# The Naked Scientists Forum

### Author Topic: Is this maths correct?  (Read 13423 times)

#### Thebox

• Neilep Level Member
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##### Re: Is this maths correct?
« Reply #150 on: 31/07/2015 22:11:49 »
x=1/52
y=2000/100000

they are obviously not equal.
They are not equal because 2000/100000 is a number you have made up, it is not the true probability in the y direction. We have told you before what it is.
Anyway, this is not the crux of your problem, it is the issue of deck skipping and it's effect on probability.

Come on old friend, we can't keep going around in circles , you need to provide actual game logs to show whether there is a fault in the RNG, or distribution. The problem does n't lie with probability.

There is no probability to the Y axis, it is ''random'' , where x is not random, we know that x is always 1/52, we also know that shuffling of x makes y and Y can  have an uncertainty measurement.

For example purposes we will use 1 , 2 and 3 in an x axis and use 3 sets of

123
123
123

x always equals 1/3 where y has more possible combinations than x, x can never have 111,
We can say the probabilities of Y have a variable range.

I will get some game logs, and show you the fault, and the rng  is not at fault, the rng is fine.

#### Colin2B

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##### Re: Is this maths correct?
« Reply #151 on: 31/07/2015 22:57:25 »
There is no probability to the Y axis, it is ''random'' , where x is not random.
There is a calculatable probability for the Y axis.
Both Y and X comprise discrete random variables, so both are random.
You are confusing random events and combinatorics.

You need some real logs

#### Thebox

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• Posts: 3160
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##### Re: Is this maths correct?
« Reply #152 on: 31/07/2015 23:35:54 »
*** HOLE CARDS ***
Dealt to holdemace486 [4s Jh]
holdemace486: folds
PedroDeucher: folds
Uncalled bet (10) returned to Evgeni104
Evgeni104 collected 20 from pot
Evgeni104: doesn't show hand
*** SUMMARY ***
Total pot 20 | Rake 0
Seat 1: holdemace486 (button) folded before Flop (didn't bet)
Seat 2: PedroDeucher (small blind) folded before Flop
Seat 3: Evgeni104 (big blind) collected (20)

*** HOLE CARDS ***
Dealt to holdemace486 [9h 2d]
PedroDeucher: folds
Evgeni104: calls 10
holdemace486: checks
*** FLOP *** [As Qs Jc]
Evgeni104: bets 20
holdemace486: folds
Uncalled bet (20) returned to Evgeni104
Evgeni104 collected 40 from pot
Evgeni104: doesn't show hand
*** SUMMARY ***
Total pot 40 | Rake 0
Board [As Qs Jc]
Seat 1: holdemace486 (big blind) folded on the Flop
Seat 2: PedroDeucher (button) folded before Flop (didn't bet)
Seat 3: Evgeni104 (small blind) collected (40)

*** HOLE CARDS ***
Dealt to holdemace486 [Qd 3d]
Evgeni104: folds
holdemace486: folds
Uncalled bet (10) returned to PedroDeucher
PedroDeucher collected 20 from pot
*** SUMMARY ***
Total pot 20 | Rake 0
Seat 1: holdemace486 (small blind) folded before Flop
Seat 2: PedroDeucher (big blind) collected (20)
Seat 3: Evgeni104 (button) folded before Flop (didn't bet)

*** HOLE CARDS ***
Dealt to holdemace486 [4c Js]
holdemace486: folds
PedroDeucher: folds
Uncalled bet (10) returned to Evgeni104
Evgeni104 collected 20 from pot
Evgeni104: doesn't show hand
*** SUMMARY ***
Total pot 20 | Rake 0
Seat 1: holdemace486 (button) folded before Flop (didn't bet)
Seat 2: PedroDeucher (small blind) folded before Flop
Seat 3: Evgeni104 (big blind) collected (20)

*** HOLE CARDS ***
Dealt to holdemace486 [3h 8h]
PedroDeucher: folds
Evgeni104: calls 10
holdemace486: checks
*** FLOP *** [td 2d Kc]
Evgeni104: bets 20
holdemace486: folds
Uncalled bet (20) returned to Evgeni104
Evgeni104 collected 40 from pot
Evgeni104: doesn't show hand
*** SUMMARY ***
Total pot 40 | Rake 0
Board [td 2d Kc]
Seat 1: holdemace486 (big blind) folded on the Flop
Seat 2: PedroDeucher (button) folded before Flop (didn't bet)
Seat 3: Evgeni104 (small blind) collected (40)

*** HOLE CARDS ***
Dealt to holdemace486 [Qc 5h]
Evgeni104: folds
holdemace486: folds
Uncalled bet (10) returned to PedroDeucher
PedroDeucher collected 20 from pot
*** SUMMARY ***
Total pot 20 | Rake 0
Seat 1: holdemace486 (small blind) folded before Flop
Seat 2: PedroDeucher (big blind) collected (20)
Seat 3: Evgeni104 (button) folded before Flop (didn't bet)

*** HOLE CARDS ***
Dealt to holdemace486 [7d Qh]
holdemace486: folds
PedroDeucher: folds
Uncalled bet (10) returned to Evgeni104
Evgeni104 collected 20 from pot
Evgeni104: doesn't show hand
*** SUMMARY ***
Total pot 20 | Rake 0
Seat 1: holdemace486 (button) folded before Flop (didn't bet)
Seat 2: PedroDeucher (small blind) folded before Flop
Seat 3: Evgeni104 (big blind) collected (20)

*** HOLE CARDS ***
Dealt to holdemace486 [Ah 2s]
PedroDeucher: folds
Evgeni104: calls 10
holdemace486: raises 420 to 440 and is all-in
Evgeni104: folds
Uncalled bet (420) returned to holdemace486
holdemace486 collected 40 from pot
holdemace486: doesn't show hand
*** SUMMARY ***
Total pot 40 | Rake 0
Seat 1: holdemace486 (big blind) collected (40)
Seat 2: PedroDeucher (button) folded before Flop (didn't bet)
Seat 3: Evgeni104 (small blind) folded before Flop

*** HOLE CARDS ***
Dealt to holdemace486 [4c 9c]
Evgeni104: folds
holdemace486: calls 10
PedroDeucher: raises 40 to 60
holdemace486: calls 40
*** FLOP *** [7s Kd 4h]
holdemace486: bets 80
PedroDeucher: calls 80
*** TURN *** [7s Kd 4h] [6h]
holdemace486: checks
PedroDeucher: bets 60
holdemace486: calls 60
*** RIVER *** [7s Kd 4h 6h] [9d]
holdemace486: bets 260 and is all-in
PedroDeucher: folds
Uncalled bet (260) returned to holdemace486
holdemace486 collected 400 from pot
holdemace486: doesn't show hand
*** SUMMARY ***
Total pot 400 | Rake 0
Board [7s Kd 4h 6h 9d]
Seat 1: holdemace486 (small blind) collected (400)
Seat 2: PedroDeucher (big blind) folded on the River
Seat 3: Evgeni104 (button) folded before Flop (didn't bet)

*** HOLE CARDS ***
Dealt to holdemace486 [Qc Ts]
holdemace486: calls 30
PedroDeucher: raises 260 to 290 and is all-in
Evgeni104: folds
holdemace486: folds
Uncalled bet (260) returned to PedroDeucher
PedroDeucher collected 90 from pot
*** SUMMARY ***
Total pot 90 | Rake 0
Seat 1: holdemace486 (button) folded before Flop
Seat 2: PedroDeucher (small blind) collected (90)
Seat 3: Evgeni104 (big blind) folded before Flop

