When are there too many 7's and conversely, not enough?

Quote: foolshope

So in 100 rolls, we should see 16.666 7's. If we saw 24, would that be "statistically significant?" What if we only saw 8?

I can't control what the dice do, they have no memory but over the long-run of my shoot, every 100 should result in 16.666 7's and if I've thrown the dice 300 times, I'd expect to see ~50 7's, but if I've seen 80, would it be fair to say that there's a statistically significant variance in my result?

I ask because under that scenario, isn't it better for me (and only me) to throw the dice X amount of times, see how many 7's, and if I've rolled enough 7's to get into "significant variance" that'd be the time to try and bet heavier knowing that I've seen "too many." Conversely, if I've thrown the dice 300 times and see 30 7's, would that be "too few" and rely on starting small with long rolls rather than big initial wagers?

My gut tells me there's something wrong w/ my logic - someone punch me so I can throw it up. :)

~N

Quote: foolshope

So part of the problem is that there are "all the 7's ever rolled in the entire universe" and the number of 7's *I've* rolled... and since I've never kept track of how many rolls of the dice I've made OR how many 7's I've rolled, I can't even make any sort of approximation or speculation, correct?

Quote: foolshope

and since I've never kept track of how many rolls of the dice I've made OR how many 7's I've rolled, I can't even make any sort of approximation or speculation, correct?

Quote: foolshope

So in 100 rolls, we should see 16.666 7's. If we saw 24, would that be "statistically significant?" What if we only saw 8?

 x      prob[X=x]     prob[X<x]    prob[X>=x]    prob[X<=x]     prob[X>x]
 5   0.0002909031  0.0000940202  0.9999059798  0.0003849233  0.9996150767
 6   0.0009211932  0.0003849233  0.9996150767  0.0013061165  0.9986938835
 7   0.0024740617  0.0013061165  0.9986938835  0.0037801782  0.9962198218
 8   0.0057521934  0.0037801782  0.9962198218  0.0095323716  0.9904676284
 9   0.0117600399  0.0095323716  0.9904676284  0.0212924115  0.9787075885
10   0.0214032726  0.0212924115  0.9787075885  0.0426956842  0.9573043158
11   0.0350235371  0.0426956842  0.9573043158  0.0777192212  0.9222807788
12   0.0519515800  0.0777192212  0.9222807788  0.1296708012  0.8703291988
13   0.0703344467  0.1296708012  0.8703291988  0.2000052479  0.7999947521
14   0.0874156695  0.2000052479  0.7999947521  0.2874209174  0.7125790826
15   0.1002366344  0.2874209174  0.7125790826  0.3876575518  0.6123424482
16   0.1065014240  0.3876575518  0.6123424482  0.4941589758  0.5058410242
17   0.1052484661  0.4941589758  0.5058410242  0.5994074418  0.4005925582
18   0.0970624742  0.5994074418  0.4005925582  0.6964699161  0.3035300839
19   0.0837802409  0.6964699161  0.3035300839  0.7802501570  0.2197498430
20   0.0678619951  0.7802501570  0.2197498430  0.8481121521  0.1518878479
21   0.0517043773  0.8481121521  0.1518878479  0.8998165294  0.1001834706
22   0.0371331437  0.8998165294  0.1001834706  0.9369496731  0.0630503269
23   0.0251859583  0.9369496731  0.0630503269  0.9621356314  0.0378643686
24   0.0161609899  0.9621356314  0.0378643686  0.9782966213  0.0217033787
25   0.0098258819  0.9782966213  0.0217033787  0.9881225031  0.0118774969
26   0.0056687780  0.9881225031  0.0118774969  0.9937912811  0.0062087189
27   0.0031073302  0.9937912811  0.0062087189  0.9968986113  0.0031013887
28   0.0016202507  0.9968986113  0.0031013887  0.9985188620  0.0014811380
29   0.0008045383  0.9985188620  0.0014811380  0.9993234003  0.0006765997
30   0.0003808148  0.9993234003  0.0006765997  0.9997042151  0.0002957849
31   0.0001719809  0.9997042151  0.0002957849  0.9998761960  0.0001238040

Quote: foolshope

So the bottom line is (I can't wait to explain this to my friend tonight!) is even if we had 10,000,000 rolls and saw 585 less 7's than what is expected, that's no reason to "bet more" and in fact, there is *no* number of "too many 7's" that can even be relied upon, hence the term "gambling."

Know our win/loss/time limits, stick to'm, have fun, generally stay away from the center of the table, and when possible - max out our odds.

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

0      0.3348979     0.0000000     1.0000000     0.3348979     0.6651020
1      0.4018775     0.3348979     0.6651020     0.7367755     0.2632244
2      0.2009387     0.7367755     0.2632244     0.9377143     0.0622856
3      0.0535836     0.9377143     0.0622856     0.9912980     0.0087019
4      0.0080375     0.9912980     0.0087019     0.9993355     0.0006644
5      0.0006430     0.9993355     0.0006644     0.9999785     0.0000214
6      0.0000214     0.9999785     0.0000214     1.0000000     0.0000000

Quote: foolshope

We play in the Seattle area and Tulalip has 10x odds... but we have different styles. I like to place the come and add odds, he likes to play $26/7 / 52/54 across with a $5 come. When a place bet is hit, he'll take the winnings and make it a come since it's rare to press from $54 across to $300 (all #s w/ $60). His reasoning is "I'm more likely to hit one number once than that same number a few times - I'd rather start with bases-loaded but "light" than loading the bases like me and immediately throwing 5X odds on a number.

Any thoughts on this? We typically end-up about the same - is that to be expected?

Quote: s2dbaker

36 or more 7s in a 100 toss session is outside of 5 standard deviations.
So if you toss the dice 100 times and see 36 or more 7s, then that would be cause for concern (but still possible).

Quote: s2dbaker

Zero 7s in 100 tosses is NOT outside of 5 standard deviations.

Quote: s2dbaker

I was thinking of a result set with an even distribution. I looked at my meager 50K trials and saw 4 as my least number of 7s. I should go by the 5 Standard Deviations % rather than actual avg- 5*stddev.