Mental
Mental
Joined: Dec 10, 2018
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Thanks for this post from:
OnceDear
November 2nd, 2022 at 7:53:54 PM permalink
Quote: ThomasK


I set up the progression in Excel as a finite state machine. It simulates even money bets in double zero roulette but doesn't use triggers for the betting sequence.
link to original post

Disclaimer: TK calculates house edge by is own bizarre definition and then wants to be treated as some kind of genius for discovering a way to alter the house edge through betting systems. Best to just ignore his claims.
GreenZero
GreenZero
Joined: Nov 16, 2021
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November 2nd, 2022 at 8:55:57 PM permalink
Quote: gordonm888

I would not say ThomasK has proven anything. I would say that he has done a simulation, with 1M trials, and produced some evidence.

First, I'm glad ThomasK did this. I haven't seen this Carsch system before and I was hoping someone would analyze it.

Secondly, I think it's appropriate to ask some questions about the simulation and try to understand what has been done. I'll start:

In the 1M trials simulation, how often was the 10-step betting sequence terminated with a loss on the 10th step, losing 93 units (while presumably winning some bets on the way through the progression?) In other words, how many times did you wager 32 units and lose?

How many times did you wager 32 units and win?

What wagers are made after all 10 steps lose?

What was the mean wager size as averaged over the roughly 1M trials?
link to original post



Bingo! and I would love to see line graph results. Just play a session until at least 5 units won and then walking away or walking away from a session loss of 93 units.

Thank you Thomas K for your info it is much appreciated.
GreenZero
GreenZero
Joined: Nov 16, 2021
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November 2nd, 2022 at 9:32:26 PM permalink
I was also looking at this progression with roulette betting 1 unit each on the 1st&2nd dozens and then betting on the 2nd&3rd dozens. Since your chances of hitting are about 66% it could work beautifully with this progression since your looking for 2 wins in a row to reset back to the beginning. I haven't done a small simulation on this yet though as a progression system involving 2 dozens get expensive really fast.
ThomasK
ThomasK
Joined: Jul 4, 2015
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November 3rd, 2022 at 3:48:15 AM permalink
Before I answer your replies individually, please see here the Excel definitions I use to simulate the progression.

While preparing the Excel to share with you, I realized a mistake which seems to be in the definition of the system. The amounts of the progression add up to 93, but you need two losses in a row on the same progression level to be eligible to move to the next level. Therefore the amount lost in the worst case is 186 units.
This means that the equivalent slot machine requires 186 coins in.

Here now the components of the Excel for Carsch with Parlay on intitial bet and its winning and corrected coin in for the slot machine:

Prepare section A.

probability(hit) =18/38

#attempts =MAX(L:L)

amount wagered =SUM(H:H)
payed =SUM(I:I)
return =B6/B5
house edge =1-B7

coin in =SUM(M:M)
cash out =SUM(N:N)
return =B11/B10
house edge =1-B12


Prepare section B.

random won? key state wager payed wager per attempt payed per attempt attempt # coin in cash out fin
=RAND() =IF(D2<=$B$1;"won";"lost") =G2&E2 1 =VLOOKUP(F2;Q:W;5;0) =IF(E2="won";2*H2;0) =IF(G2=1;H2;H2+J1) =IF(G2=1;I2;I2+K1) 1 =IF(G2=1;186;0) =IF(G3=1;MIN(1;I2);0)*(186+K2-J2)
=RAND() =IF(D3<=$B$1;"won";"lost") =G3&E3 =VLOOKUP(F2;Q:W;4;0) =VLOOKUP(F3;Q:W;5;0) =IF(E3="won";2*H3;0) =IF(G3=1;H3;H3+J2) =IF(G3=1;I3;I3+K2) =IF(G3=1;L2+1;L2) =IF(G3=1;186;0) =IF(G4=1;MIN(1;I3);0)*(186+K3-J3)


