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Clueless Gamblers Part 1 - Probability vs Certainty


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Any numbers or logic you try to put to it, It will never add up why we degen the way we do or I do rather lol. It just simply isn't logical 

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6 minutes ago, Slutsmoker666 said:

Any numbers or logic you try to put to it, It will never add up why we degen the way we do or I do rather lol. It just simply isn't logical 

One of the articles of this series will be, How Clueless Gamblers can beat the House and walk away with profit. Good luck to you LOL.

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This is certainly all correct as far as they write but has no statement whether a casino is fair or not.
That a casino is gambling should be clear to everyone.
Also that a casino collects the house share is normal but that also says nothing about whether a casino is fair.

For me, this reads more as an excuse for a casino as more and more players leave.

But I will certainly not insinuate anything.
In the end, it is always based on trust that no one can control it regardless of whether it is fair or not

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10 minutes ago, Elpresidente said:

This is certainly all correct as far as they write but has no statement whether a casino is fair or not.
That a casino is gambling should be clear to everyone.
Also that a casino collects the house share is normal but that also says nothing about whether a casino is fair.

For me, this reads more as an excuse for a casino as more and more players leave.

But I will certainly not insinuate anything.
In the end, it is always based on trust that no one can control it regardless of whether it is fair or not

It's definitely a matter of trust, and you either trust the casino or understand the provably fair algorithm.


Some players don't understand both the elements and continue to gamble and blame the casino without researching. And those gamblers are categorized as clueless gamblers.

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2 hours ago, BCGame_POP said:

It's definitely a matter of trust, and you either trust the casino or understand the provably fair algorithm.


Some players don't understand both the elements and continue to gamble and blame the casino without researching. And those gamblers are categorized as clueless gamblers.

You are of course right that many do not understand and when they lose seek their anger at the casino.
That is of course also not correct.
I also do not want to complain about the fairness and it goes only about mutual trust.
Maybe you should also show the people the fairness better.
How to verify a bet etc and that could help a little bit I think

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Just now, Elpresidente said:

You are of course right that many do not understand and when they lose seek their anger at the casino.
That is of course also not correct.
I also do not want to complain about the fairness and it goes only about mutual trust.
Maybe you should also show the people the fairness better.
How to verify a bet etc and that could help a little bit I think

As mentioned in the article, I will write a detailed article on fairness explaining each and every parameter in my upcoming parts of this series.

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Everyone has their own brain! And when he enters the casino, he must know that he can lose!!!!
Edited by rasmus1234

rasmus1234

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15 minutes ago, rasmus1234 said:
Everyone has their own brain! And when he enters the casino, he must know that he can lose!!!!

LOL, well said. 

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7 minutes ago, Coco_Father said:

Ahhh, my good sir. You have forgotten about Voltaire.... In the mid 1700's he used his skills in mathematics along with his persuasive charm and ingenuity to beat the municipal bonds lotteries throughout Paris. Being the socialite that he was, he was able to deduce that the prizes in every district throughout Paris were in most cases more than the amount of all the tickets being sold. So he recruited a team that was his very own Renaissance version of Ocean's Eleven and went to work scamming  outsmarting the officials of the city of Paris. This strategy made him a very rich man that allowed him to live his days with his thoughts rather than hard labor; providing him with the opportunity to become one of the most quoted rebellious philosophers in history.

 

Great thread. You are very wise and mostly correct. 

Interesting share sir, I will go through it, Thanks for stopping by and leaving a comment.

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Nice job. Interesting read, also I finally know who Voltaire is. I always heard the name, but never could get someone to tell me who that was. Plus, I never bothered to google the name. 😆 Brava!

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That right there, is a great write up. big ups 👍@BCGame_POP...It should be on the sign up page to all casinos lol ...Thanks

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13 minutes ago, Darolla said:

That right there, is a great write up. big ups 👍@BCGame_POP...It should be on the sign up page to all casinos lol ...Thanks

Hehehe, that will hurt casino business, LOL. Thanks for your appreciation. 

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Pop i got a question .

Does a casino owner have some botton on games that changes win rate?

I remember i made a slot game years ago and i had an option to change win rate from 20% to 80% .

In reeal gaming experience i noticed some days there is all green and some days its all red

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On 3/17/2022 at 4:08 AM, yellowstone said:

Pop i got a question .

Does a casino owner have some botton on games that changes win rate?

I remember i made a slot game years ago and i had an option to change win rate from 20% to 80% .