*** HOLE CARDS ***
PedroDeucher: folds
Evgeni104: calls 15
holdemace486: checks
*** FLOP *** [6c Jc Th]
Evgeni104: bets 30
holdemace486: folds
Uncalled bet (30) returned to Evgeni104
Evgeni104 collected 60 from pot
Evgeni104: doesn't show hand
*** SUMMARY ***
Total pot 60 | Rake 0
Board [6c Jc Th]
Seat 1: holdemace486 (big blind) folded on the Flop
Seat 2: PedroDeucher (button) folded before Flop (didn't bet)
Seat 3: Evgeni104 (small blind) collected (60)

*** HOLE CARDS ***
Dealt to holdemace486 [7s 3d]
Evgeni104: folds
holdemace486: folds
Uncalled bet (15) returned to PedroDeucher
PedroDeucher collected 30 from pot
*** SUMMARY ***
Total pot 30 | Rake 0
Seat 1: holdemace486 (small blind) folded before Flop
Seat 2: PedroDeucher (big blind) collected (30)
Seat 3: Evgeni104 (button) folded before Flop (didn't bet)

*** HOLE CARDS ***
Dealt to holdemace486 [6d 2c]
holdemace486: folds
PedroDeucher: raises 335 to 365 and is all-in
Evgeni104: folds
Uncalled bet (335) returned to PedroDeucher
PedroDeucher collected 60 from pot
*** SUMMARY ***
Total pot 60 | Rake 0
Seat 1: holdemace486 (button) folded before Flop (didn't bet)
Seat 2: PedroDeucher (small blind) collected (60)
Seat 3: Evgeni104 (big blind) folded before Flop

*** HOLE CARDS ***
Dealt to holdemace486 [2h Tc]
PedroDeucher: raises 41 to 71
Evgeni104: folds
holdemace486: folds
Uncalled bet (41) returned to PedroDeucher
PedroDeucher collected 75 from pot
*** SUMMARY ***
Total pot 75 | Rake 0
Seat 1: holdemace486 (big blind) folded before Flop
Seat 2: PedroDeucher (button) collected (75)
Seat 3: Evgeni104 (small blind) folded before Flop

*** HOLE CARDS ***
Dealt to holdemace486 [8d 5s]
Evgeni104: folds
holdemace486: folds
Uncalled bet (15) returned to PedroDeucher
PedroDeucher collected 30 from pot
*** SUMMARY ***
Total pot 30 | Rake 0
Seat 1: holdemace486 (small blind) folded before Flop
Seat 2: PedroDeucher (big blind) collected (30)
Seat 3: Evgeni104 (button) folded before Flop (didn't bet)

*** HOLE CARDS ***
Dealt to holdemace486 [6c 4h]
holdemace486: folds
PedroDeucher: folds
Uncalled bet (15) returned to Evgeni104
Evgeni104 collected 30 from pot
Evgeni104: doesn't show hand
*** SUMMARY ***
Total pot 30 | Rake 0
Seat 1: holdemace486 (button) folded before Flop (didn't bet)
Seat 2: PedroDeucher (small blind) folded before Flop
Seat 3: Evgeni104 (big blind) collected (30)

*** HOLE CARDS ***
Dealt to holdemace486 [Kd 2s]
PedroDeucher: folds
Evgeni104: calls 15
holdemace486: checks
*** FLOP *** [5d 3s 7h]
Evgeni104: bets 30
holdemace486: folds
Uncalled bet (30) returned to Evgeni104
Evgeni104 collected 60 from pot
Evgeni104: doesn't show hand
*** SUMMARY ***
Total pot 60 | Rake 0
Board [5d 3s 7h]
Seat 1: holdemace486 (big blind) folded on the Flop
Seat 2: PedroDeucher (button) folded before Flop (didn't bet)
Seat 3: Evgeni104 (small blind) collected (60)

*** HOLE CARDS ***
Dealt to holdemace486 [3h Ac]
Evgeni104: calls 30
holdemace486: calls 15
PedroDeucher: checks
*** FLOP *** [3d 2h 4s]
holdemace486: checks
PedroDeucher: checks
Evgeni104: checks
*** TURN *** [3d 2h 4s] [4d]
holdemace486: bets 480 and is all-in
PedroDeucher: folds
Evgeni104: folds
Uncalled bet (480) returned to holdemace486
holdemace486 collected 90 from pot
holdemace486: doesn't show hand
*** SUMMARY ***
Total pot 90 | Rake 0
Board [3d 2h 4s 4d]
Seat 1: holdemace486 (small blind) collected (90)
Seat 2: PedroDeucher (big blind) folded on the Turn
Seat 3: Evgeni104 (button) folded on the Turn

*** HOLE CARDS ***
holdemace486: raises 60 to 90
PedroDeucher: folds
Evgeni104: folds
Uncalled bet (60) returned to holdemace486
holdemace486 collected 75 from pot
holdemace486: doesn't show hand
*** SUMMARY ***
Total pot 75 | Rake 0
Seat 1: holdemace486 (button) collected (75)
Seat 2: PedroDeucher (small blind) folded before Flop
Seat 3: Evgeni104 (big blind) folded before Flop

*** HOLE CARDS ***
Dealt to holdemace486 [4c Js]
PedroDeucher: raises 60 to 90
Evgeni104: raises 400 to 490 and is all-in
holdemace486: folds
PedroDeucher: calls 305 and is all-in
Uncalled bet (95) returned to Evgeni104
*** FLOP *** [Jd Tc 7h]
*** TURN *** [Jd Tc 7h] [Jc]
*** RIVER *** [Jd Tc 7h Jc] [Ad]
*** SHOW DOWN ***
Evgeni104: shows [Th Ts] (a full house, Tens full of Jacks)
PedroDeucher: shows [9s 9d] (two pair, Jacks and Nines)
Evgeni104 collected 820 from pot
PedroDeucher finished the tournament in 3rd place
*** SUMMARY ***
Total pot 820 | Rake 0
Board [Jd Tc 7h Jc Ad]
Seat 1: holdemace486 (big blind) folded before Flop
Seat 2: PedroDeucher (button) showed [9s 9d] and lost with two pair, Jacks and Nines
Seat 3: Evgeni104 (small blind) showed [Th Ts] and won (820) with a full house, Tens full of Jacks

*** HOLE CARDS ***
Dealt to holdemace486 [9c Jd]
Evgeni104: calls 20
holdemace486: raises 545 to 585 and is all-in
Evgeni104: folds
Uncalled bet (545) returned to holdemace486
holdemace486 collected 80 from pot
holdemace486: doesn't show hand
*** SUMMARY ***
Total pot 80 | Rake 0
Seat 1: holdemace486 (big blind) collected (80)
Seat 3: Evgeni104 (button) (small blind) folded before Flop

*** HOLE CARDS ***
Dealt to holdemace486 [5s Ks]
holdemace486 has timed out
holdemace486: folds
Uncalled bet (20) returned to Evgeni104
holdemace486 is sitting out
Evgeni104 collected 40 from pot
Evgeni104: doesn't show hand
*** SUMMARY ***
Total pot 40 | Rake 0
Seat 1: holdemace486 (button) (small blind) folded before Flop
Seat 3: Evgeni104 (big blind) collected (40)