Because of the localization of my Excel you might need to try this version. Semicolons ";" are replaced by commas ",". I'm not able to test whether it works properly:

random won? key state wager payed wager per attempt payed per attempt attempt # coin in cash out fin
=RAND() =IF(D2<=$B$1,"won","lost") =G2&E2 1 =VLOOKUP(F2,Q:W,5,0) =IF(E2="won",2*H2,0) =IF(G2=1,H2,H2+J1) =IF(G2=1,I2,I2+K1) 1 =IF(G2=1,186,0) =IF(G3=1,MIN(1,I2),0)*(186+K2-J2)
=RAND() =IF(D3<=$B$1,"won","lost") =G3&E3 =VLOOKUP(F2,Q:W,4,0) =VLOOKUP(F3,Q:W,5,0) =IF(E3="won",2*H3,0) =IF(G3=1,H3,H3+J2) =IF(G3=1,I3,I3+K2) =IF(G3=1,L2+1,L2) =IF(G3=1,186,0) =IF(G4=1,MIN(1,I3),0)*(186+K3-J3)


Prepare section C.

key state input next wager sub-state fin
=R2&S2 1 won =R4 1 1
=R3&S3 1 lost =R6 1 1
=R4&S4 2 won 1 =2*U2 2
=R5&S5 2 lost =R6 =2*U3 2
=R6&S6 3 won =R4 1 3
=R7&S7 3 lost =R8 1 3
=R8&S8 =U8*10+V8 =S2 =R10 1 =V2
=R9&S9 =U9*10+V9 =S3 =R12 1 =V3
=R10&S10 =U10*10+V10 =S4 1 =2*U8 =V4
=R11&S11 =U11*10+V11 =S5 =R12 =2*U9 =V5
=R12&S12 =U12*10+V12 =S6 =R10 1 =V6
=R13&S13 =U13*10+V13 =S7 =R14 1 =V7
=R14&S14 =U14*10+V14 =S8 =R16 2 =V8
=R15&S15 =U15*10+V15 =S9 =R18 2 =V9
=R16&S16 =U16*10+V16 =S10 1 =2*U14 =V10
=R17&S17 =U17*10+V17 =S11 =R18 =2*U15 =V11
=R18&S18 =U18*10+V18 =S12 =R16 2 =V12
=R19&S19 =U19*10+V19 =S13 =R20 2 =V13
=R20&S20 =U20*10+V20 =S14 =R22 3 =V14
=R21&S21 =U21*10+V21 =S15 =R24 3 =V15
=R22&S22 =U22*10+V22 =S16 1 =2*U20 =V16
=R23&S23 =U23*10+V23 =S17 =R24 =2*U21 =V17
=R24&S24 =U24*10+V24 =S18 =R22 3 =V18
=R25&S25 =U25*10+V25 =S19 =R26 3 =V19
=R26&S26 =U26*10+V26 =S20 =R28 4 =V20
=R27&S27 =U27*10+V27 =S21 =R30 4 =V21
=R28&S28 =U28*10+V28 =S22 1 =2*U26 =V22
=R29&S29 =U29*10+V29 =S23 =R30 =2*U27 =V23
=R30&S30 =U30*10+V30 =S24 =R28 4 =V24
=R31&S31 =U31*10+V31 =S25 =R32 4 =V25
=R32&S32 =U32*10+V32 =S26 =R34 6 =V26
=R33&S33 =U33*10+V33 =S27 =R36 6 =V27
=R34&S34 =U34*10+V34 =S28 1 =2*U32 =V28
=R35&S35 =U35*10+V35 =S29 =R36 =2*U33 =V29
=R36&S36 =U36*10+V36 =S30 =R34 6 =V30
=R37&S37 =U37*10+V37 =S31 =R38 6 =V31
=R38&S38 =U38*10+V38 =S32 =R40 9 =V32
=R39&S39 =U39*10+V39 =S33 =R42 9 =V33
=R40&S40 =U40*10+V40 =S34 1 =2*U38 =V34
=R41&S41 =U41*10+V41 =S35 =R42 =2*U39 =V35
=R42&S42 =U42*10+V42 =S36 =R40 9 =V36
=R43&S43 =U43*10+V43 =S37 =R44 9 =V37
=R44&S44 =U44*10+V44 =S38 =R46 14 =V38
=R45&S45 =U45*10+V45 =S39 =R48 14 =V39
=R46&S46 =U46*10+V46 =S40 1 =2*U44 =V40
=R47&S47 =U47*10+V47 =S41 =R48 =2*U45 =V41
=R48&S48 =U48*10+V48 =S42 =R46 14 =V42
=R49&S49 =U49*10+V49 =S43 =R50 14 =V43
=R50&S50 =U50*10+V50 =S44 =R52 21 =V44
=R51&S51 =U51*10+V51 =S45 =R54 21 =V45
=R52&S52 =U52*10+V52 =S46 1 =2*U50 =V46
=R53&S53 =U53*10+V53 =S47 =R54 =2*U51 =V47
=R54&S54 =U54*10+V54 =S48 =R52 21 =V48
=R55&S55 =U55*10+V55 =S49 =R56 21 =V49
=R56&S56 =U56*10+V56 =S50 =R58 32 =V50
=R57&S57 =U57*10+V57 =S51 =R60 32 =V51
=R58&S58 =U58*10+V58 =S52 1 =2*U56 =V52
=R59&S59 =U59*10+V59 =S53 =R60 =2*U57 =V53
=R60&S60 =U60*10+V60 =S54 =R58 32 =V54
=R61&S61 =U61*10+V61 =S55 1 32 =V55