In reeal gaming experience i noticed some days there is all green and some days its all red

Providers offer 2-3 variations of RTP. And, the RTP has to be set by the Casino. Usually 96(plus minus) is the industry standard RTP. However, Casino can change this if they want to, but it will be displayed on the slot game, it's not something hidden. 

While we were new to slots on BCGame, we introduced No-Limit City slots, however our Dev accidentally set RTP to 93% instead of 96%, it was clearly visible to everyone, I immediately informed the team and they changed it to industry standard.

So, the answer is - YES, the casino can change the RTP but it's not something that's hidden from players. We at BCGame set highest RTP in the industry for all providers. Also, we do not change it frequently, the casino makes pretty good profit on 96 itself, so there is no point in messing around with players and losing credibility.

 

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You all are gonna laugh at this, but what about the players, and there are a handful, that joined for the sole reason of becoming SVIP and bein able to attend the awesome travel stuff mentioned in BOLD? I mean I can't be the only one. Then when I bring it up to staff I just get laughed a... Like damn false advertising much. Oh and " we haven't gotten around to removing that" isn't a valid excuse when it is being basically showcased as the main perks of the casino. Well that's my rant. Laugh away. I'm half joking as I've come to terms with this huge let down. Oh... "LOL". see? joking.

random subject changer. sorry.

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7 hours ago, Native702 said:

You all are gonna laugh at this, but what about the players, and there are a handful, that joined for the sole reason of becoming SVIP and bein able to attend the awesome travel stuff mentioned in BOLD? I mean I can't be the only one. Then when I bring it up to staff I just get laughed a... Like damn false advertising much. Oh and " we haven't gotten around to removing that" isn't a valid excuse when it is being basically showcased as the main perks of the casino. Well that's my rant. Laugh away. I'm half joking as I've come to terms with this huge let down. Oh... "LOL". see? joking.

random subject changer. sorry.

We did have plans of trips but due to covid they got postponed indefinitely. However, with the humongous interest from SVIP's, we are bringing some interesting offers for SVIP's related to travel in upcoming days. But, you must be a SVIP for that as advertised and there is no false advertisement in what we advertised, you will see some of our SVIP's making use of those benefits in the upcoming days.

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On 3/18/2022 at 3:12 AM, BCGame_POP said:

Providers offer 2-3 variations of RTP. And, the RTP has to be set by the Casino. Usually 96(plus minus) is the industry standard RTP. However, Casino can change this if they want to, but it will be displayed on the slot game, it's not something hidden. 

While we were new to slots on BCGame, we introduced No-Limit City slots, however our Dev accidentally set RTP to 93% instead of 96%, it was clearly visible to everyone, I immediately informed the team and they changed it to industry standard.

So, the answer is - YES, the casino can change the RTP but it's not something that's hidden from players. We at BCGame set highest RTP in the industry for all providers. Also, we do not change it frequently, the casino makes pretty good profit on 96 itself, so there is no point in messing around with players and losing credibility.

 

Thank you deary .i got so much great infos from your comments and recommendations in this topic .i ll be following your new posts

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On 15/3/2565 at 23 นาฬิกา 9 นาที, Coco_Father said:

อื้อหือ คนดีของฉัน คุณลืมเรื่องวอลแตร์ไปแล้ว.... ในช่วงกลางปี 1700 เขาใช้ทักษะทางคณิตศาสตร์ของเขาพร้อมกับเสน่ห์และความเฉลียวฉลาดที่โน้มน้าวใจของเขาเพื่อเอาชนะลอตเตอรีพันธบัตรเทศบาลทั่วปารีส จากการเป็นนักสังคมสงเคราะห์ที่เขาเป็น เขาสามารถสรุปได้ว่ารางวัลจากทุกเขตทั่วปารีสนั้นส่วนใหญ่แล้วจะมากกว่าจำนวนตั๋วที่ขายได้ทั้งหมด ดังนั้นเขาจึงคัดเลือกทีมที่เป็นรุ่นเรอเนซองส์ของ Ocean's Eleven และทำงานหลอกลวง  เพื่อ  ชิงไหวชิงพริบเจ้าหน้าที่ของเมืองปารีส กลวิธีนี้ทำให้เขากลายเป็นเศรษฐีที่ยอมให้เขาใช้ชีวิตตามวันเวลาของเขาด้วยความคิดมากกว่าที่จะทำงานหนัก เปิดโอกาสให้เขากลายเป็นหนึ่งในนักปรัชญาที่ดื้อรั้นที่สุดในประวัติศาสตร์

 

ด้ายที่ดี คุณฉลาดมากและถูกต้องเป็นส่วนใหญ่ 

 

On 15/3/2565 at 23 นาฬิกา 17 นาที, BCGame_POP said:

แบ่งปันที่น่าสนใจครับ, ฉันจะผ่านมันไป, ขอบคุณที่แวะมาและแสดงความคิดเห็น.