*** HOLE CARDS ***
Dealt to holdemace486 [Qh 5d]
Evgeni104: calls 20
holdemace486: folds
Evgeni104 collected 80 from pot
Evgeni104: doesn't show hand
*** SUMMARY ***
Total pot 80 | Rake 0
Seat 1: holdemace486 (big blind) folded before Flop
Seat 3: Evgeni104 (button) (small blind) collected (80)

*** HOLE CARDS ***
Dealt to holdemace486 [8s 7h]
holdemace486: folds
Uncalled bet (20) returned to Evgeni104
Evgeni104 collected 40 from pot
Evgeni104: doesn't show hand
*** SUMMARY ***
Total pot 40 | Rake 0
Seat 1: holdemace486 (button) (small blind) folded before Flop
Seat 3: Evgeni104 (big blind) collected (40)

*** HOLE CARDS ***
Dealt to holdemace486 [8d 5d]
holdemace486 has returned
Evgeni104: calls 20
holdemace486: raises 505 to 545 and is all-in
Evgeni104: folds
Uncalled bet (505) returned to holdemace486
holdemace486 collected 80 from pot
holdemace486: doesn't show hand
*** SUMMARY ***
Total pot 80 | Rake 0
Seat 1: holdemace486 (big blind) collected (80)
Seat 3: Evgeni104 (button) (small blind) folded before Flop

*** HOLE CARDS ***
Dealt to holdemace486 [3s Qc]
holdemace486: folds
Uncalled bet (20) returned to Evgeni104
Evgeni104 collected 40 from pot
Evgeni104: doesn't show hand
*** SUMMARY ***
Total pot 40 | Rake 0
Seat 1: holdemace486 (button) (small blind) folded before Flop
Seat 3: Evgeni104 (big blind) collected (40)

*** HOLE CARDS ***
Dealt to holdemace486 [2h Tc]
Evgeni104: folds
Uncalled bet (20) returned to holdemace486
holdemace486 collected 40 from pot
holdemace486: doesn't show hand
*** SUMMARY ***
Total pot 40 | Rake 0
Seat 1: holdemace486 (big blind) collected (40)
Seat 3: Evgeni104 (button) (small blind) folded before Flop

*** HOLE CARDS ***
Dealt to holdemace486 [4s Ah]
holdemace486: raises 545 to 585 and is all-in
Evgeni104: folds
Uncalled bet (545) returned to holdemace486
holdemace486 collected 80 from pot
holdemace486: doesn't show hand
*** SUMMARY ***
Total pot 80 | Rake 0
Seat 1: holdemace486 (button) (small blind) collected (80)
Seat 3: Evgeni104 (big blind) folded before Flop

holdemace486: posts big blind 40
*** HOLE CARDS ***
Dealt to holdemace486 [Qc Js]
Evgeni104: folds
Uncalled bet (20) returned to holdemace486
holdemace486 collected 40 from pot
holdemace486: doesn't show hand
*** SUMMARY ***
Total pot 40 | Rake 0
Seat 1: holdemace486 (big blind) collected (40)
Seat 3: Evgeni104 (button) (small blind) folded before Flop

*** HOLE CARDS ***
Dealt to holdemace486 [6c Qh]
holdemace486: folds
Uncalled bet (20) returned to Evgeni104
Evgeni104 collected 40 from pot
Evgeni104: doesn't show hand
*** SUMMARY ***
Total pot 40 | Rake 0
Seat 1: holdemace486 (button) (small blind) folded before Flop
Seat 3: Evgeni104 (big blind) collected (40)

*** HOLE CARDS ***
Dealt to holdemace486 [8h 2s]
Evgeni104: folds
Uncalled bet (20) returned to holdemace486
holdemace486 collected 40 from pot
holdemace486: doesn't show hand
*** SUMMARY ***
Total pot 40 | Rake 0
Seat 1: holdemace486 (big blind) collected (40)
Seat 3: Evgeni104 (button) (small blind) folded before Flop

*** HOLE CARDS ***
Dealt to holdemace486 [6h Qc]
holdemace486: folds
Uncalled bet (20) returned to Evgeni104
Evgeni104 collected 40 from pot
Evgeni104: doesn't show hand
*** SUMMARY ***
Total pot 40 | Rake 0
Seat 1: holdemace486 (button) (small blind) folded before Flop
Seat 3: Evgeni104 (big blind) collected (40)

*** HOLE CARDS ***
Dealt to holdemace486 [9h 2s]
Evgeni104: folds
Uncalled bet (20) returned to holdemace486
holdemace486 collected 40 from pot
holdemace486: doesn't show hand
*** SUMMARY ***
Total pot 40 | Rake 0
Seat 1: holdemace486 (big blind) collected (40)
Seat 3: Evgeni104 (button) (small blind) folded before Flop

*** HOLE CARDS ***
Dealt to holdemace486 [Qs 9d]
holdemace486: calls 20
Evgeni104: raises 815 to 855 and is all-in
holdemace486: folds
Uncalled bet (815) returned to Evgeni104
Evgeni104 collected 80 from pot
Evgeni104: doesn't show hand
*** SUMMARY ***
Total pot 80 | Rake 0
Seat 1: holdemace486 (button) (small blind) folded before Flop
Seat 3: Evgeni104 (big blind) collected (80)

*** HOLE CARDS ***
Dealt to holdemace486 [Ks 6s]
Evgeni104: folds
Uncalled bet (20) returned to holdemace486
holdemace486 collected 40 from pot
holdemace486: doesn't show hand
*** SUMMARY ***
Total pot 40 | Rake 0
Seat 1: holdemace486 (big blind) collected (40)
Seat 3: Evgeni104 (button) (small blind) folded before Flop

*** HOLE CARDS ***
Dealt to holdemace486 [6s 5h]
holdemace486: folds
Uncalled bet (20) returned to Evgeni104
Evgeni104 collected 40 from pot
Evgeni104: doesn't show hand
*** SUMMARY ***
Total pot 40 | Rake 0
Seat 1: holdemace486 (button) (small blind) folded before Flop
Seat 3: Evgeni104 (big blind) collected (40)

*** HOLE CARDS ***
Dealt to holdemace486 [3h Th]
Evgeni104: calls 20
holdemace486: checks
*** FLOP *** [7c 5s 4d]
holdemace486: checks
Evgeni104: checks
*** TURN *** [7c 5s 4d] [Qd]
holdemace486: checks
Evgeni104: bets 40
holdemace486: folds
Uncalled bet (40) returned to Evgeni104
Evgeni104 collected 80 from pot
Evgeni104: doesn't show hand
*** SUMMARY ***
Total pot 80 | Rake 0
Board [7c 5s 4d Qd]
Seat 1: holdemace486 (big blind) folded on the Turn
Seat 3: Evgeni104 (button) (small blind) collected (80)

*** HOLE CARDS ***
Dealt to holdemace486 [5c 4c]
holdemace486: calls 20
Evgeni104: checks
*** FLOP *** [9d 6h Ts]
Evgeni104: bets 40
holdemace486: folds
Uncalled bet (40) returned to Evgeni104
Evgeni104 collected 80 from pot
Evgeni104: doesn't show hand
*** SUMMARY ***
Total pot 80 | Rake 0
Board [9d 6h Ts]
Seat 1: holdemace486 (button) (small blind) folded on the Flop
Seat 3: Evgeni104 (big blind) collected (80)