Finalize section B.

BEWARE: Excel might take quite some time to calculate the simaulation. Start with a few thousand rows before copying down the whole worksheet.

Mark the cells D3 through N3.
Copy these cells.
Paste these cells down the worksheet.

Simulate.

By refreshing the sheet, the random rolls in column D get updated.
The overall results are displayed in section A, i.e. columns A and B.

The other finite state machines.

key state input next wager sub-state fin
=R2&S2 1 won =R4 1 1
=R3&S3 1 lost =R6 1 1
=R4&S4 2 won 1 1 2
=R5&S5 2 lost =R6 1 2
=R6&S6 3 won =R4 1 3
=R7&S7 3 lost =R8 1 3
=R8&S8 =U8*10+V8 =S2 =R10 1 =V2
=R9&S9 =U9*10+V9 =S3 =R12 1 =V3
=R10&S10 =U10*10+V10 =S4 1 1 =V4
=R11&S11 =U11*10+V11 =S5 =R12 1 =V5
=R12&S12 =U12*10+V12 =S6 =R10 1 =V6
=R13&S13 =U13*10+V13 =S7 =R14 1 =V7
=R14&S14 =U14*10+V14 =S8 =R16 2 =V8
=R15&S15 =U15*10+V15 =S9 =R18 2 =V9
=R16&S16 =U16*10+V16 =S10 1 2 =V10
=R17&S17 =U17*10+V17 =S11 =R18 2 =V11
=R18&S18 =U18*10+V18 =S12 =R16 2 =V12
=R19&S19 =U19*10+V19 =S13 =R20 2 =V13
=R20&S20 =U20*10+V20 =S14 =R22 3 =V14
=R21&S21 =U21*10+V21 =S15 =R24 3 =V15
=R22&S22 =U22*10+V22 =S16 1 3 =V16
=R23&S23 =U23*10+V23 =S17 =R24 3 =V17
=R24&S24 =U24*10+V24 =S18 =R22 3 =V18
=R25&S25 =U25*10+V25 =S19 =R26 3 =V19
=R26&S26 =U26*10+V26 =S20 =R28 4 =V20
=R27&S27 =U27*10+V27 =S21 =R30 4 =V21
=R28&S28 =U28*10+V28 =S22 1 4 =V22
=R29&S29 =U29*10+V29 =S23 =R30 4 =V23
=R30&S30 =U30*10+V30 =S24 =R28 4 =V24
=R31&S31 =U31*10+V31 =S25 =R32 4 =V25
=R32&S32 =U32*10+V32 =S26 =R34 6 =V26
=R33&S33 =U33*10+V33 =S27 =R36 6 =V27
=R34&S34 =U34*10+V34 =S28 1 6 =V28
=R35&S35 =U35*10+V35 =S29 =R36 6 =V29
=R36&S36 =U36*10+V36 =S30 =R34 6 =V30
=R37&S37 =U37*10+V37 =S31 =R38 6 =V31
=R38&S38 =U38*10+V38 =S32 =R40 9 =V32
=R39&S39 =U39*10+V39 =S33 =R42 9 =V33
=R40&S40 =U40*10+V40 =S34 1 9 =V34
=R41&S41 =U41*10+V41 =S35 =R42 9 =V35
=R42&S42 =U42*10+V42 =S36 =R40 9 =V36
=R43&S43 =U43*10+V43 =S37 =R44 9 =V37
=R44&S44 =U44*10+V44 =S38 =R46 14 =V38
=R45&S45 =U45*10+V45 =S39 =R48 14 =V39
=R46&S46 =U46*10+V46 =S40 1 14 =V40
=R47&S47 =U47*10+V47 =S41 =R48 14 =V41
=R48&S48 =U48*10+V48 =S42 =R46 14 =V42
=R49&S49 =U49*10+V49 =S43 =R50 14 =V43
=R50&S50 =U50*10+V50 =S44 =R52 21 =V44
=R51&S51 =U51*10+V51 =S45 =R54 21 =V45
=R52&S52 =U52*10+V52 =S46 1 21 =V46
=R53&S53 =U53*10+V53 =S47 =R54 21 =V47
=R54&S54 =U54*10+V54 =S48 =R52 21 =V48
=R55&S55 =U55*10+V55 =S49 =R56 21 =V49
=R56&S56 =U56*10+V56 =S50 =R58 32 =V50
=R57&S57 =U57*10+V57 =S51 =R60 32 =V51
=R58&S58 =U58*10+V58 =S52 1 32 =V52
=R59&S59 =U59*10+V59 =S53 =R60 32 =V53
=R60&S60 =U60*10+V60 =S54 =R58 32 =V54
=R61&S61 =U61*10+V61 =S55 1 32 =V55


