Recent posts
#71
Multiple / Re: bgGES Roulette ver.Inna
Last post by exe11 - Sep 17, 2024, 06:58 PMformula change. adding a new chart. generator testing
#72
TwoUp / Optimal stopping for positive ...
Last post by TwoUp - Sep 17, 2024, 03:25 PMWhen playing even chance we are presented with a predicament of should we stop taking our wins or accepting our losses or continuing.
This is known as "The optimal stopping Problem" and more commonly the dating problem or the 37% rule.
The optimal stopping problem has many variations and is an ongoing area of research, but it provides some precise insights in obtaining an advantage in an even chance game through a process of deciding when it is optimal to stop.
This video introduces the concept of optimal stopping in an entertaining way:
Now there is a special variation of the stopping problem that is solved for a fixed number of events and is partly solved for an indefinite number of events. These problems are known as the Robbins Problem and the related Chow-Robbins game where one tosses a coin and after each toss, you decide if you take the fraction of heads up to now as a payoff, otherwise you continue.
It provides an answer to betting optimally on even chance outcomes and providss a positive expectation.
A simple rule of thumb is if you are up 8 vs 5 or better then stop, otherwise continue until you break even, but we can do much better using a decision table I provide below for the first 1000 spins.
The math shows that when considering a horizon of up to 268 million spins has an upper bound the optimal stopping advantage for a perfect even chance game of 0.79295350640 or 79.2953% which is pretty spectacular for a 50/50 outcome which in simple terms has no long term advantage.
Now practically we cannot play that many outcomes but it is clear that deciding when to stop based on math provides an advantage to the player which I sfar better than 50/50.
The table below covers the opening decisions of the Chow-Robbins game, showing when to stop and when to continue, through computational analysis of the theory and shows all decision points a player has to make up to 1000 spins computed using a 10 million spin horizon.
So for starters let's consider a case where we have won on 19 reds against losing on 14 blacks, (19-14) with the difference therefore being 5.
According to the table, stopping with a difference of 5 is best even up to 23 reds vs 18 blacks "23–18", so we must therefore stop.
As can be seen in the table, the mathematical theory is complete up to a difference of 11, while for a difference of 12 the status of what to do for the outcome 116 reds vs 104 blacks "116–104" is currently unknown to science but a 12 unit win is still a win so stopping is a prudent option whether or not it is known to be optimal.
For the outcome of 16 reds vs 12 blacks (16–12), the decision is extremely close. Whilst for a run of 1 million spins the math fails to determine the optimal decision, whilst a run of 10 million spins shows that stopping is optimal.
The following table was computed for all possible outcomes up to 10 million spins.
The 3 columns are:
difference stop-with continue-with
1 1–0 2–1
2 5–3 6–4
3 9–6 10–7
4 16–12 17–13
5 23–18 24–19
6 32–26 33–27
7 42–35 43–36
8 54–46 55–47
9 67–58 68–59
10 82–72 83–73
11 98–87 99–88
12 115–103 117–105
13 134–121 135–122
14 155–141 156–142
15 176–161 177–162
16 199–183 201–185
17 224–207 225–208
18 250–232 251–233
19 277–258 279–260
20 306–286 307–287
21 336–315 338–317
22 368–346 369–347
23 401–378 402–379
24 435–411 437–413
25 471–446 473–448
26 508–482 510–484
≥ 27 stop
The above table and analysis from Rigorous computer analysis of the Chow-Robbins game
This is known as "The optimal stopping Problem" and more commonly the dating problem or the 37% rule.
The optimal stopping problem has many variations and is an ongoing area of research, but it provides some precise insights in obtaining an advantage in an even chance game through a process of deciding when it is optimal to stop.
This video introduces the concept of optimal stopping in an entertaining way:
Now there is a special variation of the stopping problem that is solved for a fixed number of events and is partly solved for an indefinite number of events. These problems are known as the Robbins Problem and the related Chow-Robbins game where one tosses a coin and after each toss, you decide if you take the fraction of heads up to now as a payoff, otherwise you continue.
It provides an answer to betting optimally on even chance outcomes and providss a positive expectation.