*** HOLE CARDS ***
Dealt to holdemace486 [6s Ks]
Evgeni104: calls 20
holdemace486: checks
*** FLOP *** [Tc 8h 8c]
holdemace486: checks
Evgeni104: bets 40
holdemace486: folds
Uncalled bet (40) returned to Evgeni104
Evgeni104 collected 80 from pot
Evgeni104: doesn't show hand
*** SUMMARY ***
Total pot 80 | Rake 0
Board [Tc 8h 8c]
Seat 1: holdemace486 (big blind) folded on the Flop
Seat 3: Evgeni104 (button) (small blind) collected (80)

*** HOLE CARDS ***
Dealt to holdemace486 [8s Qc]
holdemace486: folds
Uncalled bet (20) returned to Evgeni104
Evgeni104 collected 40 from pot
Evgeni104: doesn't show hand
*** SUMMARY ***
Total pot 40 | Rake 0
Seat 1: holdemace486 (button) (small blind) folded before Flop
Seat 3: Evgeni104 (big blind) collected (40)

*** HOLE CARDS ***
Dealt to holdemace486 [9c 2h]
Evgeni104: folds
Uncalled bet (20) returned to holdemace486
holdemace486 collected 40 from pot
holdemace486: doesn't show hand
*** SUMMARY ***
Total pot 40 | Rake 0
Seat 1: holdemace486 (big blind) collected (40)
Seat 3: Evgeni104 (button) (small blind) folded before Flop

*** HOLE CARDS ***
Dealt to holdemace486 [Qc As]
holdemace486: calls 20
Evgeni104: raises 975 to 1015 and is all-in
holdemace486: calls 445 and is all-in
Uncalled bet (530) returned to Evgeni104
*** FLOP *** [3s 2c Kh]
*** TURN *** [3s 2c Kh] [Kc]
*** RIVER *** [3s 2c Kh Kc]
 *** SHOW DOWN ***Evgeni104: shows [4c 4s] (two pair, Kings and Fours)holdemace486: shows [Qc As] (a pair of Kings)Evgeni104 collected 970 from potholdemace486 finished the tournament in 2nd placeEvgeni104 wins the tournament and receives \$6.00 - congratulations!*** SUMMARY ***Total pot 970 | Rake 0 Board [3s 2c Kh Kc Td]Seat 1: holdemace486 (button) (small blind) showed [Qc As] and lost with a pair of KingsSeat 3: Evgeni104 (big blind) showed [4c 4s] and won (970) with two pair, Kings and Fours

notice the high volume of queens and the repeat king spades 6 spades

I have a lot more of these all showing this type thing, try it with a real deck this does not happen, I have repeat variant every other game.  Qc the main repeat in this game and consider how so few hands there is.
« Last Edit: 31/07/2015 23:39:00 by Thebox »

#### alancalverd

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• life is too short to drink instant coffee
##### Re: Is this maths correct?
« Reply #153 on: 01/08/2015 10:07:11 »
43 hands x 2 dealt cards, expect 2 x 43/13 =  6 queens.  Actual = 12. Interesting.

#### Colin2B

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##### Re: Is this maths correct?
« Reply #154 on: 01/08/2015 13:15:28 »
A good start, but some way to go to prove your theory.
Two things:
You say the RNG is not at fault. What evidence are you quoting for this?

You need to tabulate all the results you have for the first 2 cards dealt.
List all the cards in a pack and at the side the number of times they occur as 1st and 2nd card dealt eg

Number.              Number
Times as 1st.      Times as 2nd
Card dealt           Card dealt
ah
ac
as
2d
2h
2c
Etc

Then we have a starting point

#### Thebox

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##### Re: Is this maths correct?
« Reply #155 on: 01/08/2015 18:06:23 »
*** HOLE CARDS ***
Dealt to holdemace486 [Ts 2d]
holdemace486: folds
VictoryDay45: raises 20 to 40
greenman370: calls 20
*** FLOP *** [6c 9c 6s]
VictoryDay45: checks
greenman370: checks
*** TURN *** [6c 9c 6s] [Jc]
VictoryDay45: checks
greenman370: checks
*** RIVER *** [6c 9c 6s Jc] [4c]
VictoryDay45: checks
greenman370: bets 40
VictoryDay45: calls 40
*** SHOW DOWN ***
greenman370: shows [4s Tc] (a flush, Jack high)
VictoryDay45: mucks hand
greenman370 collected 160 from pot
*** SUMMARY ***
Total pot 160 | Rake 0
Board [6c 9c 6s Jc 4c]
Seat 1: holdemace486 (button) folded before Flop (didn't bet)
Seat 2: VictoryDay45 (small blind) mucked [Ah 2c]
Seat 3: greenman370 (big blind) showed [4s Tc] and won (160) with a flush, Jack high

*** HOLE CARDS ***
Dealt to holdemace486 [3c 9s]
VictoryDay45: raises 20 to 40
greenman370: calls 30
holdemace486: folds
*** FLOP *** [Tc Ts 5d]
greenman370: checks
VictoryDay45: bets 40
greenman370: folds
Uncalled bet (40) returned to VictoryDay45
VictoryDay45 collected 100 from pot
VictoryDay45: doesn't show hand
*** SUMMARY ***
Total pot 100 | Rake 0
Board [Tc Ts 5d]
Seat 1: holdemace486 (big blind) folded before Flop
Seat 2: VictoryDay45 (button) collected (100)
Seat 3: greenman370 (small blind) folded on the Flop

*** HOLE CARDS ***
Dealt to holdemace486 [Kc Qh]
greenman370: folds
holdemace486: raises 40 to 60
VictoryDay45: folds
Uncalled bet (40) returned to holdemace486
holdemace486 collected 40 from pot
holdemace486: doesn't show hand
*** SUMMARY ***
Total pot 40 | Rake 0
Seat 1: holdemace486 (small blind) collected (40)
Seat 2: VictoryDay45 (big blind) folded before Flop
Seat 3: greenman370 (button) folded before Flop (didn't bet)

*** HOLE CARDS ***
Dealt to holdemace486 [Qs 6d]
holdemace486: folds
VictoryDay45: raises 40 to 60
greenman370: calls 40
*** FLOP *** [5d Jh 4c]
VictoryDay45: bets 60
greenman370: folds
Uncalled bet (60) returned to VictoryDay45
VictoryDay45 collected 120 from pot
VictoryDay45: doesn't show hand
*** SUMMARY ***
Total pot 120 | Rake 0
Board [5d Jh 4c]
Seat 1: holdemace486 (button) folded before Flop (didn't bet)
Seat 2: VictoryDay45 (small blind) collected (120)
Seat 3: greenman370 (big blind) folded on the Flop

*** HOLE CARDS ***
Dealt to holdemace486 [5s 7d]
VictoryDay45: folds
greenman370: raises 20 to 40
holdemace486: folds
Uncalled bet (20) returned to greenman370
greenman370 collected 40 from pot
greenman370: doesn't show hand
*** SUMMARY ***
Total pot 40 | Rake 0
Seat 1: holdemace486 (big blind) folded before Flop
Seat 2: VictoryDay45 (button) folded before Flop (didn't bet)
Seat 3: greenman370 (small blind) collected (40)