key state input next wager sub-state fin
=R2&S2 1 won 1 1 1
=R3&S3 1 lost =R6 1 1
=R4&S4 2 won 1 =2*U2 2
=R5&S5 2 lost =R6 =2*U3 2
=R6&S6 3 won 1 1 3
=R7&S7 3 lost =R8 1 3
=R8&S8 =U8*10+V8 =S2 1 1 =V2
=R9&S9 =U9*10+V9 =S3 =R12 1 =V3
=R10&S10 =U10*10+V10 =S4 1 =2*U8 =V4
=R11&S11 =U11*10+V11 =S5 =R12 =2*U9 =V5
=R12&S12 =U12*10+V12 =S6 1 1 =V6
=R13&S13 =U13*10+V13 =S7 =R14 1 =V7
=R14&S14 =U14*10+V14 =S8 1 2 =V8
=R15&S15 =U15*10+V15 =S9 =R18 2 =V9
=R16&S16 =U16*10+V16 =S10 1 =2*U14 =V10
=R17&S17 =U17*10+V17 =S11 =R18 =2*U15 =V11
=R18&S18 =U18*10+V18 =S12 1 2 =V12
=R19&S19 =U19*10+V19 =S13 =R20 2 =V13
=R20&S20 =U20*10+V20 =S14 1 3 =V14
=R21&S21 =U21*10+V21 =S15 =R24 3 =V15
=R22&S22 =U22*10+V22 =S16 1 =2*U20 =V16
=R23&S23 =U23*10+V23 =S17 =R24 =2*U21 =V17
=R24&S24 =U24*10+V24 =S18 1 3 =V18
=R25&S25 =U25*10+V25 =S19 =R26 3 =V19
=R26&S26 =U26*10+V26 =S20 1 4 =V20
=R27&S27 =U27*10+V27 =S21 =R30 4 =V21
=R28&S28 =U28*10+V28 =S22 1 =2*U26 =V22
=R29&S29 =U29*10+V29 =S23 =R30 =2*U27 =V23
=R30&S30 =U30*10+V30 =S24 1 4 =V24
=R31&S31 =U31*10+V31 =S25 =R32 4 =V25
=R32&S32 =U32*10+V32 =S26 1 6 =V26
=R33&S33 =U33*10+V33 =S27 =R36 6 =V27
=R34&S34 =U34*10+V34 =S28 1 =2*U32 =V28
=R35&S35 =U35*10+V35 =S29 =R36 =2*U33 =V29
=R36&S36 =U36*10+V36 =S30 1 6 =V30
=R37&S37 =U37*10+V37 =S31 =R38 6 =V31
=R38&S38 =U38*10+V38 =S32 1 9 =V32
=R39&S39 =U39*10+V39 =S33 =R42 9 =V33
=R40&S40 =U40*10+V40 =S34 1 =2*U38 =V34
=R41&S41 =U41*10+V41 =S35 =R42 =2*U39 =V35
=R42&S42 =U42*10+V42 =S36 1 9 =V36
=R43&S43 =U43*10+V43 =S37 =R44 9 =V37
=R44&S44 =U44*10+V44 =S38 1 14 =V38
=R45&S45 =U45*10+V45 =S39 =R48 14 =V39
=R46&S46 =U46*10+V46 =S40 1 =2*U44 =V40
=R47&S47 =U47*10+V47 =S41 =R48 =2*U45 =V41
=R48&S48 =U48*10+V48 =S42 1 14 =V42
=R49&S49 =U49*10+V49 =S43 =R50 14 =V43
=R50&S50 =U50*10+V50 =S44 1 21 =V44
=R51&S51 =U51*10+V51 =S45 =R54 21 =V45
=R52&S52 =U52*10+V52 =S46 1 =2*U50 =V46
=R53&S53 =U53*10+V53 =S47 =R54 =2*U51 =V47
=R54&S54 =U54*10+V54 =S48 1 21 =V48
=R55&S55 =U55*10+V55 =S49 =R56 21 =V49
=R56&S56 =U56*10+V56 =S50 1 32 =V50
=R57&S57 =U57*10+V57 =S51 =R60 32 =V51
=R58&S58 =U58*10+V58 =S52 1 =2*U56 =V52
=R59&S59 =U59*10+V59 =S53 =R60 =2*U57 =V53
=R60&S60 =U60*10+V60 =S54 1 32 =V54
=R61&S61 =U61*10+V61 =S55 1 32 =V55
"When it comes to probability and statistics, intuition is a bad advisor. Don't speculate. Calculate." - a math textbook author (name not recalled)
ThomasK
ThomasK
Joined: Jul 4, 2015
  • Threads: 7
  • Posts: 124
November 3rd, 2022 at 8:04:05 AM permalink
Quote: lilredrooster

