This is a question to the Wizard and anyone else who has a firm grasp of probability theory and who understands odds.

Based on probability and odds, which of the following betting options on a zero number wheel, is the best?

1) After 31 spins of the wheel, flat bet the 19 numbers that don't show. Bet these numbers 6 times.

2) After 32 spins of the wheel, flat bet the 18 numbers that don't show. Bet these numbers 5 times.

3) After 33 spins of the wheel, flat bet the 17 numbers that don't show. Bet these numbers 4 times.

Thanks in advance for your mathematical analysis.

- Notnab

Quote:NotnabHello,

This is a question to the Wizard and anyone else who has a firm grasp of probability theory and who understands odds.

Based on probability and odds, which of the following betting options on a zero number wheel, is the best?

1) After 31 spins of the wheel, flat bet the 19 numbers that don't show. Bet these numbers 6 times.

2) After 32 spins of the wheel, flat bet the 18 numbers that don't show. Bet these numbers 5 times.

3) After 33 spins of the wheel, flat bet the 17 numbers that don't show. Bet these numbers 4 times.

Thanks in advance for your mathematical analysis.

- Notnab

I am assuming by 'zero number wheel' you really mean a European wheel with a single zero.

By far number 3 is the best of the options.

Number 1 has you making 19 x 6 = 104 bets

Number 2 has you making 18 x 5 = 90 bets

Number 3 has you making 17 x 4 = 68 bets

Since each bet has you losing around 2.6% of your bet, the fewer bets you make means the less money you will tend to lose. So making 68 bad bets is preferable to 90 or 104 bad bets.

Thanks for your response.

Yes, I'm referring to the European wheel and I'm basing the method of play on the following stats:

After 37 spins only 28 numbers will hit (01%) 9 won't hit

After 37 spins only 27 numbers will hit (04%) 10 won't hit

After 37 spins only 26 numbers will hit (09%) 11 won't hit

After 37 spins only 25 numbers will hit (16%) 12 won't hit

After 37 spins only 24 numbers will hit (20%) 13 won't hit

After 37 spins only 23 numbers will hit (20%) 14 won't hit

After 37 spins only 22 numbers will hit (15%) 15 won't hit

After 37 spins only 21 numbers will hit (08%) 16 won't hit

After 37 spins only 20 numbers will hit (04%) 17 won't hit

After 37 spins only 19 numbers will hit(1.2%) 18 won't hit

How does the above affect your perspective?

You are not the first person, and won't be the last, that has asked pretty much this exact question on this site. No numbers are due, the past performance of the wheel has no effect on the future. The expected distribution of #s that hit in 37 spins cannot help you predict which ones will hit next. There is no such thing as a roulette 'cycle'.

Your best strategy at roulette is to make the LEAST amount of bets possible while still having fun. Hence SOOPOO's answer.

Quote:SOOPOOI am assuming by 'zero number wheel' you really mean a European wheel with a single zero.

By far number 3 is the best of the options.

Number 1 has you making 19 x 6 = 104 bets

Number 2 has you making 18 x 5 = 90 bets

Number 3 has you making 17 x 4 = 68 bets

Since each bet has you losing around 2.6% of your bet, the fewer bets you make means the less money you will tend to lose. So making 68 bad bets is preferable to 90 or 104 bad bets.

Doesn't fewer bets result in greater deviation?

Quote:dwheatleyIt doesn't.

You are not the first person, and won't be the last, that has asked pretty much this exact question on this site. No numbers are due, the past performance of the wheel has no effect on the future. The expected distribution of #s that hit in 37 spins cannot help you predict which ones will hit next. There is no such thing as a roulette 'cycle'.

Your best strategy at roulette is to make the LEAST amount of bets possible while still having fun. Hence SOOPOO's answer.

The method doesn't involve prediction / due numbers.

If you spin a roulette wheel every 37 spins, you will not see all 37 numbers land. It will not happen in your lifetime.

A cycle of 37 spins will always result in less than 37 numbers landing.

Quote:NotnabThe method doesn't involve prediction / due numbers.

If you spin a roulette wheel every 37 spins, you will not see all 37 numbers land. It will not happen in your lifetime.

A cycle of 37 spins will always result in less than 37 numbers landing.

Always?

Would you care to demonstrate how 37 spins absolutely cannot result in each of the 37 numbers hitting once? I will tell you the e th probability of 37 spins yielding every number once:

37/37 * 36/37 * 35/37 * 34/37 * 33/37 * 32/37 * 31/37 * 30/37 * 29/37 * 28/37 * 27/37 * 26/37 * 25/37 * 24/37 * 23/37 * 22/37 * 21/37 * 20/37 * 19/37 * 18/37 * 17/37 * 16/37 * 15/37 * 14/37 * 13/37 * 12/37 * 11/37 * 10/37 * 9/37 * 8/37 * 7/37 * 6/37 * 5/37 * 4/37 * 3/37 * 2/37 * 1/37 =

Quick Pause: Interestingly, you are less than 50% to have the first eight numbers all be different!

---Less than 20% to have the first eleven numbers be different!

---Less than 10% on the first thirteen!!!

---Barely over 0.5% on the first eighteen!!!

.0000000000000001303986462 or 0.00000000000001303986462%

I am surprised to find that hitting the same number nine consecutive times is slightly more probable than this result. If it has ever been proven that the same number has hit nine (or more) consecutive times, then I would be willing to be that we've spun for the cycle at least once in the course of human gambling events. It would be an unprovable bet, though.

