How much do we still not know?

[Vman96]

You know that I wrote that "week comment" because you said you got a Royal earlier this month. When you forget the positive results, results will become DaBurglar like.

5 Royals in 24 hours? Did he claim to only play single-line when doing it?

Depends on the game, but if he is a DDB player the odds in any given hand is 1 in 39,989 for 9/5 DDB using basic strategy.

Given 8400 hands in 24 hours...the probability of making 5 Royals (or more) in one day on single-play would be roughly:

350,000 to 1

This assumes on a single-play machine. That's very important to note. Because if he is counting a dealt Royal at 5-play as 5 Royals in one day, that is much easier to accomplish. I personally have had 6 Royals in one day by that definition...for $40 each...

Not quite sure how you exactly did the math, but he has about a 20% chance to hit a Royal in that stretch of 8400 hands, and (0.2)^5 = 1 in 3125. But this assumes he gets a new stretch of 8400 hands each time he hits a Royal, which he obviously doesn't.

To solve a question like this, it's best to use the binomial distribution:
http://en.wikipedia.org/wiki/Binomial_distribution

A spreadsheet in Excel did the number crunching for me. And FYI, if the record is 7 single-line Royals for the day, that would be about 336,000,000 to 1 if everyone played 8400 hands. But it is possible given the length of time the casino has been open slash some players will play more than 8400 hands, thereby increasing their chances.

[sam434343]

See when it comes to math and a RNG chips, math can be thrown out the window. Because if all you math experts(not trying insult but in someways I am) would listen to what your are saying( RF on average 40,000+ to 1) then in very next sentence you say your figures don't add up right 336,000,000 to 1(getting those in one day) and this is why I say math does not add up right when it comes to RNG chips, the out come can be anything, then you say on average the math adds up right, but on other times it dosnt. So what you math experts are doing is when does add right you use it to your favor, when it dosnt add up to the normal figures you use BS to get around it. Like I have said in past post any math expert and anything you written on this post(videopoker.com) in past ten years or longer we take court/federal dosnt matter and in there I will make you look like a fool are any of you willing to gamble ten years of your life behind bars (prison) I am! Also I have feeling lot you are hidden(on this internet site) but I am willing to meet in court of law? Vman96 this is not directed towards you,just tired of listening math figures and then when they don't add up right you change the figures,if your are truly math experts you understand what I am talking about if not then you are not a math expert don't care what degree or school you gone to, you are just all talk of what learned in Unversity and you think that's all there is to math, the true math experts are way beyond that. Sam

[shadowman]

Sam, it's all about probabilities. Some people get that, others don't.

[onemoretry]

Sam, it's all about probabilities. Some people get that, others don't.

I think Sam may be one of the "others".

[sam434343]

See shadowman and onemoretry I dealt with conman all the time on the streets and they could (try)(and try and insult people oneoretry)talk there way out crimes but they end up in prison like I said in my post tell me your real name and state and we will meet in a court of law. You both don't need to tell where you live have already turned your online names over to law agency that includes you shawdowman and you onemoretry we find out who the real conman is! They will be tracking both of you down we find out who get arrested if you have done anything wrong!You both are going to find out how much power I have in the law enforcement. Sam

[shadowman]

Sam, you're going to be real disappointed. Maybe instead of bloviating on topics you have no clue about, you should keep quiet, ask questions, listen and learn.

The math behind VP is quite simple (as math goes) and a survey of the math departments at universities across the country would agree 100% with what you have been told here. You'd be laughed out of court if you tried to prosecute on the basis that somehow the math being explained on this forum is wrong.

Now, as to your threats. I recommend you apologize immediately. There is no place here for silly threats like the one you just made.

[edog743]

Boy, people say I take stuff to personally. Sam you sure have me beat.

[sam434343]

shadowman this has nothing to do with math,and you can talk to other people like that but you wont with me. This will be my last post to you, will let the law take its course.

[shadowman]

sam:

1) "See when it comes to math and a RNG chips, math can be thrown out the window."

2) "if all you math experts(not trying insult but in someways I am) would listen to what your are saying"

3) "So what you math experts are doing is when does add right you use it to your favor, when it dosnt add up to the normal figures you use BS to get around it."

4) "any math expert and anything you written on this post(videopoker.com) in past ten years or longer we take court/federal dosnt matter "

5) "just tired of listening math figures and then when they don't add up right you change the figures,if your are truly math experts you understand what I am talking about if not then you are not a math expert"

And finally:

"this has nothing to do with math"

I wonder what it is about ...

[Vman96]

I am confused on what sam is trying to argue here, especially with regard to "taking us to court". Trying to prosecute us for doing mathematics on the internet? And sam, I didn't "change any numbers around". You just didn't understand exactly what I wrote because I either explained it poorly slash in too little detail, you read what I wrote too quickly, or you haven't touched math in 40 years. I could write out the results Excel gave me by hand, I suppose.

Aww, screw it, go ahead and burn me at the stake if you want sam. All these calculations use the binomial distribution:

P(n,k) = C(n,k) *p^k *q^(n-k)

where n = number of hands played = 8400
where k = number of Royals hit

where P(n,k) is the probability of making exactly k Royal Flushes while playing n = 8400 hands

where C(n,k) is the number of ways to choose which hands the k Royal Flushes occur among the n = 8400 hands played.

where p = probability of making a Royal in one single hand =(1/39,989)

where q = probability of NOT making a Royal in one single hand = (39,988/39,989)

In any given set of 8400 hands:

Probability of 0 Royals (k=0):
1*(1/39,989)^0 *(39,988/39,989)^8400 = 0.8105352943 = 81.05% of the time


Probability of 1 Royal (k=1):
8400*(1/39,989)^1 *(39,988/39,989)^8399 = 0.1702634909 = 17.03% of the time


Probability of 2 Royals (k=2):
[8400*8399/(2*1)]*(1/39,989)^2 *(39,988/39,989)^8398 = 0.0178809025 = 1.79% of the time


Probability of 3 Royals (k=3):
[8400*8399*8398/(3*2*1)]*(1/39,989)^3 *(39,988/39,989)^8397 = 0.0012517407 = 0.125% of the time


Probability of 4 Royals (k=4):
[8400*8399*8398*8397/(4*3*2*1)]*(1/39,989)^4 *(39,988/39,989)^8396 = 6.57126295282548E-005 = 0.00657% of the time

Probability of 5 Royals (k=5):
[8400*8399*8398*8397*8396/(5*4*3*2*1)]*(1/39,989)^5 *(39,988/39,989)^8395 = 2.75944402080238E-006 = 0.000276% of the time


Probability of 6 Royals (k=6):
[8400*8399*8398*8397*8396*8395/(6*5*4*3*2*1)]*(1/39,989)^6 *(39,988/39,989)^8394 = 9.65520179163581E-008 = 0.00000966% of the time

Probability of 7 or more Royals since the probability of getting anywhere from 0 to 8400 Royals in 8400 hands happens EVERY time, take the probability of one minus the all above terms:
1 - 0.8105352943 - 0.1702634909 - 0.0178809025 - 0.0012517407 - 6.57126295282548E-005- 2.75944402080238E-006 - 9.65520179163581E-008

= 2.97283209161E-009 = 0.000000297% of the time or 1 in approximately 336 million.