*** HOLE CARDS ***
Dealt to holdemace486 [3s 9d]
greenman370: folds
holdemace486: folds
Uncalled bet (10) returned to VictoryDay45
VictoryDay45 collected 20 from pot
VictoryDay45: doesn't show hand
*** SUMMARY ***
Total pot 20 | Rake 0
Seat 1: holdemace486 (small blind) folded before Flop
Seat 2: VictoryDay45 (big blind) collected (20)
Seat 3: greenman370 (button) folded before Flop (didn't bet)

*** HOLE CARDS ***
holdemace486: raises 40 to 60
VictoryDay45: folds
greenman370: folds
Uncalled bet (40) returned to holdemace486
holdemace486 collected 50 from pot
holdemace486: doesn't show hand
*** SUMMARY ***
Total pot 50 | Rake 0
Seat 1: holdemace486 (button) collected (50)
Seat 2: VictoryDay45 (small blind) folded before Flop
Seat 3: greenman370 (big blind) folded before Flop

*** HOLE CARDS ***
Dealt to holdemace486 [4c 9d]
VictoryDay45: folds
greenman370: calls 10
holdemace486: checks
*** FLOP *** [Tc 5h 8c]
greenman370: bets 20
holdemace486: folds
Uncalled bet (20) returned to greenman370
greenman370 collected 40 from pot
greenman370: doesn't show hand
*** SUMMARY ***
Total pot 40 | Rake 0
Board [Tc 5h 8c]
Seat 1: holdemace486 (big blind) folded on the Flop
Seat 2: VictoryDay45 (button) folded before Flop (didn't bet)
Seat 3: greenman370 (small blind) collected (40)

*** HOLE CARDS ***
Dealt to holdemace486 [Th 2d]
greenman370: folds
holdemace486: folds
Uncalled bet (10) returned to VictoryDay45
VictoryDay45 collected 20 from pot
VictoryDay45: doesn't show hand
*** SUMMARY ***
Total pot 20 | Rake 0
Seat 1: holdemace486 (small blind) folded before Flop
Seat 2: VictoryDay45 (big blind) collected (20)
Seat 3: greenman370 (button) folded before Flop (didn't bet)

*** HOLE CARDS ***
Dealt to holdemace486 [Jd 8c]
holdemace486: folds
VictoryDay45: raises 40 to 60
greenman370: calls 40
*** FLOP *** [7s 3d 7h]
VictoryDay45: bets 60
greenman370: calls 60
*** TURN *** [7s 3d 7h] [Ac]
VictoryDay45: checks
greenman370: bets 80
VictoryDay45: folds
Uncalled bet (80) returned to greenman370
greenman370 collected 240 from pot
greenman370: doesn't show hand
*** SUMMARY ***
Total pot 240 | Rake 0
Board [7s 3d 7h Ac]
Seat 1: holdemace486 (button) folded before Flop (didn't bet)
Seat 2: VictoryDay45 (small blind) folded on the Turn
Seat 3: greenman370 (big blind) collected (240)

*** HOLE CARDS ***
Dealt to holdemace486 [3c 9c]
VictoryDay45: calls 20
greenman370: calls 10
holdemace486: checks
*** FLOP *** [5h 2d 3s]
greenman370: bets 20
holdemace486: raises 40 to 60
VictoryDay45: raises 330 to 390 and is all-in
greenman370: folds
holdemace486: folds
Uncalled bet (330) returned to VictoryDay45
VictoryDay45 collected 200 from pot
VictoryDay45: doesn't show hand
*** SUMMARY ***
Total pot 200 | Rake 0
Board [5h 2d 3s]
Seat 1: holdemace486 (big blind) folded on the Flop
Seat 2: VictoryDay45 (button) collected (200)
Seat 3: greenman370 (small blind) folded on the Flop

*** HOLE CARDS ***
Dealt to holdemace486 [td Qc]
greenman370: raises 60 to 90
holdemace486: folds
VictoryDay45: folds
Uncalled bet (60) returned to greenman370
greenman370 collected 75 from pot
greenman370: doesn't show hand
*** SUMMARY ***
Total pot 75 | Rake 0
Seat 1: holdemace486 (small blind) folded before Flop
Seat 2: VictoryDay45 (big blind) folded before Flop
Seat 3: greenman370 (button) collected (75)

*** HOLE CARDS ***
Dealt to holdemace486 [Tc 9s]
holdemace486: folds
VictoryDay45: raises 60 to 90
greenman370: folds
Uncalled bet (60) returned to VictoryDay45
VictoryDay45 collected 60 from pot
VictoryDay45: doesn't show hand
*** SUMMARY ***
Total pot 60 | Rake 0
Seat 1: holdemace486 (button) folded before Flop (didn't bet)
Seat 2: VictoryDay45 (small blind) collected (60)
Seat 3: greenman370 (big blind) folded before Flop

*** HOLE CARDS ***
Dealt to holdemace486 [9s Jh]
VictoryDay45: calls 30
greenman370: calls 15
holdemace486: checks
*** FLOP *** [Qc 8h 2d]
greenman370: checks
holdemace486: checks
VictoryDay45: checks
*** TURN *** [Qc 8h 2d] [Ac]
greenman370: checks
holdemace486: checks
VictoryDay45: bets 45
greenman370: folds
holdemace486: folds
Uncalled bet (45) returned to VictoryDay45
VictoryDay45 collected 90 from pot
VictoryDay45: doesn't show hand
*** SUMMARY ***
Total pot 90 | Rake 0
Board [Qc 8h 2d Ac]
Seat 1: holdemace486 (big blind) folded on the Turn
Seat 2: VictoryDay45 (button) collected (90)
Seat 3: greenman370 (small blind) folded on the Turn

*** HOLE CARDS ***
Dealt to holdemace486 [8h Jd]
greenman370: raises 30 to 60
holdemace486: folds
VictoryDay45: folds
Uncalled bet (30) returned to greenman370
greenman370 collected 75 from pot
greenman370: doesn't show hand
*** SUMMARY ***
Total pot 75 | Rake 0
Seat 1: holdemace486 (small blind) folded before Flop
Seat 2: VictoryDay45 (big blind) folded before Flop
Seat 3: greenman370 (button) collected (75)

*** HOLE CARDS ***
Dealt to holdemace486 [8d Kc]
holdemace486: folds
VictoryDay45: raises 60 to 90
greenman370: folds
Uncalled bet (60) returned to VictoryDay45
VictoryDay45 collected 60 from pot
VictoryDay45: doesn't show hand
*** SUMMARY ***
Total pot 60 | Rake 0
Seat 1: holdemace486 (button) folded before Flop (didn't bet)
Seat 2: VictoryDay45 (small blind) collected (60)
Seat 3: greenman370 (big blind) folded before Flop

*** HOLE CARDS ***
Dealt to holdemace486 [2s 6d]
VictoryDay45: folds
greenman370: calls 15
holdemace486: checks
*** FLOP *** [5s 9s Jd]
greenman370: bets 30
holdemace486: folds
Uncalled bet (30) returned to greenman370
greenman370 collected 60 from pot
greenman370: doesn't show hand
*** SUMMARY ***
Total pot 60 | Rake 0
Board [5s 9s Jd]
Seat 1: holdemace486 (big blind) folded on the Flop
Seat 2: VictoryDay45 (button) folded before Flop (didn't bet)
Seat 3: greenman370 (small blind) collected (60)

