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    opietaylor93#81905 commented  · 

    Hello, I have a mathematics and probability masters degree and find this sort of stuff fascinating. I work with major platforms and machinery that specializes in randomizing, odds and probability. While most stuff does seem random and by “chance”; complex calculations allow us to understand that with enough rinse and repeat (for laymen's terms) proves that there is always some sort of pattern associated with numbers. For example, I have done some calculations that are correct (you can check yourself) that prove that the shuffling system in MTG Arena is not truly a chance factor. Here is what I found.

    I have played hundreds of matches in Arena, paid hundreds of dollars for gems to play in limited events and been a great reoccurring customer to MTGA. Here is the equation I used which is tried and true and also correct without any errors:

    This applies to any stretch of lands you pull off the top with or without a shuffle, The math stays the same. I personally experience this problem in about 45-60% (this is out of 100 games at a time that I studied) of my games which should be enough proof that this is obviously a money grab via Wizards of the Coast.

    First we calculate the odds that 5 specific consecutive cards are all lands. (My ratio is 6.1 lands 57% of the time but here is what 5 looks like for easy round numbers).

    Think of it like drawing 5 cards one at a time.

    Step-by-step logic
    First card is a land:

    17/40

    There are 17 lands out of 40 cards.

    Second card is also a land:

    Now there are:

    16 lands left

    39 total cards left

    16/39

    Third card:

    15/38

    Fourth card:

    14/37

    Fifth card:

    13/36

    Now multiply them
    Because all 5 events must happen:

    (17/40)×(16/39)×(15/38)×(14/37)×(13/36)

    Why multiply?

    Because:

    That equals:
    ≈0.0094≈ 0.0094≈0.0094

    Which is:

    0.94%

    That’s the chance that one specific 5-card stretch is all lands.

    Just to be clear, this happens with an average of 6.1 lands drawn back to back over a course of 100 games 57% of the time. (I started recording late last year just to matter of fact.) Here are the odds that I had my specifically designed probability computer system put together just to be certain.

    Step 1 — What is the true probability of 6 lands in a row?
    Earlier we established:

    For a 40-card deck with 17 lands:

    Probability of at least one 6-land streak somewhere in the deck ≈ 1%

    That means:

    p=0.01p = 0.01p=0.01

    So in any given game, you have about a 1 in 100 chance of seeing a 6-land streak.

    Step 2 — What would 57% mean?
    57% over 100 games means:

    57 games out of 100

    But if the true probability is 1%, then over 100 games you would expect:

    100 × 0.01= 1 game

    So the expectation is:

    Expected = 1 game

    Claimed = 57 games

    That’s 57× higher than mathematically expected.

    Step 3 — What are the odds of that happening naturally?
    This is a binomial probability problem.

    We ask:

    That probability is effectively:

    ≈10−100 or smaller≈ 10^{-100} { or smaller}≈10−100 or smaller

    To put that in perspective:

    Odds of winning the Powerball jackpot: ~1 in 292 million

    This event: far, far, far less likely than winning the lottery multiple times in a row

    In practical terms:

    The probability is effectively zero.
    Not “very unlikely.”
    Not “rare.”
    Mathematically indistinguishable from impossible.

    Step 4 — The “Average of 6.1 Lands in a Row” Claim
    This makes it even more impossible.

    Why?

    Because:

    7-land streak odds ≈ 0.3%

    8-land streak odds are even smaller

    9-land streak odds are microscopic

    To average 6.1 lands in a row 57% of games means you are regularly hitting 6, 7, maybe 8 land streaks constantly.

    That violates what’s called the law of large numbers.

    With a fair shuffle, over time results converge toward expected probability — not explode away from it.

    Step 5 — Could It Happen Without Manipulation?
    Only if:

    The deck does NOT actually contain 17 lands.

    The shuffle is not random.

    The data collection is biased (memory bias).

    The sample size is misreported.

    There is a physical issue (clumping from insufficient shuffling).

    But under:

    True randomness

    Proper shuffle

    17 lands

    It is not statistically plausible.

    This will be posted for everyone of your customers who have this issue to see. I hope that you can figure it out before the uproar gets too loud for you to handle.

