lottery game (astonishingly bad payoff) that is based on roulette. It returns $24 for a $1 single number bet. People were trying to figure out if playing 20 in a row was a good strategy or not.
April 14th, 2018 at 10:55:13 PM
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working this all out by hand can be fun and mistakes can happen.Quote: voxI just would like to know how to calculate that.
always check results with a calculator I say.
I use online calculator at times
http://vassarstats.net/binomialX.html
n=10
k=1
p=1/36
P: 1 or more out of 10
0.245506616101
you could do this too
n=10
k=0
p=1/36
P: exactly 0 out of 10
0.754493383899
subtract that from 1 for at least 1 success
this is for experiments where there are only 2 possible outcomes
success or failure
Binomial Probabilities
interesting
Sally
I Heart Vi Hart
April 15th, 2018 at 2:27:50 AM
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Jurisdiction??Quote: voxThank you so much! There's a new lottery game (astonishingly bad payoff) that is based on roulette. It returns $24 for a $1 single number bet. People were trying to figure out if playing 20 in a row was a good strategy or not.
April 15th, 2018 at 2:27:50 AM
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Jurisdiction??Quote: voxThank you so much! There's a new lottery game (astonishingly bad payoff) that is based on roulette. It returns $24 for a $1 single number bet. People were trying to figure out if playing 20 in a row was a good strategy or not.
April 15th, 2018 at 5:18:24 AM
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Ohio. It's called The Lucky One and it's drawn after every keno drawing, so something like once every four minutes.
April 15th, 2018 at 7:48:20 AM
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like hereQuote: voxOhio. It's called The Lucky One
https://www.ohiolottery.com/Games/The-Lucky-One#2
33.3% house edge
$10.95 average win over 20 games given a win
of course given a loss is a loss of $20
chance of 0 wins = 56.926%
(35/36)^20
at least 1 win = 1-(35/36)^20 = 43.074%
Sally
I Heart Vi Hart
April 15th, 2018 at 8:49:46 AM
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Quote: voxThank you so much! There's a new lottery game (astonishingly bad payoff) that is based on roulette. It returns $24 for a $1 single number bet. People were trying to figure out if playing 20 in a row was a good strategy or not.
24-1 payout on a 36 number wheel?
April 15th, 2018 at 10:08:17 AM
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You can also bet odd/even or high/low. The payout being 1 to 2 for a 25% edge.
Such creative bets.
Such creative bets.
It’s all about making that GTA
April 17th, 2018 at 10:08:16 PM
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That's even worse than I thought, Sally. Thanks for that. Keno is popular in bars here, displayed on TVs, so we get to talking about such things but none of us had the math skills to figure it out. Worse even than Keno. I won't be donating any money to that game, lol.
April 20th, 2018 at 2:38:38 PM
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Only replying here because it looks like the original poster got their answer.
Would either of you be able to show me the pen and paper calculations for an inside bet hitting in craps vs the 7?
Yes there are 6 ways to hit the 7, 5 ways for the 6 and 8 (each), and 4 was for the 5 and 9.
But what is it to say any of the 5, 6, 8, 9 hitting instead of the 7?
Is it as easy as 18 out of 36 for the inside numbers at 50% chance.
And then 6 out of 36 chance of the seven, for 16.66%?
Where I get lost is how to compare the probability of one as a group vs the seven
Sorry if that's confusing
Would either of you be able to show me the pen and paper calculations for an inside bet hitting in craps vs the 7?
Yes there are 6 ways to hit the 7, 5 ways for the 6 and 8 (each), and 4 was for the 5 and 9.
But what is it to say any of the 5, 6, 8, 9 hitting instead of the 7?
Is it as easy as 18 out of 36 for the inside numbers at 50% chance.
And then 6 out of 36 chance of the seven, for 16.66%?
Where I get lost is how to compare the probability of one as a group vs the seven
Sorry if that's confusing
April 20th, 2018 at 5:34:18 PM
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3 inside numbers per 7. You got it right.
When a rock is thrown into a pack of dogs, the one that yells the loudest is the one who got hit.
April 20th, 2018 at 9:13:42 PM
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18 ways an inside # can be rolledQuote: DialedN07But what is it to say any of the 5, 6, 8, 9 hitting instead of the 7?
Is it as easy as 18 out of 36 for the inside numbers at 50% chance.
And then 6 out of 36 chance of the seven, for 16.66%?
and 6 ways a 7 can be rolled.
so we are concerned about 24 ways only.
6/24 is the probability of getting not one of the 18 ways
that is 25%
so 75% for at least 1 of the 18 ways
how about at least 2 of the inside #s before a 7?
.75*.75=0.5625 (about 5 out of 9)
how about at least 3?
0.75^3=0.421875 (less than 4 out of 9)
one can take it from there
nice question
winsome johnny (not Win some johnny)
April 22nd, 2018 at 2:06:23 PM
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Quote: 7craps18 ways an inside # can be rolled
and 6 ways a 7 can be rolled.
so we are concerned about 24 ways only.
6/24 is the probability of getting not one of the 18 ways
that is 25%
so 75% for at least 1 of the 18 ways
how about at least 2 of the inside #s before a 7?
.75*.75=0.5625 (about 5 out of 9)
how about at least 3?
0.75^3=0.421875 (less than 4 out of 9)
one can take it from there
nice question
7Craps. Thanks!
Can I go full nerd for a second?
On a $15 table, I have $145-147 on the table on the come out and subsequent point shot.
If I hit two inside numbers and half all of my bets, I have between a $20 and $39 profit. (Call it $28 avg)
There is a 56% chance that I hit two of my numbers before the 7. BUT one seven out on the first roll wipes $146 off the table. I have to hit two inside numbers 5.22 times to make up for it (assuming no roll goes over two numbers before the 7.