*** HOLE CARDS ***
Dealt to holdemace486 [6d 9d]
greenman370: folds
holdemace486: folds
Uncalled bet (15) returned to VictoryDay45
VictoryDay45 collected 30 from pot
VictoryDay45: doesn't show hand
*** SUMMARY ***
Total pot 30 | Rake 0
Seat 1: holdemace486 (small blind) folded before Flop
Seat 2: VictoryDay45 (big blind) collected (30)
Seat 3: greenman370 (button) folded before Flop (didn't bet)

*** HOLE CARDS ***
Dealt to holdemace486 [5c 5h]
holdemace486: raises 60 to 90
VictoryDay45: folds
greenman370: folds
Uncalled bet (60) returned to holdemace486
holdemace486 collected 75 from pot
holdemace486: doesn't show hand
*** SUMMARY ***
Total pot 75 | Rake 0
Seat 1: holdemace486 (button) collected (75)
Seat 2: VictoryDay45 (small blind) folded before Flop
Seat 3: greenman370 (big blind) folded before Flop

*** HOLE CARDS ***
Dealt to holdemace486 [6h Js]
VictoryDay45: folds
greenman370: calls 15
holdemace486: checks
*** FLOP *** [Tc Ah 3d]
greenman370: bets 30
holdemace486: folds
Uncalled bet (30) returned to greenman370
greenman370 collected 60 from pot
greenman370: doesn't show hand
*** SUMMARY ***
Total pot 60 | Rake 0
Board [Tc Ah 3d]
Seat 1: holdemace486 (big blind) folded on the Flop
Seat 2: VictoryDay45 (button) folded before Flop (didn't bet)
Seat 3: greenman370 (small blind) collected (60)

*** HOLE CARDS ***
Dealt to holdemace486 [Tc 8h]
greenman370: raises 30 to 60
holdemace486: folds
VictoryDay45: calls 30
*** FLOP *** [3d 7d Ad]
VictoryDay45: checks
greenman370: bets 60
VictoryDay45: calls 60
*** TURN *** [3d 7d Ad] [Qh]
VictoryDay45: checks
greenman370: checks
*** RIVER *** [3d 7d Ad Qh] [Qc]
VictoryDay45: bets 120
greenman370: folds
Uncalled bet (120) returned to VictoryDay45
VictoryDay45 collected 255 from pot
VictoryDay45: doesn't show hand
*** SUMMARY ***
Total pot 255 | Rake 0
Board [3d 7d Ad Qh Qc]
Seat 1: holdemace486 (small blind) folded before Flop
Seat 2: VictoryDay45 (big blind) collected (255)
Seat 3: greenman370 (button) folded on the River

*** HOLE CARDS ***
Dealt to holdemace486 [Ts 4h]
holdemace486: folds
VictoryDay45: raises 60 to 90
greenman370: folds
Uncalled bet (60) returned to VictoryDay45
VictoryDay45 collected 60 from pot
VictoryDay45: doesn't show hand
*** SUMMARY ***
Total pot 60 | Rake 0
Seat 1: holdemace486 (button) folded before Flop (didn't bet)
Seat 2: VictoryDay45 (small blind) collected (60)
Seat 3: greenman370 (big blind) folded before Flop

*** HOLE CARDS ***
Dealt to holdemace486 [5c Qd]
VictoryDay45: calls 40
greenman370: calls 20
holdemace486: checks
*** FLOP *** [Jc 4c 9h]
greenman370: checks
holdemace486: checks
VictoryDay45: checks
*** TURN *** [Jc 4c 9h] [6s]
greenman370: bets 80
holdemace486: folds
VictoryDay45: calls 80
*** RIVER *** [Jc 4c 9h 6s] [8s]
greenman370: bets 120
VictoryDay45: folds
Uncalled bet (120) returned to greenman370
greenman370 collected 280 from pot
greenman370: doesn't show hand
*** SUMMARY ***
Total pot 280 | Rake 0
Board [Jc 4c 9h 6s 8s]
Seat 1: holdemace486 (big blind) folded on the Turn
Seat 2: VictoryDay45 (button) folded on the River
Seat 3: greenman370 (small blind) collected (280)

*** HOLE CARDS ***
Dealt to holdemace486 [7s 4d]
greenman370: raises 40 to 80
holdemace486: folds
VictoryDay45: calls 40
*** FLOP *** [6h Qc 2h]
VictoryDay45: checks
greenman370: bets 80
VictoryDay45: calls 80
*** TURN *** [6h Qc 2h] [As]
VictoryDay45: checks
greenman370: bets 80
VictoryDay45: raises 80 to 160
greenman370: folds
Uncalled bet (80) returned to VictoryDay45
VictoryDay45 collected 500 from pot
VictoryDay45: doesn't show hand
*** SUMMARY ***
Total pot 500 | Rake 0
Board [6h Qc 2h As]
Seat 1: holdemace486 (small blind) folded before Flop
Seat 2: VictoryDay45 (big blind) collected (500)
Seat 3: greenman370 (button) folded on the Turn

*** HOLE CARDS ***
Dealt to holdemace486 [Qc 7d]
holdemace486: folds
VictoryDay45: raises 855 to 895 and is all-in
greenman370: folds
Uncalled bet (855) returned to VictoryDay45
VictoryDay45 collected 80 from pot
VictoryDay45: doesn't show hand
*** SUMMARY ***
Total pot 80 | Rake 0
Seat 1: holdemace486 (button) folded before Flop (didn't bet)
Seat 2: VictoryDay45 (small blind) collected (80)
Seat 3: greenman370 (big blind) folded before Flop

*** HOLE CARDS ***
Dealt to holdemace486 [7h Kd]
VictoryDay45: folds
greenman370: calls 20
holdemace486: checks
*** FLOP *** [9c 8c Ts]
greenman370: bets 300 and is all-in
holdemace486: folds
Uncalled bet (300) returned to greenman370
greenman370 collected 80 from pot
greenman370: doesn't show hand
*** SUMMARY ***
Total pot 80 | Rake 0
Board [9c 8c Ts]
Seat 1: holdemace486 (big blind) folded on the Flop
Seat 2: VictoryDay45 (button) folded before Flop (didn't bet)
Seat 3: greenman370 (small blind) collected (80)

*** HOLE CARDS ***
Dealt to holdemace486 [2c 3s]
greenman370: folds
holdemace486: folds
Uncalled bet (20) returned to VictoryDay45
VictoryDay45 collected 40 from pot
VictoryDay45: doesn't show hand
*** SUMMARY ***
Total pot 40 | Rake 0
Seat 1: holdemace486 (small blind) folded before Flop
Seat 2: VictoryDay45 (big blind) collected (40)
Seat 3: greenman370 (button) folded before Flop (didn't bet)

*** HOLE CARDS ***
Dealt to holdemace486 [3c 9c]
holdemace486: folds
VictoryDay45: calls 20
greenman370: raises 80 to 120
VictoryDay45: folds
Uncalled bet (80) returned to greenman370
greenman370 collected 80 from pot
greenman370: doesn't show hand
*** SUMMARY ***
Total pot 80 | Rake 0
Seat 1: holdemace486 (button) folded before Flop (didn't bet)
Seat 2: VictoryDay45 (small blind) folded before Flop
Seat 3: greenman370 (big blind) collected (80)