    -Anonymous

    opietaylor93#81905 supported this idea  · 
    An error occurred while saving the comment
    opietaylor93#81905 commented  · 

    Hello, I have a mathematics and probability masters degree and find this sort of stuff fascinating. I work with major platforms and machinery that specializes in randomizing, odds and probability. While most stuff does seem random and by “chance”; complex calculations allow us to understand that with enough rinse and repeat (for laymen's terms) proves that there is always some sort of pattern associated with numbers. For example, I have done some calculations that are correct (you can check yourself) that prove that the shuffling system in MTG Arena is not truly a chance factor. Here is what I found.

    I have played hundreds of matches in Arena, paid hundreds of dollars for gems to play in limited events and been a great reoccurring customer to MTGA. Here is the equation I used which is tried and true and also correct without any errors:

    This applies to any stretch of lands you pull off the top with or without a shuffle, The math stays the same. I personally experience this problem in about 45-60% (this is out of 100 games at a time that I studied) of my games which should be enough proof that this is obviously a money grab via Wizards of the Coast.

    First we calculate the odds that 5 specific consecutive cards are all lands. (My ratio is 6.1 lands 57% of the time but here is what 5 looks like for easy round numbers).

    Think of it like drawing 5 cards one at a time.

    Step-by-step logic

    First card is a land:

    17/40

    There are 17 lands out of 40 cards.

    Second card is also a land:

    Now there are:

    16 lands left

    39 total cards left

    16/39

    Third card:

    15/38

    Fourth card:

    14/37

    Fifth card:

    13/36

    Now multiply them

    Because all 5 events must happen:

    (17/40)×(16/39)×(15/38)×(14/37)×(13/36)

    Why multiply?

    Because:

    Probability of A AND B AND C AND D AND E
    = multiply each step together.

    That equals:

    ≈0.0094≈ 0.0094≈0.0094

    Which is:

    0.94%

    That’s the chance that one specific 5-card stretch is all lands.

    Just to be clear, this happens with an average of 6.1 lands drawn back to back over a course of 100 games 57% of the time. (I started recording late last year just to matter of fact.) Here are the odds that I had my specifically designed probability computer system put together just to be certain.

    Step 1 — What is the true probability of 6 lands in a row?

    Earlier we established:

    For a 40-card deck with 17 lands:

    Probability of at least one 6-land streak somewhere in the deck ≈ 1%

    That means:

    p=0.01p = 0.01p=0.01

    So in any given game, you have about a 1 in 100 chance of seeing a 6-land streak.

    Step 2 — What would 57% mean?

    57% over 100 games means:

    57 games out of 100

    But if the true probability is 1%, then over 100 games you would expect:

    100 × 0.01= 1 game

    So the expectation is:

    Expected = 1 game

    Claimed = 57 games

    That’s 57× higher than mathematically expected.

    Step 3 — What are the odds of that happening naturally?

    This is a binomial probability problem.

    We ask:

    If each game has a 1% chance of a 6-land streak, what’s the probability of getting 57 or more successes out of 100 games?

    That probability is effectively:

    ≈10−100 or smaller≈ 10^{-100} { or smaller}≈10−100 or smaller

    To put that in perspective:

    Odds of winning the Powerball jackpot: ~1 in 292 million

    This event: far, far, far less likely than winning the lottery multiple times in a row

    In practical terms:

    The probability is effectively zero.

    Not “very unlikely.”
    Not “rare.”
    Mathematically indistinguishable from impossible.

    Step 4 — The “Average of 6.1 Lands in a Row” Claim

    This makes it even more impossible.

    Why?

    Because:

    7-land streak odds ≈ 0.3%

    8-land streak odds are even smaller

    9-land streak odds are microscopic

    To average 6.1 lands in a row 57% of games means you are regularly hitting 6, 7, maybe 8 land streaks constantly.

    That violates what’s called the law of large numbers.

    With a fair shuffle, over time results converge toward expected probability — not explode away from it.

    Step 5 — Could It Happen Without Manipulation?

    Only if:

    The deck does NOT actually contain 17 lands.

    The shuffle is not random.

    The data collection is biased (memory bias).

    The sample size is misreported.

    There is a physical issue (clumping from insufficient shuffling).

    But under:

    True randomness

    Proper shuffle

    17 lands

    It is not statistically plausible.

    This will be posted for everyone of your customers who have this issue to see. I hope that you can figure it out before the uproar gets too loud for you to handle.