Quote: ThomasK




This picture is not meant to be readable but to give an impression and overview of the simulation.

The house edge of the slot machine is roughly around 0.51%.

Parlaying the wager plus the winning amount, raises the slot machine's house edge slightly to something around 0.59%.

Progressions on winnings, here the two step Parlay, are a bad choice on negative expectation games anyway, so I removed the Parlay step and ended the progression after the first win. The house edge of the slot machine now drops to roughly 0.13%.




so, to summarize:

you have 𝙋𝙍𝙊𝙑𝙀𝙉 that with this progression the house edge is increased when parlays are used and is reduced dramatically when they are not

Congratulations - you are surely due for consideration for a Fields Medal in Mathematics for your 𝙋𝙍𝙊𝙊𝙁𝙎

you have 𝙋𝙍𝙊𝙑𝙀𝙉 something that no one else in history has ever proven - right here on WOV - everyone here is so lucky to have seen it here first - WOV should perhaps be mentioned when you are awarded the Fields Medal

you might want to consider providing a readable documentation of your findings when you submit your work to the Judges - but on the other hand - maybe that's not necessary - your 𝙋𝙍𝙊𝙊𝙁𝙎 are tremendously compelling even without readable documentation


.
link to original post



What I'm doing here is not proving but is rather applying the idea that you brought up yourself in the thread MARTINGALE SO DIFFERENT WHEN___. And there I supported your finding with some mathematical evidence. (Thank you, gordonm888, for your clarification of the terms.)

What is different now and what makes you so annoyed?
"When it comes to probability and statistics, intuition is a bad advisor. Don't speculate. Calculate." - a math textbook author (name not recalled)
lilredrooster
lilredrooster
Joined: May 8, 2015
  • Threads: 218
  • Posts: 5442
November 3rd, 2022 at 8:14:16 AM permalink
Quote: ThomasK

Quote: lilredrooster

Quote: ThomasK




This picture is not meant to be readable but to give an impression and overview of the simulation.

The house edge of the slot machine is roughly around 0.51%.

Parlaying the wager plus the winning amount, raises the slot machine's house edge slightly to something around 0.59%.