What are the odds of hitting my 56% probability 5 or more times in a row?
*sorry, it makes sense to me. Sorry if O didn't explain it well!
April 22nd, 2018 at 4:43:17 PM
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at least 2 #sQuote: DialedN07There is a 56% chance that I hit two of my numbers before the 7.
here is a handy table
p = .75
q = .25
| X inside #s | prob X (p^X*q) | X or more #s | X or more #s |
|---|---|---|---|
| 0 | 0.25 | from X to 50 | (p^X) |
| 1 | 0.1875 | 0.749999575 | 0.75 |
| 2 | 0.140625 | 0.562499575 | 0.5625 |
| 3 | 0.10546875 | 0.421874575 | 0.421875 |
| 4 | 0.079101563 | 0.316405825 | 0.31640625 |
| 5 | 0.059326172 | 0.237304263 | 0.237304688 |
| 6 | 0.044494629 | 0.177978091 | 0.177978516 |
| 7 | 0.033370972 | 0.133483462 | 0.133483887 |
| 8 | 0.025028229 | 0.10011249 | 0.100112915 |
| 9 | 0.018771172 | 0.075084262 | 0.075084686 |
| 10 | 0.014078379 | 0.05631309 | 0.056313515 |
| 11 | 0.010558784 | 0.042234711 | 0.042235136 |
| 12 | 0.007919088 | 0.031675927 | 0.031676352 |
| 13 | 0.005939316 | 0.023756839 | 0.023757264 |
| 14 | 0.004454487 | 0.017817523 | 0.017817948 |
| 15 | 0.003340865 | 0.013363036 | 0.013363461 |
| 16 | 0.002505649 | 0.010022171 | 0.010022596 |
| 17 | 0.001879237 | 0.007516522 | 0.007516947 |
| 18 | 0.001409428 | 0.005637285 | 0.00563771 |
| 19 | 0.001057071 | 0.004227858 | 0.004228283 |
| 20 | 0.000792803 | 0.003170787 | 0.003171212 |
| 21 | 0.000594602 | 0.002377984 | 0.002378409 |
| 22 | 0.000445952 | 0.001783382 | 0.001783807 |
| 23 | 0.000334464 | 0.00133743 | 0.001337855 |
| 24 | 0.000250848 | 0.001002967 | 0.001003391 |
| 25 | 0.000188136 | 0.000752119 | 0.000752543 |
| 26 | 0.000141102 | 0.000563983 | 0.000564408 |
| 27 | 0.000105826 | 0.000422881 | 0.000423306 |
| 28 | 7.93698E-05 | 0.000317055 | 0.000317479 |
| 29 | 5.95274E-05 | 0.000237685 | 0.000238109 |
| 30 | 4.46455E-05 | 0.000178157 | 0.000178582 |
| 31 | 3.34841E-05 | 0.000133512 | 0.000133937 |
| 32 | 2.51131E-05 | 0.000100028 | 0.000100452 |
| 33 | 1.88348E-05 | 7.49146E-05 | 7.53393E-05 |
| 34 | 1.41261E-05 | 5.60797E-05 | 5.65045E-05 |
| 35 | 1.05946E-05 | 4.19536E-05 | 4.23784E-05 |
| 36 | 7.94594E-06 | 3.1359E-05 | 3.17838E-05 |
| 37 | 5.95946E-06 | 2.34131E-05 | 2.38378E-05 |
| 38 | 4.46959E-06 | 1.74536E-05 | 1.78784E-05 |
| 39 | 3.3522E-06 | 1.2984E-05 | 1.34088E-05 |
| 40 | 2.51415E-06 | 9.63184E-06 | 1.00566E-05 |
| 41 | 1.88561E-06 | 7.1177E-06 | 7.54244E-06 |
| 42 | 1.41421E-06 | 5.23209E-06 | 5.65683E-06 |
| 43 | 1.06066E-06 | 3.81788E-06 | 4.24262E-06 |
| 44 | 7.95492E-07 | 2.75723E-06 | 3.18197E-06 |
| 45 | 5.96619E-07 | 1.96173E-06 | 2.38647E-06 |
| 46 | 4.47464E-07 | 1.36511E-06 | 1.78986E-06 |
| 47 | 3.35598E-07 | 9.17651E-07 | 1.34239E-06 |
| 48 | 2.51699E-07 | 5.82053E-07 | 1.00679E-06 |
| 49 | 1.88774E-07 | 3.30354E-07 | 7.55096E-07 |
| 50 | 1.4158E-07 | 1.4158E-07 | 5.66322E-07 |
56%*56%*56%*56%*56%Quote: DialedN07BUT one seven out on the first roll wipes $146 off the table. I have to hit two inside numbers 5.22 times to make up for it (assuming no roll goes over two numbers before the 7.
What are the odds of hitting my 56% probability 5 or more times in a row?
*sorry, it makes sense to me. Sorry if O didn't explain it well!
or 56%^5
easy for a calculator
making those place 5 and 9 are really poor bets.
A buy on the 4 and 10 with vig on win only pays way more over time.
to see this
think...
$600 on place 6 pays $700
should pay $720 so the casino short pays $20
ok, not that bad
$600 on place 5 (or 9) pays $840
should pay $900 so the casino short pays $60
ouch!!
you may not make and win a $600 place bet but
you actually do over many bets and many wins.
have fun with your betting system
as the house edge will get more the more you play
it is in the payoffs
Sally
I Heart Vi Hart
April 23rd, 2018 at 2:19:47 PM
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Just so happens I ran into a talented di the other day. The $600 buy nine paid $870. The $800 buy nine paid $1160
When a rock is thrown into a pack of dogs, the one that yells the loudest is the one who got hit.