A simple rule of thumb is if you are up 8 vs 5 or better then stop, otherwise continue until you break even, but we can do much better using a decision table I provide below for the first 1000 spins.
The math shows that when considering a horizon of up to 268 million spins has an upper bound the optimal stopping advantage for a perfect even chance game of 0.79295350640 or 79.2953% which is pretty spectacular for a 50/50 outcome which in simple terms has no long term advantage.
Now practically we cannot play that many outcomes but it is clear that deciding when to stop based on math provides an advantage to the player which I sfar better than 50/50.
The table below covers the opening decisions of the Chow-Robbins game, showing when to stop and when to continue, through computational analysis of the theory and shows all decision points a player has to make up to 1000 spins computed using a 10 million spin horizon.
So for starters let's consider a case where we have won on 19 reds against losing on 14 blacks, (19-14) with the difference therefore being 5.
According to the table, stopping with a difference of 5 is best even up to 23 reds vs 18 blacks "23–18", so we must therefore stop.
As can be seen in the table, the mathematical theory is complete up to a difference of 11, while for a difference of 12 the status of what to do for the outcome 116 reds vs 104 blacks "116–104" is currently unknown to science but a 12 unit win is still a win so stopping is a prudent option whether or not it is known to be optimal.
For the outcome of 16 reds vs 12 blacks (16–12), the decision is extremely close. Whilst for a run of 1 million spins the math fails to determine the optimal decision, whilst a run of 10 million spins shows that stopping is optimal.
The following table was computed for all possible outcomes up to 10 million spins.
The 3 columns are:
difference stop-with continue-with
1 1–0 2–1
2 5–3 6–4
3 9–6 10–7
4 16–12 17–13
5 23–18 24–19
6 32–26 33–27
7 42–35 43–36
8 54–46 55–47
9 67–58 68–59
10 82–72 83–73
11 98–87 99–88
12 115–103 117–105
13 134–121 135–122
14 155–141 156–142
15 176–161 177–162
16 199–183 201–185
17 224–207 225–208
18 250–232 251–233
19 277–258 279–260
20 306–286 307–287
21 336–315 338–317
22 368–346 369–347
23 401–378 402–379
24 435–411 437–413
25 471–446 473–448
26 508–482 510–484
≥ 27 stop
The above table and analysis from Rigorous computer analysis of the Chow-Robbins game
#73
FreeRoulette / Free Tools Weekend 9/14
Last post by FreeRoulette - Sep 13, 2024, 03:13 PMAll roulette tools free this weekend promo
https://tracker.potads.uk/
Username and password
FreeWeekend159
See tool in action https://www.youtube.com/watch?v=GEd09sPthW4&t=6s
https://tracker.potads.uk/
Username and password
FreeWeekend159
See tool in action https://www.youtube.com/watch?v=GEd09sPthW4&t=6s
#74
Money management / ALL-IN TO FREE PLAY (Money Man...
Last post by VLS - Sep 13, 2024, 01:17 AMHello dear friends,
I recommend a money management scheme I call "ALL-IN TO FREE PLAY" (fondly abbreviated A2F), which I believe complements the betting flow for "streaky" systems well.
This adaptable approach was designed with 100-unit banks in mind, yet it can be as valid with other session-bankroll limits.
A2F is the logical continuation of my 75% Money Management strategy, consisting of two stages:
ALL-IN
The game begins with the goal of doubling the bank as soon as possible.
Your principal is your session bank, and your interest is represented by your wins per hit.
With a /10 (suggested), /5 (medium), or /3 (minimum) unit division, you reinvest everything or "go all in" to reduce the number of hits needed to achieve the +100% session units won, which closes this stage.
After doubling the bank, you secure your original 100 units and create a second 100-unit bankroll strictly based on the wins for stage two (yes, there are likely some leftovers after the split).
This second bank then becomes the main one.
FREE PLAY
Since this free-play bank is "sponsored by the casino" and your original bank is already secured, every unit you win is truly yours, risk-free.
After every hit, you split the net winnings:
By continually splitting and adding the reinvestment percentage, you ensure the unit grows as you go, creating a virtuous cycle.