 

On 16/3/2565 at 1 นาฬิกา 55 นาที, Native702 said:

งานที่ดี. น่าอ่านจัง ในที่สุดก็รู้แล้วว่าวอลแตร์เป็นใคร ฉันได้ยินชื่อมาโดยตลอด แต่ไม่มีใครบอกได้ว่าใครเป็นใคร นอกจากนี้ ฉันไม่เคยสนใจชื่อ google เลย 😆บราวา!

 

On 16/3/2565 at 22 นาฬิกา 7 นาที, Darolla said:

ตรงนั้นมีการเขียนที่ดี อัพใหญ่ 👍ป๋องแป๋ง...มันควรจะอยู่ในหน้าลงทะเบียนของทุกคาสิโน lol ...ขอบคุณ

 

On 18/3/2565 at 6 นาฬิกา 42 นาที, BCGame_POP said:

ผู้ให้บริการเสนอRTP 2-3 รูปแบบ และคาสิโนจะต้องกำหนด RTP โดยปกติ96 (บวกลบ)เป็น RTP มาตรฐานอุตสาหกรรม อย่างไรก็ตาม คาสิโนสามารถเปลี่ยนแปลงสิ่งนี้ได้หากต้องการ แต่มันจะปรากฏในเกมสล็อตซึ่งไม่ใช่สิ่งที่ซ่อนเร้น 

ในขณะที่เรายังใหม่กับสล็อตบน BCGame เราได้เปิดตัวสล็อต No-Limit City อย่างไรก็ตาม ผู้พัฒนาของเราตั้งค่า RTP เป็น 93% โดยไม่ได้ตั้งใจ แทนที่จะเป็น 96% ซึ่งทุกคนมองเห็นได้ชัดเจน ฉันแจ้งทีมทันทีและพวกเขาก็เปลี่ยนให้เป็นมาตรฐานอุตสาหกรรม .

ดังนั้น คำตอบคือ - ใช่คาสิโนสามารถเปลี่ยน RTP ได้ แต่ไม่ใช่สิ่งที่ซ่อนเร้นจากผู้เล่น พวกเราที่ BCGame กำหนด RTP สูงสุดในอุตสาหกรรมสำหรับผู้ให้บริการทั้งหมด นอกจากนี้ เราไม่เปลี่ยนบ่อย คาสิโนทำกำไรได้ดีใน 96 เอง ดังนั้นจึงไม่มีประโยชน์ที่จะไปยุ่งกับผู้เล่นและสูญเสียความน่าเชื่อถือ

 

 

On 18/3/2565 at 7 นาฬิกา 58 นาที, Native702 said:

พวกคุณทุกคนจะต้องหัวเราะเยาะเรื่องนี้ แต่แล้วผู้เล่นจำนวนหนึ่งที่มีเพียงไม่กี่คนที่เข้าร่วมด้วยเหตุผลเดียวของการเป็น SVIP และสามารถเข้าร่วมกิจกรรมการเดินทางที่ยอดเยี่ยมที่กล่าวถึงใน BOLD ได้? ฉันหมายความว่าฉันไม่สามารถเป็นคนเดียว พอผมเล่าให้พนักงานฟัง ผมก็หัวเราะก... เหมือนโฆษณาจอมปลอมมาก โอ้และ "เรายังไม่ได้ลบสิ่งนั้น" ไม่ใช่ข้อแก้ตัวที่ถูกต้องเมื่อมีการจัดแสดงโดยทั่วไปว่าเป็นข้อดีหลักของคาสิโน นั่นคือการพูดจาโผงผางของฉัน หัวเราะออกไป ฉันล้อเล่นครึ่งหนึ่งเมื่อฉันยอมรับกับความผิดหวังครั้งใหญ่นี้ เอ่อ... "ฮ่าๆ" ดู? ล้อเล่น.

เปลี่ยนเรื่องแบบสุ่ม ขอโทษ.

