[Sparky]

Consider that there are two players playing Texas Hold'em Poker, one player has Q-K, while the other player has 3-4. People would assume that the person with the Q-K has the stronger hand, though if one considers that the Q-K player has already won the last three hands, then his probability of winning this hand is actually less than 50%.

When two people are playing poker, the probability of anyone winning is 50%, and it doesn't matter what the hand is or what the rules are. So in this sense, considering that Q-K player has won the last three hands, then probability of winning four times in a row is actually very small.

In this particular hand, since the winning probability of the Q-K player is less than 50%, it's highly likely that the 3-4 player will get a double 3, double 4, or even a straight to win the hand. Unless the Q-K player can scare the 3-4 player away with an all-in, it's probably a better idea to fold and check the next hand.

 

[LexImperialis]

This is not how poker works.

K-Q has 64% win chance and 3-4 has 34% win chance right off the bat.

This is because if none of them got a pair, the K-Q would win. If both of them got a pair, the K-Q would win.

 

[Sparky]

This is not how poker works.

K-Q has 64% win chance and 3-4 has 34% win chance right off the bat.

This is because if none of them got a pair, the K-Q would win. If both of them got a pair, the K-Q would win.

Yes, though in a random shuffle card game, each player in a two player match has 50% win chance, and the K-Q player already won three hands, so his fourth-win-in-a-row probability is very low, so his winning chance is actually less than 50%.

 

[MsMojiMoe]

As a Texas Hold’em player this 1. Isn’t how the game is played

but more importantly, you just describe a very very common mistake most humans make about probability…

And guess what it’s called….. drum roll

The gamblers fallacy…. There’s other names too..… it’s called a gamblers fallacy because you see it a lot in gambling but it actually connects to a lot in life because of how the human mind works.

I even know this fallacy, and I still fall for it

so a coin is flipped three times and all three times is heads…. if you were to bet $1000 what the fourth coin would be…. If you’re most people you’re gonna say tails…. but the truth is heads is still equally as probable…. It’s still 50-50…. The coin doesn’t remember that it landed on heads three times in a row.

we do this, because for some reason, the human mind believes there’s a natural balancing force in the universe… or in nature… or somewhere… even for random acts…… i’m guilty myself, but I’m aware of it…. We generally underestimate the likelihood of streaks occurring by chance…. we believe that something needs to change due to the gamblers fallacy.

however, there is no such balancing force, the coin cannot remember what was played previously. Casinos love, the gamblers fallacy… because it creates the illusion in the gambler’s mind that they can predict where “the balance” Will go next…

however, this fallacy doesn’t just pertain to gambling… this fallacy can be applied anywhere There is a sequence of decisions …..

think of any multiple tests you ever took and you answer “A” three or five times in a row, do you question it, does it feel weird or wrong? do you feel like you need to put a balance/change to it? Or the probability that the next answer is “A” feels off.
This is this fallacy at work if you feel awkward about it….

The University of Chicago review found that asylum judges were 19% less likely to approve an asylum seeker if they had just approve the previous two.

The same person applying for a loan, ppl were more likely to get approved for a loan if the previous two ppl before them were rejected… and was more likely to be rejected if the previous two were approved..

similar findings were also found with baseball umpires

take a closer look at the independent and inter-dependent events around you…
independent events are not influenced by a balancing forces of nature.

 

[Sparky]

As a Texas Hold’em player this 1. Isn’t how the game is played

but more importantly, you just describe a very very common mistake most humans make about probability…

And guess what it’s called….. drum roll

The gamblers fallacy…. There’s other names too..… it’s called a gamblers fallacy because you see it a lot in gambling but it actually connects to a lot in life because of how the human mind works.