I would also venture to say it will happen in my lifetime. If you look at all of the casinos, on-line casinos, video games, play-for-fun on-line, video roulette, etc. etc. etc., Every repeated result would be a new series with the repeated number the first of the series, because the 37/37 spin is obviously a given. Whether or not I will be there when it happens, however, is a different matter entirely. ; )

Quote:NotnabDoesn't fewer bets result in greater deviation?

Since you seem like a nice guy making an honest attempt at learning something, let me steer you in the right direction.

Learn these terms.....

Expected value

Variance

Once you have a firm grasp on what those two terms are you can then craft questions that the 'math guys' can then answer in a meaningful way.

Quote:NotnabBased on probability and odds, which of the following betting options on a zero number wheel, is the best?

I can show some values. You can choose what is the best.

You also be doing a lot of waiting. Why?

Where is the value in waiting so long?

Quote:Notnab1) After 31 spins of the wheel, flat bet the 19 numbers that don't show. Bet these numbers 6 times.

4.81% of every 31 spin sets will on average result in 19 numbers not showing

48,112 out of 1 million trials

win prob = 19/37 for 6 spins

x prob[X=x] prob[X<x] prob[X>=x] prob[X<=x] prob[X>x]

0 0.0132564 0.0000000 1.0000000 0.0132564 0.9867436

1 0.0839570 0.0132564 0.9867436 0.0972134 0.9027866

2 0.2215533 0.0972134 0.9027866 0.3187667 0.6812333

3 0.3118157 0.3187667 0.6812333 0.6305823 0.3694177

4 0.2468541 0.6305823 0.3694177 0.8774364 0.1225636

5 0.1042273 0.8774364 0.1225636 0.9816637 0.0183363

6 0.0183363 0.9816637 0.0183363 1.0000000 0.0000000

7.97% of every 32 spin sets will on average result in 18 numbers not showingQuote:Notnab2) After 32 spins of the wheel, flat bet the 18 numbers that don't show. Bet these numbers 5 times.

79,657 out of 1 million trials

win prob = 18/37 for 5 spins

x prob[X=x] prob[X<x] prob[X>=x] prob[X<=x] prob[X>x]

0 0.0357075 0.0000000 1.0000000 0.0357075 0.9642925

1 0.1691408 0.0357075 0.9642925 0.2048483 0.7951517

2 0.3204772 0.2048483 0.7951517 0.5253255 0.4746745

3 0.3036100 0.5253255 0.4746745 0.8289355 0.1710645

4 0.1438153 0.8289355 0.1710645 0.9727508 0.0272492

5 0.0272492 0.9727508 0.0272492 1.0000000 0.0000000

11.91% of every 33 spin sets will on average result in 17 numbers not showingQuote:Notnab3) After 33 spins of the wheel, flat bet the 17 numbers that don't show. Bet these numbers 4 times.

119,080 out of 1 million trials

win prob = 17/37

x prob[X=x] prob[X<x] prob[X>=x] prob[X<=x] prob[X>x]

0 0.0853715 0.0000000 1.0000000 0.0853715 0.9146285

1 0.2902632 0.0853715 0.9146285 0.3756348 0.6243652

2 0.3700856 0.3756348 0.6243652 0.7457204 0.2542796

3 0.2097152 0.7457204 0.2542796 0.9554355 0.0445645

4 0.0445645 0.9554355 0.0445645 1.0000000 0.0000000

Thanks in advance for your mathematical analysis.

- Notnab

It should never affect anyone's perspective.Quote:NotnabSoopoo,

Thanks for your response.

Yes, I'm referring to the European wheel and I'm basing the method of play on the following stats:

After 37 spins only 28 numbers will hit (01%) 9 won't hit

After 37 spins only 27 numbers will hit (04%) 10 won't hit

After 37 spins only 26 numbers will hit (09%) 11 won't hit

After 37 spins only 25 numbers will hit (16%) 12 won't hit

After 37 spins only 24 numbers will hit (20%) 13 won't hit

After 37 spins only 23 numbers will hit (20%) 14 won't hit

After 37 spins only 22 numbers will hit (15%) 15 won't hit

After 37 spins only 21 numbers will hit (08%) 16 won't hit

After 37 spins only 20 numbers will hit (04%) 17 won't hit

After 37 spins only 19 numbers will hit(1.2%) 18 won't hit

How does the above affect your perspective?

The past only shows what has happened in a sequence of events

and

does no better than a blind squirrel picking the next numbers to win.

Any computer simulation will prove this to be absolutely true using RNG numbers or internet listed actual spins.

Where are the results of your computer simulations?

If you have none, time for you to learn to do them.

There will be power in your findings that none of us here can ever give you.

BTW, your %s are really rounded

no show | unique #s | probability |
---|---|---|

20 | 17 | 0.051300% |

19 | 18 | 0.282190% |

18 | 19 | 1.174500% |

17 | 20 | 3.605390% |

16 | 21 | 8.384150% |

15 | 22 | 14.835930% |

14 | 23 | 19.936310% |

13 | 24 | 20.475660% |

12 | 25 | 15.925890% |

11 | 26 | 9.406580% |

10 | 27 | 4.159970% |

9 | 28 | 1.364840% |

8 | 29 | 0.328120% |

7 | 30 | 0.054960% |