 

On 18/3/2565 at 15 นาฬิกา 32 นาที, BCGame_POP said:

เรามีแพลนไปเที่ยวแต่เนื่องจากโควิดทำให้เลื่อนออกไปอย่างไม่มีกำหนด อย่างไรก็ตาม ด้วยความสนใจอย่างมากจาก SVIP เรากำลังนำเสนอข้อเสนอที่น่าสนใจสำหรับ SVIP ที่เกี่ยวข้องกับการเดินทางในอีกไม่กี่วันข้างหน้า แต่คุณจะต้องเป็น SVIP สำหรับสิ่งนั้นตามที่โฆษณาไว้ และไม่มีโฆษณาที่เป็นเท็จในสิ่งที่เราโฆษณา คุณจะเห็น SVIP บางส่วนของเราใช้ประโยชน์จากผลประโยชน์เหล่านั้นในอีกไม่กี่วันข้างหน้า

 

8 hours ago, yellowstone said:

ขอบคุณที่รัก ฉันได้รับข้อมูลดีๆ มากมายจากความคิดเห็นและคำแนะนำของคุณในหัวข้อนี้ ฉันจะติดตามโพสต์ใหม่ของคุณ

 

ขอให้โชดดีทุกคนนะครับ

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On 3/15/2022 at 11:09 AM, Coco_Father said:

Ahhh, my good sir. You have forgotten about Voltaire.... In the mid 1700's he used his skills in mathematics along with his persuasive charm and ingenuity to beat the municipal bonds lotteries throughout Paris. Being the socialite that he was, he was able to deduce that the prizes in every district throughout Paris were in most cases more than the amount of all the tickets being sold. So he recruited a team that was his very own Renaissance version of Ocean's Eleven and went to work scamming  outsmarting the officials of the city of Paris. This strategy made him a very rich man that allowed him to live his days with his thoughts rather than hard labor; providing him with the opportunity to become one of the most quoted rebellious philosophers in history.

 

Great thread. You are very wise and mostly correct. 

I honestly didn't know this about Voltaire. I find it hilarious because all I knew of him was Candide. It's a great book, one of the only "classics" forced upon me in high school and college to make me genuinely laugh. It tackles both the inadequate nature of optimism and the uselessness of philosophical thinking. In one part an earthquake has candide being crushed by rubble and his companion Pangloss decides to help by considering why an earthquake might happen rather than assisting him out of the mess. Yet Voltaire manages to use this wit he has in real life to take action and game the systems he mocked in this book and find financial comfort to become a "great philosopher" and yet he spent only 3 days writing such a book. That's crazy 😂 thanks for the info, he might be one of the most interesting historical figures ever and I had no clue.

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On 3/15/2022 at 7:39 PM, Coco_Father said:

Ahhh, my good sir. You have forgotten about Voltaire.... In the mid 1700's he used his skills in mathematics along with his persuasive charm and ingenuity to beat the municipal bonds lotteries throughout Paris. Being the socialite that he was, he was able to deduce that the prizes in every district throughout Paris were in most cases more than the amount of all the tickets being sold. So he recruited a team that was his very own Renaissance version of Ocean's Eleven and went to work scamming  outsmarting the officials of the city of Paris. This strategy made him a very rich man that allowed him to live his days with his thoughts rather than hard labor; providing him with the opportunity to become one of the most quoted rebellious philosophers in history.

 

Great thread. You are very wise and mostly correct. 

 

On 3/15/2022 at 7:39 PM, Coco_Father said:

Ahhh, my good sir. You have forgotten about Voltaire.... In the mid 1700's he used his skills in mathematics along with his persuasive charm and ingenuity to beat the municipal bonds lotteries throughout Paris. Being the socialite that he was, he was able to deduce that the prizes in every district throughout Paris were in most cases more than the amount of all the tickets being sold. So he recruited a team that was his very own Renaissance version of Ocean's Eleven and went to work scamming  outsmarting the officials of the city of Paris. This strategy made him a very rich man that allowed him to live his days with his thoughts rather than hard labor; providing him with the opportunity to become one of the most quoted rebellious philosophers in history.

 

Great thread. You are very wise and mostly correct. 

 

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On 3/16/2022 at 8:20 AM, BCGame_POP said:

Hehehe, that will hurt casino business, LOL. Thanks for your appreciation. 

So you don't think it is a good idea to be up front and honest about the circumstances beforehand? You would hurt the casino business by not posting accurate and realistic information that corresponds to the actual gameplay? Gameplay that is to be expected and easily proven by analyzing the results?