View attachment 918801



I even know this fallacy, and I still fall for it
View attachment 918802


so a coin is flipped three times and all three times is heads…. if you were to bet $1000 what the fourth coin would be…. If you’re most people you’re gonna say tails…. but the truth is heads is still equally as probable…. It’s still 50-50…. The coin doesn’t remember that it landed on heads three times in a row.

we do this, because for some reason, the human mind believes there’s a natural balancing force in the universe… or in nature… or somewhere… even for random acts…… i’m guilty myself, but I’m aware of it…. We generally underestimate the likelihood of streaks occurring by chance…. we believe that something needs to change due to the gamblers fallacy.

however, there is no such balancing force, the coin cannot remember what was played previously. Casinos love, the gamblers fallacy… because it creates the illusion in the gambler’s mind that they can predict where “the balance” Will go next…

however, this fallacy doesn’t just pertain to gambling… this fallacy can be applied anywhere There is a sequence of decisions …..

think of any multiple tests you ever took and you answer “A” three or five times in a row, do you question it, does it feel weird or wrong? do you feel like you need to put a balance/change to it? Or the probability that the next answer is “A” feels off.
This is this fallacy at work if you feel awkward about it….

The University of Chicago review found that asylum judges were 19% less likely to approve an asylum seeker if they had just approve the previous two.

The same person applying for a loan, ppl were more likely to get approved for a loan if the previous two ppl before them were rejected… and was more likely to be rejected if the previous two were approved..

similar findings were also found with baseball umpires

take a closer look at the independent and inter-dependent events around you…
independent events are not influenced by a balancing forces of nature.

Have you ever taken Statistics 101? It should've also been taught in basic algebra class, in which if something has a chance of 50% happening, then having it happen two times in a row is 25%, having it happen three times in a row is 12.5%, four times in a row is 6.25%, etc.

Also, flipping a coin is not "pure random chance that depends on previous outcomes", it's the "probability of something either landing head or tail, based on previous outcomes"

 

[recycled_lube_oil]

What about the Monty Hall problem though?

If you were to offer me 3 doors, behind one door is a goat, behind another is a Porsche, behind the other is nothing.
I have a 33% chance of picking the winning door.

I pick door A, you now open door B and show me the goat. Should I stay with door A or pick door C?
Well obviously I will pick door C, as when I chose door A, there was a 33% chance, however if I now pick door C, I have a 50% chance of winning.

As mad as this sounds, it is true.

The College Mathematics Journal, Vol. 42, No. 1 (January 2011), pp. 71-74

 

[MsMojiMoe]

Have you ever taken Statistics 101? It should've also been taught in basic algebra class, in which if something has a chance of 50% happening, then having it happen two times in a row is 25%, having it happen three times in a row is 12.5%, four times in a row is 6.25%, etc.

Also, flipping a coin is not "pure random chance that depends on previous outcomes", it's the "probability of something either landing head or tail, based on previous outcomes"

Yes

what is this theorem or formula called because I don’t remember it….

I will look at it and see where we are misunderstanding,…. It’s probably due to “independent.” Which I mention in my first post, which should have told you I knew statistics…. But I will read it and see why you think this. When things are not “independent“ is where it gets complicated….called Bayesian view/probability (which has a lot of theorems…this view, ppl get confuse…this why a lot of ppl believe if you throw 3 heads, then the fourth will be tails or it’s overdue….


each throw of the coin, is an INDEPENDENT act…therefore the probability is always the same chance…. The previous conditions have nothing to do with the outcome… or the probability.

like the lottery…. Some people think the more people that is playing the harder it is for you to win which is completely untrue…. In fact, the chances are exactly the same whether one person plays or 1 million people play… unless each person was sign certain numbers and it wasn’t just random picks…then it become interdependent…

throwing dice, there’s no interdependent relationship with each throw….it’s completely “independent“
———-
Basic probability formula… in statistics.

 

[Sparky]

Yes

what is this theorem or formula called because I don’t remember it….

