roulette probability question

I don't gamble with an expectation of winning, but still want a fair game. I just left 5Dimes bonus casino, where I played 111 rounds of roulette. I figure I should win 54 and lose 57 making even-money bets. I won 44 and lost 67. Should I be suspicious, based on the wide variance from expected result? I'm probably making a calculation error, but it seems the odds are about 100:1 against that happening. What's your input?

What do you think?

That out of 111 you "SHOULD" have won exactly 55.5, no more and no less and that this would somehow prove to you and all assembled that the wheel was fair and Ford was in his Flivver and all was right with the world!

Or is it that you would take 5.26 percent of 111 and consider that a valid "excess loss" so that 60.726 losses would be fair, right and just and the wheel would smile as you departed satisfied that it had treated you exactly correct.

I would not play on an online casino I didn't trust but I would not use those figure to make a decision about a wheel and its honesty.

I don't trust 5d, I don't think anyone should. Yet those figures tell me nothing.

My questions are:

Did I figure the likelihood of losing 10 more/winning 10 less than expected in 111 rounds correctly at about 100:1, and

Is that much variance a cause for concern?

Actually, none of your speculation about my thoughts are correct. I appreciate that the figures tell you nothing, but then why reply at all?

Wellll...if you played 111 rounds 100 times, you'd expect this to happen at least once. Why be suspicious because it happened this time?

Based on your expected wins, you are playing European Roulette. The standard deviation on the number of wins is (111*(18/37)*(19/37))^.5 = 5.26.

Your round was (54-44)/5.26 standard deviations low (1.899 standard deviations). The probability of getting this result or worse is 2.88%, or 1 in 34.7, so you had a bad run, but there is no evidence of cheating.

Quote: CrystalMath

Based on your expected wins, you are playing European Roulette. The standard deviation on the number of wins is (111*(18/37)*(19/37))^.5 = 5.26.

Your round was (54-44)/5.26 standard deviations low (1.899 standard deviations). The probability of getting this result or worse is 2.88%, or 1 in 34.7, so you had a bad run, but there is no evidence of cheating.

Thank you. The voice of reason in my head told me the same thing, even with my roughed-out-pessimistic calculation. But confirmation supports confidence. I appreciate your emotional support.

Quote: CrystalMath

Your round was (54-44)/5.26 standard deviations low (1.899 standard deviations). The probability of getting this result or worse is 2.88%, or 1 in 34.7, so you had a bad run, but there is no evidence of cheating.

When one can use the Binomial Distribution for such small samples instead of the normal distribution, in Excel
=BINOMDIST(44,111,18/37,TRUE)

returns 0.0352175 (3.52%) or 1 in 28.4 for 44 or less wins.
still nothing to write home about

Stat Trek's Binomial Calculator
They also give a tutorial on this subject and many others

Quote: rdw4potus

Wellll...if you played 111 rounds 100 times, you'd expect this to happen at least once. Why be suspicious because it happened this time?

I know. You're right. Admittedly, I played VP there yesterday and won $50 off of $750 in bets. I didn't start thinking "Wow! The RNG's screwing up!" Like I said above, sometimes it just feels better hearing the voice of reason from someone else. Thank you for your input.

Quote: mustangsally

When one can use the Binomial Distribution for such small samples instead of the normal distribution, in Excel
=BINOMDIST(44,111,18/37,TRUE)

returns 0.0352175 (3.52%) or 1 in 28.4 for 44 or less wins.
still nothing to write home about

Stat Trek's Binomial Calculator
They also give a tutorial on this subject and many others

After I posted, I realized that I should have used the binomial instead because of the small sample size. I get ahead of myself sometimes.

Quote: CrystalMath

After I posted, I realized that I should have used the binomial instead because of the small sample size. I get ahead of myself sometimes.

But you are still CrystalMath, so that makes up for it.
How about 1million players playing 111 spins.
here are the cumulative results (wins or less) from a simulation of course.

so the final results can easily be more than 3sd when 1million is involved (.27%)

wins or less	freq	freq/100
29	1	0.00%
30	8	0.00%
31	10	0.00%
32	20	0.00%
33	42	0.00%
34	101	0.01%
35	192	0.02%
36	386	0.04%
37	802	0.08%
38	1519	0.15%
39	2832	0.28%
40	4911	0.49%
41	8393	0.84%
42	13960	1.40%
43	22439	2.24%
44	35025	3.50%
45	52513	5.25%
46	76576	7.66%
47	108138	10.81%
48	147777	14.78%
49	196008	19.60%
50	252747	25.27%
51	316598	31.66%
52	387103	38.71%
53	461391	46.14%
54	536898	53.69%