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On 3/14/2022 at 5:43 PM, BCGame_POP said:

This article is a part of a series of articles that I will be writing on the forum, which debunks all the myths associated with Gambling.
Gambling is essentially a game of luck, and no strategy is foolproof. If strategies had specific outcomes every single time, all the mathematicians in this world would have been billionaires. We never heard any mathematician or nerds working out some formulas and cracked the mysterious code.

There were instances in history where few people used techniques to beat the house - like card counting and identifying a specific period where the bonuses offered by a particular casino or lottery surpassed the house edge. However, these incidents happen extremely rarely, and your funds would be forfeited if you are caught.

We often come across instances that raise our eyebrows like:

  1. How can I have 20+ reds in a row on 2x on dice?
  2. How can a slot game drain my balance indefinitely without giving a win?
  3. How can Dice or Limbo give 3 or 4 reds in a row on 1.01x?
  4. How does a slot game not pay more than 1x for more than 20+ bonus buys?

And the list goes on and on.
I will clear a few things about Odds and Probability to give you an understanding of how different events occur in Gambling.

1. Every outcome is independent of the previous result:


Take Coin Flip, for example - the odds of heads or tails is 50% for a single roll. Theoretically, for every 100 coin flips, you are supposed to have 50 heads and 50 tails. However, there could be a lot of variance when you practically do it.
You might have a specific outcome, Heads or Tails, several times in a row.
Flip 1 - The odds of Heads is 50%
Flip 2 - The odds of Heads still remains 50%
Flip 3 - Still, the odds remains the same for Heads which is 50%.
So, on...
In practical gambling, this means that when you roll dice on 2x, if you had 4 or 5 reds in a row, it does not necessarily increase your chances of hitting the green on the following rolls. Even on the next roll, the chance of hitting a RED or GREEN remains the same.|
However, if you roll it indefinitely, the number of REDS and GREEN will eventually even out.

Few common misconceptions on this subject:

  • Does the games payout follow a pattern?
    No, since every outcome is independent, the new outcome doesn't follow or depend on the previous result.
  • Increasing bet size after a certain number of losses in a row:

The bet size doesn't have any impact, as the odds remain the same regardless of your bet amount. This is the reason why every martingale strategy fails at some point. At some point, you will have soo many losses in a row that virtually no bankroll can hold in the long term.

2. Casino manipulates the outcomes of a Game:


Casinos do not control anyone's gameplay because they don't have to. A casino already has an advantage over the player(House-Edge). Secondly, you can verify the randomness of bets on our Provable Verification tools(will discuss this subject in a different article extensively).

What is House Edge?

It's fundamentally a mathematical advantage that a casino has over the players.


Take an example of Dice; the house edge of this popular casino game is 1% (lowest in the industry). When you play dice on 50% chance, the payout should be 2x. However, due to house edge, the payout remains 1.98x. This is how the casino makes money on the overall wagered amount in the long term.


Usually, original games like Crash, Dice, Limbo, Keno, etc., have a house edge of 1%. Theoretically, you are bound to lose 1$ for every 100$ you wager. Similarly, slot games have an higher house-edge which varies around 1-10%.

  • Does that mean that you can never win at a casino?

Many people lose; however, some people win at a casino. This is where Variance and Volatility come into the picture.

3. Variance and Volatility:


I will keep it in fundamental terms, and you can do your research about these two terms on Google.


Variance - means inconsistency of an outcome.


We know that we are bound to have 50 reds and 50 greens on 2x on Dice on average for every 100 rolls. However, this theory occurs when you roll the game indefinitely, and the outcome is very inconsistent in practice for a few 100 rolls, or even several 1000's of rolls.
This is how some people have extremely good runs, and some have terrible runs. The variance could be 20%, 30% or maybe more depending on the game and multiplier you chose.


Volatility - in gambling refers to how frequently a game pays.


Game of Plinko, for example. The odds of hitting a 1000x is around once in every 30,000+ rolls. Which necessarily doesn't mean that you hit a 1000x for every 30k rolls. You have to keep rolling it indefinitely, and at some point the theoretical value matches the practical outcome. 


If you take a Slot Game like Tombstone RIP by no-limit city, which has a max win potential of 300kx - 85% of all free spins will not be money back(meaning dead spins). That means the remaining 15% of all free spin sessions are filled with most RTP. For example, 15% of the RTP is on hits between 1.500x and 3.500x. If you want to go for the 300.000x win cap, you must hope to upgrade to super freespins (it happens 1/109).

