2 Questions

I've got the opportunity to play on 2 craps tables that are identical except one has a $1 minimum bet w/ 10x odds and the other is a $5 w/ 10x odds.

1: If my comfort zone for odds on the pass is $20, I'm better off playing at the $1 minimum and doing $2 w/ 20 behind, right?

2: If in 50 opportunities to make a point and you see 37 7-outs... would that be statistically significant or is the sample size too small?

~N

Quote: foolshope

2: If in 50 opportunities to make a point and you see 37 7-outs... would that be statistically significant or is the sample size too small?
~N

To me, you have already answered your first question.
As a line bettor, one should put as much money on the odds bet so you have the best chance to end up even or ahead.
your expected loss with $2 flat bets is about as low as it can get.

Q2.
37 7outs in 50 points.

Since the probability of hitting any point is 201/495 or 0.406060606 you are also asking about seeing only 13 point winners in 50 attempts.
This is a simple binomial distribution.
I would use Excel BINOMDIST function

For exactly 13 point winners:
=BINOMDIST(13,50,201/495,FALSE) = 1.2308% or about 1 in 81

13 point winners or less:
=BINOMDIST(13,50,201/495,TRUE) = 2.292% or about 1 in 44


To answer your question: "would that be statistically significant" I say no.

Since the probability of NOT hitting any point is 294/495 or 0.59393939

EV for 50 established points NOT hitting is ~29.7 or 30 (50*(294/495))
Standard Deviation is SQRT(N*P*Q) = 3.4726
Looks to be at the 2 SD mark. About 2.5% of the time it could get worse for the pass line points

Good Luck!
Let us know your final results.

What I don't understand is why is $20 not $20? Why is it better to do $2 and $20 instead of $5 and $20? Is it the difference b/w the $2 and the $5 since that bet only pays even money no matter what the point is?

I am a bit stunned about 2nd part. In my 50 attempts I saw 37 7-outs... if it stayed the same through 100 that would be 74 in 100... and that's not significant. Makes me want to go play video poker!

~N

Quote: foolshope

What I don't understand is why is $20 not $20?

I do not understand your Q. $20 odds is $20 odds no matter what the flat bet is.

Quote: foolshope

Why is it better to do $2 and $20 instead of $5 and $20? Is it the difference b/w the $2 and the $5 since that bet only pays even money no matter what the point is?

From the EV point of view 2/20 is slightly better with a -$1.41 expected loss at, say 50 trials, where a 5/20 would be -$3.54 expected loss.

The key for any line bettor is to still have more money on the odds part of the bet than the flat part.

The average bet for the 5/20 would be: $18.33, with SD: 24.15
The average bet for the 2/20 would be: $15.33, with SD: 21.62
So, it is not really fair to compare the two bets since the overall action of the 5/20 would be higher.

a 1/26 would be the same 18.33 average bet as the 5/20, if you could find that, and I doubt one could.

a 2/24 (12x odds) would be 18.00 average bet and SD 25.61, now slightly better than the 5/20.

Quote: foolshope

I am a bit stunned about 2nd part. In my 50 attempts I saw 37 7-outs... if it stayed the same through 100 that would be 74 in 100... and that's not significant. Makes me want to go play video poker!

~N

So you were on the other side of good luck.

"if it stayed the same through 100 that would be 74 in 100" is a different question.

EV for 100 established points NOT hitting is ~59.4 or 60 (100*(294/495))
Standard Deviation is SQRT(N*P*Q) = 4.911
So, 14/4.911 = 2.85 SD.
Still under the 3 SD range and that is to be expected in a small sample size.
Or about 1 in 612 of seeing 74 or more points shot down in 100 attempts. Not as common as 37/50 but still not uncommon.

Now...
EV for 200 established points NOT hitting is ~118.8 or 119 (200*(294/495))
Standard Deviation is SQRT(N*P*Q) = 6.9451
Same 148/200 ratio
So, 29/6.9451 = 4.18 SD. Now we are past 4 SD.
Or about 1 in 90,656 of seeing 148 or more points shot down in 200 attempts.
Now this distribution result would be an eye opener and a bankroll killer for the pass line bettor.

I would then not be surprised to see the 74/100 results
and probably not play long enough to see the 148/200 distribution.
I am also 100% certain it has happened at least once somehere.

Quote: foolshope

What I don't understand is why is $20 not $20? Why is it better to do $2 and $20 instead of $5 and $20?

Or put another way: Every $1 increment on the flat bet can be expected to lose 1.41¢. All you're doing is increasing your flat bet $3, so you can expect to lose an extra 4.2¢ per bet.

The more you risk against a house edge the worse for you. Why risk $25 when you can risk $22 and have lower HE as well?

For some time now have been running sessions with Wincraps at 10x odds, stay tuned for a blog post someday. The reality is you are pushing the HE so low at 10x free odds that what is going on with the -EV is losing it's importance to the outcome. Yes the negative expectation is still there. But at 4x odds the HE is going to take a more certain toll. The variance at 10x is dominant, in other words.