*** HOLE CARDS ***
Dealt to holdemace486 [2s Kc]
VictoryDay45: calls 40
greenman370: calls 20
holdemace486: checks
*** FLOP *** [Ks 8c Js]
greenman370: checks
holdemace486: checks
VictoryDay45: checks
*** TURN *** [Ks 8c Js] [2c]
greenman370: checks
holdemace486: bets 40
VictoryDay45: folds
greenman370: folds
Uncalled bet (40) returned to holdemace486
holdemace486 collected 120 from pot
holdemace486: doesn't show hand
*** SUMMARY ***
Total pot 120 | Rake 0
Board [Ks 8c Js 2c]
Seat 1: holdemace486 (big blind) collected (120)
Seat 2: VictoryDay45 (button) folded on the Turn
Seat 3: greenman370 (small blind) folded on the Turn

*** HOLE CARDS ***
Dealt to holdemace486 [3s Kh]
greenman370: folds
holdemace486: folds
Uncalled bet (20) returned to VictoryDay45
VictoryDay45 collected 40 from pot
VictoryDay45: doesn't show hand
*** SUMMARY ***
Total pot 40 | Rake 0
Seat 1: holdemace486 (small blind) folded before Flop
Seat 2: VictoryDay45 (big blind) collected (40)
Seat 3: greenman370 (button) folded before Flop (didn't bet)

*** HOLE CARDS ***
Dealt to holdemace486 [Qh 7s]
holdemace486: folds
VictoryDay45: folds
Uncalled bet (20) returned to greenman370
greenman370 collected 40 from pot
greenman370: doesn't show hand
*** SUMMARY ***
Total pot 40 | Rake 0
Seat 1: holdemace486 (button) folded before Flop (didn't bet)
Seat 2: VictoryDay45 (small blind) folded before Flop
Seat 3: greenman370 (big blind) collected (40)

*** HOLE CARDS ***
Dealt to holdemace486 [Kc 9c]
VictoryDay45: calls 40
greenman370: raises 80 to 120
holdemace486: folds
VictoryDay45: calls 80
*** FLOP *** [9d 5s 3d]
greenman370: bets 280 and is all-in
VictoryDay45: folds
Uncalled bet (280) returned to greenman370
greenman370 collected 280 from pot
greenman370: doesn't show hand
*** SUMMARY ***
Total pot 280 | Rake 0
Board [9d 5s 3d]
Seat 1: holdemace486 (big blind) folded before Flop
Seat 2: VictoryDay45 (button) folded on the Flop
Seat 3: greenman370 (small blind) collected (280)

*** HOLE CARDS ***
Dealt to holdemace486 [7s Ac]
greenman370: folds
holdemace486: raises 125 to 185 and is all-in
VictoryDay45: calls 125
*** FLOP *** [4h 5h 2d]
*** TURN *** [4h 5h 2d] [2c]
*** RIVER *** [4h 5h 2d 2c] [Qs]
*** SHOW DOWN ***
holdemace486: shows [7s Ac] (a pair of Deuces)
VictoryDay45: shows [Th 9h] (a pair of Deuces - lower kicker)
holdemace486 collected 370 from pot
*** SUMMARY ***
Total pot 370 | Rake 0
Board [4h 5h 2d 2c Qs]
Seat 1: holdemace486 (small blind) showed [7s Ac] and won (370) with a pair of Deuces
Seat 2: VictoryDay45 (big blind) showed [Th 9h] and lost with a pair of Deuces
Seat 3: greenman370 (button) folded before Flop (didn't bet)

*** HOLE CARDS ***
holdemace486: raises 60 to 120
VictoryDay45: folds
greenman370: calls 60
*** FLOP *** [3s 6d 2h]
greenman370: bets 60
holdemace486: raises 190 to 250 and is all-in
greenman370: calls 190
*** TURN *** [3s 6d 2h] [As]
*** RIVER *** [3s 6d 2h As] [9h]
*** SHOW DOWN ***
greenman370: shows [4c 5d] (a straight, Deuce to Six)
holdemace486: shows [Ad 6s] (two pair, Aces and Sixes)
greenman370 collected 770 from pot
holdemace486 finished the tournament in 3rd place
*** SUMMARY ***
Total pot 770 | Rake 0
Board [3s 6d 2h As 9h]
Seat 1: holdemace486 (button) showed [Ad 6s] and lost with two pair, Aces and Sixes
Seat 2: VictoryDay45 (small blind) folded before Flop
Seat 3: greenman370 (big blind) showed [4c 5d] and won (770) with a straight, Deuce to Six

nines this time, and it is nothing to do with the random generator because that only does the shuffle, it is all about frequency and the spacing is just not right.

#### chiralSPO

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• Neilep Level Member
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##### Re: Is this maths correct?
« Reply #156 on: 01/08/2015 19:14:58 »
In the first set of hands presented: 42 hands shown (84 cards drawn) if each card has a 1/52 chance of being drawn, we would expect to find each card appearing once or twice (1.6 times) throughout this whole set. This is what was observed:

Ac 1
Ah 2
As 1
2c 2
2d 1
2h 2
2s 2
3c 0
3d 2
3h 3
3s 1
4c 4
4d 0
4h 1
4s 2
5c 1
5d 2
5h 2
5s 2
6c 2
6d 1
6h 0
6s 3
7c 0
7d 1
7h 1
7s 1
8c 0
8d 2
8h 2
8s 3
9c 3
9d 1
9h 1
9s 0
Tc 2
Td 0
Th 1
Ts 1
Jc 0
Jd 1
Jh 1
Js 3
Qc 6
Qd 1
Qh 3
Qs 1
Kc 0
Kd 1
Kh 0
Ks 3

So how well does this match up to what we would expect from a completely random selection?

Frequency  0       1       2       3       4       5       6       7
observed:  10     19     14      7       1       0       1       0
expected:  10.0  18.2  14.3  7.4     2.9    0.9    0.2   0.002 (calculations shown below)

52*(50/52)42 = 10.0
52*42*((50/52)41)*(2/52) = 18.2
52*(42*41/2)*((50/52)^39)*(2/52)^2 = 14.3
52*(42*41*40/(3*2))*((50/52)^39)*(2/52)^3 = 7.4
52*(42*41*40*39/(4*3*2))*((50/52)^38)*(2/52)^4 = 2.9
52*(42*41*40*39*38/(5*4*3*2))*((50/52)^37)*(2/52)^5 = 0.9
52*(42*41*40*39*38*37/(6*5*4*3*2))*((50/52)^36)*(2/52)^6 = 0.2
52*(42*41*40*39*38*37*36/(7*6*5*4*3*2))*((50/52)^35)*(2/52)^7 = 0.002

This does not appear to be very different from a random distribution (based on this one simple test of a fairly small data set).

If you wanted to prove something about time dependence you would need to include timestamps in the data--but there is no point trying to show a pattern with respect to one variable, when the results are very well matched to a random distribution...
« Last Edit: 02/08/2015 02:28:38 by chiralSPO »

#### alancalverd

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• life is too short to drink instant coffee
##### Re: Is this maths correct?
« Reply #157 on: 02/08/2015 00:52:22 »
Powerful stuff, CS.

If Qc=6 is considered exceptional, then 4c = 4 is also exceptional. The problem is one of perception: minor but entirely normal deviations of obs/exp have an unreasonable significance, both psychologically and to the outcome of the game, if they involve aces or picture cards.