Progressions on winnings, here the two step Parlay, are a bad choice on negative expectation games anyway, so I removed the Parlay step and ended the progression after the first win. The house edge of the slot machine now drops to roughly 0.13%.




so, to summarize:

you have 𝙋𝙍𝙊𝙑𝙀𝙉 that with this progression the house edge is increased when parlays are used and is reduced dramatically when they are not

Congratulations - you are surely due for consideration for a Fields Medal in Mathematics for your 𝙋𝙍𝙊𝙊𝙁𝙎

you have 𝙋𝙍𝙊𝙑𝙀𝙉 something that no one else in history has ever proven - right here on WOV - everyone here is so lucky to have seen it here first - WOV should perhaps be mentioned when you are awarded the Fields Medal

you might want to consider providing a readable documentation of your findings when you submit your work to the Judges - but on the other hand - maybe that's not necessary - your 𝙋𝙍𝙊𝙊𝙁𝙎 are tremendously compelling even without readable documentation


.
link to original post



What I'm doing here is not proving but is rather applying the idea that you brought up yourself in the thread MARTINGALE SO DIFFERENT WHEN___. And there I supported your finding with some mathematical evidence. (Thank you, gordonm888, for your clarification of the terms.)

What is different now and what makes you so annoyed?
link to original post




and this from my thread that you referenced:


Quote: ThomasK



My point though is, that the Wizard always emphasizes that betting systems can't even dent the house edge. Our calculations seem to suggest otherwise.




I only claimed that it was a thing I had never thought of before - and it kinna astonished and interested me

𝙄 𝙣𝙚𝙫𝙚𝙧 𝙘𝙡𝙖𝙞𝙢𝙚𝙙 𝙩𝙝𝙖𝙩 𝙞𝙩 𝙥𝙚𝙧𝙢𝙖𝙣𝙚𝙣𝙩𝙡𝙮 𝙘𝙝𝙖𝙣𝙜𝙚𝙙 𝙩𝙝𝙚 𝙝𝙤𝙪𝙨𝙚 𝙚𝙙𝙜𝙚 𝙖𝙨 𝙮𝙤𝙪 𝙝𝙖𝙫𝙚 - you clearly stated that in your 1 million trials the house edge was reduced - and I believe you were stating or implying that the one million trials were a sufficient number of trials to assert that the house edge was permanently altered

I only pointed out that it could be a very long time for the house edge to be asserted - and I should have been clearer on that - that is the only thing I was getting at

I'm not annoyed - I just think your post is misleading and could be hurtful to newbies in that they might endlessly chase a progression that can overcome the HA - being influenced by your posts - believing that such a progression may actually exist when it doesn't

imo you need to clarify exactly what your point is - is it that the progression will actually reduce the house edge_____????

or if not, what exactly are you saying - in plain English please - not in abstruse calculations



.
"believe half of what you see and none of what you hear" - Edgar Allan Poe
Mental
Mental
Joined: Dec 10, 2018
  • Threads: 7
  • Posts: 476
November 3rd, 2022 at 9:24:23 AM permalink
Quote: lilredrooster

I'm not annoyed - I just think your post is misleading and could be hurtful to newbies in that they might endlessly chase a progression that can overcome the HA - being influenced by your posts - believing that such a progression may actually exist when it doesn't

imo you need to clarify exactly what your point is - is it that the progression will actually reduce the house edge_____????

or if not, what exactly are you saying - in plain English please - not in abstruse calculation.
link to original post

Ah, but the opaque calculations and the equivalent slot machine concept are the smoke and mirrors that TK needs to support his bizarre claims.
ThomasK
ThomasK
Joined: Jul 4, 2015
  • Threads: 7
  • Posts: 124
November 3rd, 2022 at 10:42:10 AM permalink
Quote: gordonm888

I would not say ThomasK has proven anything. I would say that he has done a simulation, with 1M trials, and produced some evidence.

First, I'm glad ThomasK did this. I haven't seen this Carsch system before and I was hoping someone would analyze it.

Secondly, I think it's appropriate to ask some questions about the simulation and try to understand what has been done. I'll start:

In the 1M trials simulation, how often was the 10-step betting sequence terminated with a loss on the 10th step, losing 93 units (while presumably winning some bets on the way through the progression?) In other words, how many times did you wager 32 units and lose?