I will look at it and see where we are misunderstanding,…. It’s probably due to “independent.” Which I mention in my first post, which should have told you I knew statistics…. But I will read it and see why you think this. When things are not “independent“ is where it gets complicated….called Bayesian view/probability (which has a lot of theorems…this view, ppl get confuse…this why a lot of ppl believe if you throw 3 heads, then the fourth will be tails or it’s overdue….


each throw of the coin, is an INDEPENDENT act…therefore the probability is always the same chance…. The previous conditions have nothing to do with the outcome… or the probability.

like the lottery…. Some people think the more people that is playing the harder it is for you to win which is completely untrue…. In fact, the chances are exactly the same whether one person plays or 1 million people play… unless each person was sign certain numbers and it wasn’t just random picks…then it become interdependent…

throwing dice, there’s no interdependent relationship with each throw….it’s completely “independent“
———-
Basic probability formula… in statistics.
View attachment 918849

You are thinking of "independent" in terms of one out of infinite possibilities, in which case it's either 1 or 0. When the possibilities are restricted, like the case of a two-sided coin or poker cards, then Broad Probability comes into play.

 

[Sparky]

What about the Monty Hall problem though?

If you were to offer me 3 doors, behind one door is a goat, behind another is a Porsche, behind the other is nothing.
I have a 33% chance of picking the winning door.

I pick door A, you now open door B and show me the goat. Should I stay with door A or pick door C?
Well obviously I will pick door C, as when I chose door A, there was a 33% chance, however if I now pick door C, I have a 50% chance of winning.

As mad as this sounds, it is true.

The College Mathematics Journal, Vol. 42, No. 1 (January 2011), pp. 71-74

To an outside observer, the person picking between two doors has 50% chance of winning, though to the individual, it's always just 33% chance of picking the correct door in the Monty Hall.

 

[chad86tsi]

Have you ever taken Statistics 101? It should've also been taught in basic algebra class, in which if something has a chance of 50% happening, then having it happen two times in a row is 25%, having it happen three times in a row is 12.5%, four times in a row is 6.25%, etc.

Also, flipping a coin is not "pure random chance that depends on previous outcomes", it's the "probability of something either landing head or tail, based on previous outcomes"

The probability of guessing a single coin flip correctly is 50%, 2^1=2 or 1 in 2. The chance of doing so 4 times in a row is 6.25%, 2^4=16, or 1 in 16. Each individual coin flip it's still 50/50. Each coin flip is it's own single event. 4 is a row is still 4 single events. Past events don't change this single-event fact. even if th elast 100 were the same, the next single event (101'st) is still a 2^1 event.

Don't believe it? try it yourself with 100 coin flips. Do 100 single events, then do 4 in a row 25 times. The pattern will emerge. You will get the 100 single events right about half the time, and the chance you'll get a 4-in-a-row perhaps once or twice, or none at all.

If the gambling objective to is guess 4 in a row, then you are correct 2^4. if the objective to is guess the next (single event), the last are irrelevant, it's still 2^1.

 

[SouDesuNyan]

That's like saying you've flipped 3 tails in a row, so the chance of it being head on the next flip is higher than 50% because "it's due". No, the next flip is still 50% head/tails.

 

[SouDesuNyan]

The implementation of poker winning odds given existing information is an interesting problem though. It can be calculated directly through iterating every possible hand to determine your odds (# of winning results divided by all possibilities). I don't think this brute force method would use up too much time because there are only a small number of "slots" and each slot would have less than 52 possibilities.

 

[Sparky]

That's like saying you've flipped 3 tails in a row, so the chance of it being head on the next flip is higher than 50% because "it's due". No, the next flip is still 50% head/tails.

The probability of guessing a single coin flip correctly is 50%, 2^1=2 or 1 in 2. The chance of doing so 4 times in a row is 6.25%, 2^4=16, or 1 in 16. Each individual coin flip it's still 50/50. Each coin flip is it's own single event. 4 is a row is still 4 single events. Past events don't change this single-event fact. even if th elast 100 were the same, the next single event (101'st) is still a 2^1 event.

Don't believe it? try it yourself with 100 coin flips. Do 100 single events, then do 4 in a row 25 times. The pattern will emerge. You will get the 100 single events right about half the time, and the chance you'll get a 4-in-a-row perhaps once or twice, or none at all.