As you can see, there is a chance to win big on long positive streaks.
After doubling the bank at full speed, there is absolutely zero risk from this point forward.
Your overall balance can only increase with the free-play bank that the casino kindly sponsors, helping you increase your averages with no risk and no win limits. 😇
Vic
I recommend a money management scheme I call "ALL-IN TO FREE PLAY" (fondly abbreviated A2F), which I believe complements the betting flow for "streaky" systems well.
This adaptable approach was designed with 100-unit banks in mind, yet it can be as valid with other session-bankroll limits.
A2F is the logical continuation of my 75% Money Management strategy, consisting of two stages:
ALL-IN
- Win goal: +100 units.
- Compounding: 100% reinvestment.
The game begins with the goal of doubling the bank as soon as possible.
Your principal is your session bank, and your interest is represented by your wins per hit.
With a /10 (suggested), /5 (medium), or /3 (minimum) unit division, you reinvest everything or "go all in" to reduce the number of hits needed to achieve the +100% session units won, which closes this stage.
After doubling the bank, you secure your original 100 units and create a second 100-unit bankroll strictly based on the wins for stage two (yes, there are likely some leftovers after the split).
This second bank then becomes the main one.
FREE PLAY
- Win goal: Unlimited.
- Compounding: 50% reinvestment.
Since this free-play bank is "sponsored by the casino" and your original bank is already secured, every unit you win is truly yours, risk-free.
After every hit, you split the net winnings:
- 50% goes to enlarging the base session unit.
- 50% is yours as the net won amount for the spin, adding to your balance.
By continually splitting and adding the reinvestment percentage, you ensure the unit grows as you go, creating a virtuous cycle.
As you can see, there is a chance to win big on long positive streaks.
After doubling the bank at full speed, there is absolutely zero risk from this point forward.
Your overall balance can only increase with the free-play bank that the casino kindly sponsors, helping you increase your averages with no risk and no win limits. 😇
Vic
#75
Coding requests / Foundational modules
Last post by VLS - Sep 12, 2024, 07:41 PMHello again folks! What are some foundational modules you would consider RIBOT must definitely include?
For instance:
Progression generators.
Actuals transformers (from numbers to betting locations: RB, EO, HL, D1/D2/D3, C1/C2/C3, etc.).
Spin-by-spin location trackers.
Feel free to suggest specific ones as the current soft reboot's focus is on the foundational modules, since they form a basis to build the bot upon.
Cheers!
For instance:
Progression generators.
Actuals transformers (from numbers to betting locations: RB, EO, HL, D1/D2/D3, C1/C2/C3, etc.).
Spin-by-spin location trackers.
Feel free to suggest specific ones as the current soft reboot's focus is on the foundational modules, since they form a basis to build the bot upon.
Cheers!
#76
General discussion / Re: Roulette life
Last post by VLS - Sep 10, 2024, 06:06 AMQuote from: Winner on Sep 05, 2024, 06:27 PMWhat happened to this forum?
It's back online 👍
#77
General discussion / Re: Roulette life
Last post by Winner - Sep 06, 2024, 12:14 PMOk thanks Victor !
#78
General discussion / Re: Roulette life
Last post by VLS - Sep 06, 2024, 12:09 AMWelcome to the community @Winner.
It says HTTP error 500 which is a generic error related to the server:
Source: https://en.wikipedia.org/wiki/List_of_HTTP_status_codes
This error is not related to visitors' configuration (cookies/cache/connection).
Hopefully Kav is aware so he can contact his webmaster to fix it 👍
It says HTTP error 500 which is a generic error related to the server:
Quote500 Internal Server Error
A generic error message, given when an unexpected condition was encountered and no more specific message is suitable.
Source: https://en.wikipedia.org/wiki/List_of_HTTP_status_codes
This error is not related to visitors' configuration (cookies/cache/connection).
Hopefully Kav is aware so he can contact his webmaster to fix it 👍
#80
General discussion / Roulette life
Last post by Winner - Sep 05, 2024, 06:27 PMWhat happened to this forum?