Probability is a fickle witch. Yet there are things you can do to help level the playing field. Here is a prelude to this post regarding Expected Values taken from the original Post. Expected Value What would your reaction to craps be if you could find a number of ways to know what to expect at outcome? Would these results be at a mediocre or an encouraging rate of occurrence? A link provided gives you results paralleling this example. https://nces.ed.gov/nceskids/chances/ Three trials each having an average hand of 9 rolls was initiated. You can see how probability is skewed all over the place yet there is volumes of information contained in this example. What do you see? Mssthis1, is this kind of probability skew that you saw in your trials?

Yep, I'm seeing similar numbers. I need to take the tame to take more samples but I'm interested in the percentage of times that you can go 10 box number rolls without seeing a seven. To simplify things I'm just doing 10 roll samples and ignoring the horn numbers. So far 3 sevens in 10 rolls is the most and 0 is the least. 0 sevens have occurred 11.11% of the time but the sample is too small to draw any conclusions yet. as far as your 3 samples. Horn numbers are only 22% of expected. Fours are 311% of expected. Most numbers are downtown. A person laying the 10 same bet every time would be ahead 1 bet minus the vig. A person laying the 4 may or may not of got killed. Depends on when the sevens fell. I'd be strongly considering switching to lay bets until the horn numbers caught up to trend somewhat as long as the sevens continued to be that evenly dispersed. Would need more samples to make a concrete derision.

Last time I tracked 360 rolls... 2 - 10 expected (11 rolled) 3 - 20 expected (16 rolled) 4 - 30 expected (34 rolled) 5 - 40 expected (36 rolled) 6 - 50 expected (54 rolled) 7 - 60 expected (59 rolled) 8 - 50 expected (43 rolled) 9 - 40 expected (48 rolled) 10 - 30 expected (32 rolled) 11 - 20 expected (19 rolled) 12 - 10 expected (9 rolled) I suspect the more we roll...the numbers will tend to morph toward balancing out the pyramid. In this case...the 9 was working harder. 10 roll samples are meaningless, IMO. Anything can happen in 10 rolls.

OAP Pre-post Reply: Don't suspect anything you mental midget...The Law of Large Numbers will show the numbers moving further apart although the pyramid will become balanced.

Wincraps sample from a new session I started yesterday, wargaming a lay bet strategy. Never made it to level II on my betting scheme. Have I found the keys to the vault or does it need more testing after seeing these numbers?

The last time I ran bonetracker on 500 in-house rolls showed: 2 - 13 expected (8 rolled) 3 - 28 expected (29 rolled) 4 - 41 expected (54 rolled) 5 - 55 expected (59 rolled) 6 - 69 expected (80 rolled) 7 - 83 expected (58 rolled) 8 - 69 expected (79 rolled) 9 - 55 expected (38 rolled) 10 - 41 expected (46 rolled) 11 - 28 expected (36 rolled) 12 - 13 expected (13 rolled) If this was the so-called Wong challenge I would have killed it on this session (if I remember Lil Joe had to get what 78 or below): Chi-Square for the sample and set used was 0.04

Far it be from me to advise, there is a however. Do yourself a favor and do nothing but follow the dice, no strategies, no systems. The dice will show you the way. BS777 is right. The LLN has no business at a live session, it can't see over 400 shooters in a session to tell you how to bet.

It's one thing to understand the math, it is something else entirely, to understand, what the math "means". .

I don't think he was talking about Flash Gordon I think he was talking about Flash's brother law Gordon Kudos

Following the dice,is of NO value whatsoever, because your bets have to, LEAD the dice. The dice do not give a shit, what you want them to roll, or what you have already seen them roll. It would be nice, if the game were this simple, it is not, but some of the players ARE. .

Dude, where did this come from? "Chi-Square for the sample and set used was 0.04"? I didn't calculate the the Chi-Square statistic but just by eye-balling your data, there's no way you got 0.04 as the Chi-Square statistic.