How many times did you wager 32 units and win?

What wagers are made after all 10 steps lose?

What was the mean wager size as averaged over the roughly 1M trials?
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Thank you for your questions.

I answer based on the corrected loss of 186 units in the case of a complete losing progression. I will also refer to the progression with the Parlay on the winning wager plus its winning. (I guess this is the original idea of Carsch.)

First I'd like to explain that a single level in this progression needs three (sub-)states to cover both requirements: two winnings in a row or two losses in a row. The graph looks like this:



After two losses in a row the next higher level, i.e the next higher amount, is selected.
Two winnings in a row end the current progression and a new progression can be started.
Remark: The transition from state 2 to state 1 is given here for the first level. Sub-state 2 on every level will
transition to the initial state 1, not to sub-state 1 of the same level. Therefore two winnings in a row on any level will end the current progression and a new progression can be started at state 1.

Now here for the frequencies of the states to answer your questions. All figures given here are only valid for the random set I took the snap shot of. Refreshing the worksheet will vary the results.



The 20-step betting sequence was terminated with a loss on the 20th step, losing 186 units, 332 times or 0.21% of all attempts. See state 323 lost, copied to cell H32. This sub-state 3 would transition to the next level, but since it is the last level in the progression, the progression ends here and a new progression can be started.

The winning states are all those that win in sub-state 2, terminating the current progression and resetting to state 1 for a new progression. The winning sub-states 2 are extracted in columns F and G. They sum up to 159643 winning progressions.
99.79% of all attempted progressions will be won.
0.21% of all attempted progressions will lose 186 units.

The amounts wagered can be determined from the states and their frequencies (columns J and K).
The average wager per progression results in 13.6 units.
The average wager per roll results in 2.1 units.
"When it comes to probability and statistics, intuition is a bad advisor. Don't speculate. Calculate." - a math textbook author (name not recalled)
unJon
unJon
Joined: Jul 1, 2018
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November 3rd, 2022 at 10:58:47 AM permalink
Quote: Mental

Quote: lilredrooster

I'm not annoyed - I just think your post is misleading and could be hurtful to newbies in that they might endlessly chase a progression that can overcome the HA - being influenced by your posts - believing that such a progression may actually exist when it doesn't

imo you need to clarify exactly what your point is - is it that the progression will actually reduce the house edge_____????

or if not, what exactly are you saying - in plain English please - not in abstruse calculation.
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Ah, but the opaque calculations and the equivalent slot machine concept are the smoke and mirrors that TK needs to support his bizarre claims.
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Iím more charitable than you. I think the equivalent slot machine works to point out a deficiency in the usefulness of the concept of house edge. Happy to elaborate but donít want to threadjack.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
ThomasK
ThomasK
Joined: Jul 4, 2015
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November 3rd, 2022 at 11:59:10 AM permalink
Quote: unJon

Quote: Mental

Quote: lilredrooster

I'm not annoyed - I just think your post is misleading and could be hurtful to newbies in that they might endlessly chase a progression that can overcome the HA - being influenced by your posts - believing that such a progression may actually exist when it doesn't

imo you need to clarify exactly what your point is - is it that the progression will actually reduce the house edge_____????

or if not, what exactly are you saying - in plain English please - not in abstruse calculation.
link to original post

Ah, but the opaque calculations and the equivalent slot machine concept are the smoke and mirrors that TK needs to support his bizarre claims.
link to original post



Iím more charitable than you. I think the equivalent slot machine works to point out a deficiency in the usefulness of the concept of house edge. Happy to elaborate but donít want to threadjack.
link to original post



Thank you, unJon, for intervening..
May I invite you, Mental, lilredrooster, and unJon to continue this discussion over here?
unJon and I came to terms to use "house edge" only for the casino and "element of risk" only for players, although the confirmation for the proper usage of "element of risk" is pending.
Furthermore, differentiating between both has its own ambiguities.
I'd like to discuss this with you over there and hopefully I'll be able to use "plain English" only.
"When it comes to probability and statistics, intuition is a bad advisor. Don't speculate. Calculate." - a math textbook author (name not recalled)

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