    -Anonymous

    An error occurred while saving the comment
    opietaylor93#81905 commented  · 

    Hello, I have a mathematics and probability masters degree and find this sort of stuff fascinating. I work with major platforms and machinery that specializes in randomizing, odds and probability. While most stuff does seem random and by “chance”; complex calculations allow us to understand that with enough rinse and repeat (for laymen's terms) proves that there is always some sort of pattern associated with numbers. For example, I have done some calculations that are correct (you can check yourself) that prove that the shuffling system in MTG Arena is not truly a chance factor. Here is what I found.

    I have played hundreds of matches in Arena, paid hundreds of dollars for gems to play in limited events and been a great reoccurring customer to MTGA. Here is the equation I used which is tried and true and also correct without any errors:

    This applies to any stretch of lands you pull off the top with or without a shuffle, The math stays the same. I personally experience this problem in about 45-60% (this is out of 100 games at a time that I studied) of my games which should be enough proof that this is obviously a money grab via Wizards of the Coast.

    First we calculate the odds that 5 specific consecutive cards are all lands. (My ratio is 6.1 lands 57% of the time but here is what 5 looks like for easy round numbers).

    Think of it like drawing 5 cards one at a time.

    Step-by-step logic

    First card is a land:

    17/40

    There are 17 lands out of 40 cards.

    Second card is also a land:

    Now there are:

    16 lands left

    39 total cards left

    16/39

    Third card:

    15/38

    Fourth card:

    14/37

    Fifth card:

    13/36

    Now multiply them

    Because all 5 events must happen:

    (17/40)×(16/39)×(15/38)×(14/37)×(13/36)

    Why multiply?

    Because:

    Probability of A AND B AND C AND D AND E
    = multiply each step together.

    That equals:

    ≈0.0094≈ 0.0094≈0.0094

    Which is:

    0.94%

    That’s the chance that one specific 5-card stretch is all lands.

    Just to be clear, this happens with an average of 6.1 lands drawn back to back over a course of 100 games 57% of the time. (I started recording late last year just to matter of fact.) Here are the odds that I had my specifically designed probability computer system put together just to be certain.

    Step 1 — What is the true probability of 6 lands in a row?

    Earlier we established:

    For a 40-card deck with 17 lands:

    Probability of at least one 6-land streak somewhere in the deck ≈ 1%

    That means:

    p=0.01p = 0.01p=0.01

    So in any given game, you have about a 1 in 100 chance of seeing a 6-land streak.

    Step 2 — What would 57% mean?

    57% over 100 games means:

    57 games out of 100

    But if the true probability is 1%, then over 100 games you would expect:

    100 × 0.01= 1 game

    So the expectation is:

    Expected = 1 game

    Claimed = 57 games

    That’s 57× higher than mathematically expected.

    Step 3 — What are the odds of that happening naturally?

    This is a binomial probability problem.

    We ask:

    If each game has a 1% chance of a 6-land streak, what’s the probability of getting 57 or more successes out of 100 games?

    That probability is effectively:

    ≈10−100 or smaller≈ 10^{-100} { or smaller}≈10−100 or smaller

    To put that in perspective:

    Odds of winning the Powerball jackpot: ~1 in 292 million

    This event: far, far, far less likely than winning the lottery multiple times in a row

    In practical terms:

    The probability is effectively zero.

    Not “very unlikely.”
    Not “rare.”
    Mathematically indistinguishable from impossible.

    Step 4 — The “Average of 6.1 Lands in a Row” Claim

    This makes it even more impossible.

    Why?

    Because:

    7-land streak odds ≈ 0.3%

    8-land streak odds are even smaller

    9-land streak odds are microscopic

    To average 6.1 lands in a row 57% of games means you are regularly hitting 6, 7, maybe 8 land streaks constantly.

    That violates what’s called the law of large numbers.

    With a fair shuffle, over time results converge toward expected probability — not explode away from it.

    Step 5 — Could It Happen Without Manipulation?

    Only if:

    The deck does NOT actually contain 17 lands.

    The shuffle is not random.

    The data collection is biased (memory bias).

    The sample size is misreported.

    There is a physical issue (clumping from insufficient shuffling).

    But under:

    True randomness

    Proper shuffle

    17 lands

    It is not statistically plausible.

    This will be posted for everyone of your customers who have this issue to see. I hope that you can figure it out before the uproar gets too loud for you to handle.

    -Anonymous

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