RTP stands for Return To Player. Usually, slots have an RTP of around 96%, which means you get back 96$ for every 100$ you spend in a very long term. Casino charges a 4% fee as a part of house edge and entertainment provided.

So depending on the game you chose, the volatility or the frequency at which the game pays differs. This is why one of our slot games, Egyptian Adventure, pays less frequently due to its highly volatile nature.

Understand the games that you are playing, budget your bankroll accordingly. If you do 1$ spins with a bankroll of 100$ on Tombstone RIP, there is a high chance that your balance will be drained in the next 100-150 rolls. However, if you choose a game like Saviour Sword or Cave, things are entirely different as these games have low payout potential, so they pay very frequently.

I am concluding my part 1 on this series and opening the thread for discussion. I will go through all your comments on this topic and get back to them one by one. Feel free to ask any kind of questions on this topic.  I will be back with another article on this "Clueless Gamblers" series shortly.

It is impossible to state that, "Every outcome is independent of the previous result" and speak truthfully. RTP is a predetermined outcome that is guaranteed to be in the casinos favor. This means that every spin has a direct effect on the next one. I know this from extensive gameplay. Take for example winning and losing. To be honest,  my experience has shown me that most of the wins are almost guaranteed to be followed by a series of losses. Any person who says otherwise is just enabling the deception and misinformation. The spins are too predictable. The proof is in the results. I don't understand how we have these discussions or disagreements when the proof is in the results. The patterns are clear. They are written in green and red. The only thing consistent about playing slots is always plan on losing your money. As soon as you deposit it with the intent to spend it on slots, consider it gone already. From my experience we are about 95 percent likely to lose with no possibility of getting up enough to consider withdrawal. This brings up another question. How are the games described with a similar rating on RTP when one is clearly following the RTP and allowing pretty much no room for any kind of realistic gain worth withdrawal? Then other games you can see it allows more room for a withdrawable situation. Yet they can be rated as similar? This is very deceptive. We are given this unreliable form of measuring the possibility of reward when it has been shown many times that a game can have a very high RTP, yet when analyzing the  results of the sessions prove time and time again never to be rewarding to the player. It just solidifies  the answers to our questions. I am against casinos comparing their slots with anything like a coin flip. I really hope you are not doing anything like that here. It is important to be clear and honest about the circumstances because you do not want to hinder the decisions a customer makes correct? As you stated above the casino makes enough with just a house edge correct? To add deceptive practices proves this isn't true, as it adds a layer of unexpected loss. Yes a gamble means we have a chance to lose but it doesn't mean it is fair game to lie to people and try to cover up a seriously corrupt system and blame it on the uncertainty of its nature. This is where the results can come into play and easily debunk any misinformation. If you see a consistent pattern of outcomes gravitating to one side and it is always the side of the people who have control over the games what does that say? 

 

 

"In most illustrations of the gambler's fallacy and the reverse gambler's fallacy, the trial (e.g. flipping a coin) is assumed to be fair. In practice, this assumption may not hold. For example, if a coin is flipped 21 times, the probability of 21 heads with a fair coin is 1 in 2,097,152. Since this probability is so small, if it happens, it may well be that the coin is somehow biased towards landing on heads, or that it is being controlled by hidden magnets, or similar.In this case, the smart bet is "heads" because Bayesian inference from the empirical evidence — 21 heads in a row — suggests that the coin is likely to be biased toward heads. Bayesian inference can be used to show that when the long-run proportion of different outcomes is unknown but exchangeable (meaning that the random process from which the outcomes are generated may be biased but is equally likely to be biased in any direction) and that previous observations demonstrate the likely direction of the bias, the outcome which has occurred the most in the observed data is the most likely to occur again."

"For example, if the a priori probability of a biased coin is say 1%, and assuming that such a biased coin would come down heads say 60% of the time, then after 21 heads the probability of a biased coin has increased to about 32%.""

My whole point is if the games are rigged then that's ok, just don't lie to people about it. That's fraud. 

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This is all great and interesting information, and I look forward to learning more.  I want to learn more about the Blackjack on this site and if the probability resets after each shuffle, etc.   The dealer getting 4 Blackjacks in a row over multiple sessions or beating high cards by 1 should be rare, I would think, but I will admit I am clueless so I am hoping to learn more there.   

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