If the gambling objective to is guess 4 in a row, then you are correct 2^4. if the objective to is guess the next (single event), the last are irrelevant, it's still 2^1.

The issue is not the odds of guessing correctly, it's getting heads four times in a row. If you consider head or tail out of infinite possibilities, or 1/infinity, then it's single event, meaning getting 10 heads in a row is as 50% as getting 100 tails in a row. However, in the case where there are two possibilities, then it's just 1/(2^4) chance in getting heads four times in a row, or 1/16.

 

[SouDesuNyan]

The issue is not the odds of guessing correctly, it's getting heads four times in a row. If you consider head or tail out of infinite possibilities, or 1/infinity, then it's single event, meaning getting 10 heads in a row is as 50% as getting 100 tails in a row. However, in the case where there are two possibilities, then it's just 1/(2^4) chance in getting heads four times in a row, or 1/16.

The odds of getting four heads in a row given that you already have three heads in a row is 50%.

 

[chad86tsi]

The issue is not the odds of guessing correctly, it's getting heads four times in a row. If you consider head or tail out of infinite possibilities, or 1/infinity, then it's single event, meaning getting 10 heads in a row is as 50% as getting 100 tails in a row. However, in the case where there are two possibilities, then it's just 1/(2^4) chance in getting heads four times in a row, or 1/16.

if it's heads 4 times in a row, that's 2^4. On the 5th time it's 2^1 still. The odds of the 5th single try is still 2^1, but looking backwards in time at all 5, it's 2^5. If you are betting ahead of time for 5 tries, that's also a 2^5 bet. If you are just betting on the last try of 5, that's a 2^1 bet, the last 4 don't change the 2^1 math of the single event. Since you don't bet backwards, you can't use the backwards formula to predict a future event. You are only ever betting on future events.

Another way to express it is the odds look like this for 5 tries on a random event that has 1 of 2 possibilities:
1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 0.03125 (3.125%)

Each event is the same 1/2, and none of them alters the value of the preceding nor following values. Strung together, their odds of being alike diminish, but each event is still the same singular 1/2 event. If we look at that string of 5 events, the odds on the 3rd event isn't altered by the first two, nor the following two. That 3rd event can only be one of 2 possibilities, even if all the others were wanted or unwanted, or randomly mixed. It's value and odds of occurring were still 1/2. Every event is it's own event. Stringing them together is a different kind of bet, and one you aren't actually offered in any game I'm aware of.


The odds of getting a full house in texas holdem is 1 in 693.

on the second hand, the odds are still 1in 693

the odds on the 3rd hand is still 1 in 693.

the odds of a 4th being a full house like the last 3 are astronomical strung together, but in that single hand, it's still 1 in 693 event. You aren't betting on the last 3 hands combined with the 4th, you are betting on the 4th, and only the 4th hand. The odds are still a single event with odds of 1 in 693 for a full house. The cards are shuffled each time, nothing dilutes or multiplies the odds. Same with a coin flip.

If you don't want to believe this, please don't take up gambling.

 

[Sparky]

That's like saying you've flipped 3 tails in a row, so the chance of it being head on the next flip is higher than 50% because "it's due". No, the next flip is still 50% head/tails.

if it's heads 4 times in a row, that's 2^4. On the 5th time it's 2^1 still. The odds of the 5th single try is still 2^1, but looking backwards in time at all 5, it's 2^5. If you are betting ahead of time for 5 tries, that's also a 2^5 bet. If you are just betting on the last try of 5, that's a 2^1 bet, the last 4 don't change the 2^1 math of the single event. Since you don't bet backwards, you can't use the backwards formula to predict a future event. You are only ever betting on future events.