Feynman wrote a couple of good essays on the subject of significant coincidence.

#### Thebox

• Neilep Level Member
• Posts: 3160
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##### Re: Is this maths correct?
« Reply #158 on: 02/08/2015 09:41:00 »
I tried to post a larger set of hands, was limited to words so was unable, this set of hand sis more obvious than the previous two sets o hands I posted.

The problem is clusters.

I will post some parts to show what I mean.

4hAs/6h6c/jh2h/kh6d/2hjh/qc2c/3d7h/kh3s/ks5s/td7s/ac7d/td4h/

I have done you the first few hands, below my game when I am playing it shows my cards I have received, it is much easier to see when there is colour there, notice in these first few hands the repeat values in a short space of time.

continued -

I would accuse a live dealer of not shuffling properly and cards being stuck together.

continued-

3h4h/jdjs/tsks/js2s/4d8h/5s2s/js5s/jc2c/8s2d/9htd/4h5s/9d/5d/

final part

5ckc/ks7h/6s9c/8d2s/7hqh/2d6c/kdqs/8cjd/6d2d/8sjs/jhkc/8c8h/6h7c/3c2d/3h8c/
4d6c/ks3s/ts9d/qdjs/ks2s/3d2d/tstc/3c4h/2s8c/3s6d/4d3c/5d9s/9ctd/2s6d/8hth/3d5d/3htc/3h9d/4das/5skh/ts5h/9hts/td6d/8sjd/6cqd/ksjd/8c4s/5hkc/jd3s/6d6h/ts2c/jdts/kdkc/5c5h/9d6h/jh6d/4s3c/7hjh/7hqc/8ckh/tdth/2d5c/9has/

« Last Edit: 02/08/2015 10:45:22 by Thebox »

#### Thebox

• Neilep Level Member
• Posts: 3160
• Thanked: 45 times
##### Re: Is this maths correct?
« Reply #159 on: 02/08/2015 10:53:33 »
This what is wrong with the intersection odds.

6c
kd
7h
6c
5h
as
9d
6c

By deck skipping , it allowed to me receive deck 1, 4, 8 giving me 3 of the same values in a row.

It causes clusters of values by skipping the designated path over time.

Following a standard course over time without skipping deviation I would of received 6c,kd,7h,6c,5h,as,9d,6c over time which spaces out 6c over time in this example.

Please feel free to experiment using a single deck the patterns and spaces are different compared to multiple decks and choice.

I have just got out my deck of cards I will deal to the rules and record my cards I get with a live deck here and now.

hand 1 - jc8d
hand 2 - ts2d
hand 3 - thqs
hand 4 - 4s7s
hand 5 - tc6s
hand 6-  asjc
hand 8-  qh4h
hand 9-  kc3h
hand10-  4s6d

we can see within ten hands a difference of pattern and a better variation of hands.

The next ten hands,

h1- 3h7d
h2- js8d
h3-6d2d
h4-4s7d
h5-jhjs
h6-3hah
h7-jh9d
h8- 5c8s
h9-5h8d
ht-kh3d

again much more even distribution over time.

n) over a period of time of X equals (a)

(n) over a period of time of Y equals (b)

t=............................................

x=.........n...................................n

y=...nn........n....n...........n.......n......

relative to (n) the probability spacing over time Y≠X

x=(a)
Y=(b)

(a)/t≠(b)/t
distance

« Last Edit: 02/08/2015 12:53:26 by Thebox »

#### Colin2B

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##### Re: Is this maths correct?
« Reply #160 on: 02/08/2015 16:49:21 »
There are 2 things to consider.
First, is the distribution random. ChiralSPO has kindly done the donkey work for us and it is a good match.

Secondly, if it is random then there is the same probability that the same cards will occur side by side as they will be fully separated or indeed in any position.

As Alan says, confirmation bias and the brain's pattern seeking mechanism means we notice certain items and events more than others.
Every time you claim to be disadvantaged by the deck skipping, someone else will think you have been advantaged compared to themselves.

If you feel the need to try posting all your data, how about attaching a file? PDF?

#### alancalverd

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##### Re: Is this maths correct?
« Reply #161 on: 03/08/2015 22:51:22 »
Quote
By deck skipping , it allowed to me receive deck 1, 4, 8 giving me 3 of the same values in a row.

A priori and a posteriori are very different conditions. If you were skipping a priori, what made you choose 1, 4 and 8?

#### Thebox

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##### Re: Is this maths correct?
« Reply #162 on: 04/08/2015 10:25:20 »
Quote
By deck skipping , it allowed to me receive deck 1, 4, 8 giving me 3 of the same values in a row.

A priori and a posteriori are very different conditions. If you were skipping a priori, what made you choose 1, 4 and 8?

It would actually unknown which deck you receive, the distribution of the decks is defined by when a table finishes its hand it gets  new deck from the system queue, my example was to show what happens. My observation shows this, with a single deck the distribution spacing of frequency rate of repeat occurrence is different to that of online as seen in my few examples, all my examples show the same thing,  the last 2 examples I posted were fresh examples , I played them to get the examples, every time it is noticeable by observation.
I do not know what to even call it, by I am certain you understand exactly what I am saying.

I have found a way to combat the problem sort of, by using less time games , but this does not fix the problem .

I am unsure how to upload a pdf file to show that every game is the same by observation you can see this to be true.

#### Thebox

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##### Re: Is this maths correct?
« Reply #163 on: 08/08/2015 09:06:26 »
Else where has directed me to this-http://bactra.org/notebooks/ergodic-theory.html

can anyone please explain this, I can not understand it.

#### Colin2B

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##### Re: Is this maths correct?
« Reply #164 on: 08/08/2015 14:40:48 »
Else where has directed me to this-http://bactra.org/notebooks/ergodic-theory.html

can anyone please explain this, I can not understand it.
You would need to learn a lot more maths before you could understand this.

#### Thebox

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##### Re: Is this maths correct?
« Reply #165 on: 09/08/2015 13:24:20 »

You would need to learn a lot more maths before you could understand this.

I am not sure that maths can ever explain moving values  forward in time.

#### Thebox

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##### Re: Is this maths correct?
« Reply #166 on: 09/08/2015 13:31:14 »

You would need to learn a lot more maths before you could understand this.

I am not sure that maths can ever explain moving values  forward in time.
or can it?

P(n)/y=(x)∩(n)/t2
t1

this

in this grid the rows are randomly shuffled,

nnnnn
nnnnn
nnnnn
nnnnn
nnnnn

i can tell you that each row has a 1/5 chance, of any value being in the first column.

n
n
n
n
n

however we know that all the first column, could have the same value,

1
1
1
1
1

so if several rows of values were set, and you were designated a column, you are aligned an unknown chance of the values aligned.
what happens if we add a random distribution of your alignment to other outputs?

a
b
c
d
e

if we receive in order, edcba, that is a continuation of time, where as if we received e and then b, we would be bringing b, forward in time, to a specific point of time.

so what is the chances from the columns of the values?

P(n)/y=(x)∩(n)

y=decks

x=players

n=variant

P=probability

∩=intercept

« Last Edit: 09/08/2015 14:12:10 by Thebox »

#### The Naked Scientists Forum

##### Re: Is this maths correct?
« Reply #166 on: 09/08/2015 13:31:14 »