Another way to express it is the odds look like this for 5 tries on a random event that has 1 of 2 possibilities:
1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 0.03125 (3.125%)

Each event is the same 1/2, and none of them alters the value of the preceding nor following values. Strung together, their odds of being alike diminish, but each event is still the same singular 1/2 event. If we look at that string of 5 events, the odds on the 3rd event isn't altered by the first two, nor the following two. That 3rd event can only be one of 2 possibilities, even if all the others were wanted or unwanted, or randomly mixed. It's value and odds of occurring were still 1/2. Every event is it's own event. Stringing them together is a different kind of bet, and one you aren't actually offered in any game I'm aware of.


The odds of getting a full house in texas holdem is 1 in 693.

on the second hand, the odds are still 1in 693

the odds on the 3rd hand is still 1 in 693.

the odds of a 4th being a full house like the last 3 are astronomical strung together, but in that single hand, it's still 1 in 693 event. You aren't betting on the last 3 hands combined with the 4th, you are betting on the 4th, and only the 4th hand. The odds are still a single event with odds of 1 in 693 for a full house. The cards are shuffled each time, nothing dilutes or multiplies the odds. Same with a coin flip.

If you don't want to believe this, please don't take up gambling.

You guys are thinking of it being either head or tails out of infinite possibilities, not when there are only two possibilities.

So, getting a fifth head in a row is not 50% when you have four heads in a row, when there are only two possibilities. If it's a head or tail out of infinite possibilities, then it would be 50%. In this case, the possibility of getting four heads in a row is about 6.25%, while that for getting five heads in a row is 3.125%.

 

[chad86tsi]

You guys are thinking of it being either head or tails out of infinite possibilities, not when there are only two possibilities.

So, getting a fifth head in a row is not 50% when you have four heads in a row, when there are only two possibilities. If it's a head or tail out of infinite possibilities, then it would be 50%. In this case, the possibility of getting four heads in a row is about 6.25%, while that for getting five heads in a row is 3.125%.

It's 50% when you aren't betting forward for 5 turns. Is there a casino that lets you bet a sequence of turns like that?

No casino lets you bet on what happened in the past, so knowing the past is of no value to you.

When you bet on red or black on the roulette wheel, you can see what happened in the past, but you are betting on what happens next. What happens next is not predicated on what already happened. The "what happened in the past board" is useless for predicting the future, but it's there for people that don't understand this to bet based on their false beliefs. It's an idiot-aid, which is why it's there. That board probably makes them more money than anything.

I could roll a 6 sided die and get a specific sequence over the course of 50 turns that a casino will pay a 1 in a million payout. The next roll is still one in 6 chance because that die only has 6 sides, there are only 6 possible outcomes. Where does this idea of yours about infinite possibilities exist when there are only 6 sides on that cube?

Unless you bet on all 50 turns in advance at the beginning to turn out in that specific sequence, nothing will change the odds of that last roll, it's still 1 in 6 as there are only 6 possible outcomes of that single roll. There are no infinity dice, or coins, or cards.

 

[SouDesuNyan]

You guys are thinking of it being either head or tails out of infinite possibilities, not when there are only two possibilities.

So, getting a fifth head in a row is not 50% when you have four heads in a row, when there are only two possibilities. If it's a head or tail out of infinite possibilities, then it would be 50%. In this case, the possibility of getting four heads in a row is about 6.25%, while that for getting five heads in a row is 3.125%.

Maybe it's a language barrier thing, but I don't understand what you're trying to say. This is basic high school probability. There's no "infinite possibilities" in this problem.

 

[Sparky]

It's 50% when you aren't betting forward for 5 turns. Is there a casino that lets you bet a sequence of turns like that?

No casino lets you bet on what happened in the past, so knowing the past is of no value to you.

When you bet on red or black on the roulette wheel, you can see what happened in the past, but you are betting on what happens next. What happens next is not predicated on what already happened. The "what happened in the past board" is useless for predicting the future, but it's there for people that don't understand this to bet based on their false beliefs. It's an idiot-aid, which is why it's there. That board probably makes them more money than anything.

I could roll a 6 sided die and get a specific sequence over the course of 50 turns that a casino will pay a 1 in a million payout. The next roll is still one in 6 chance because that die only has 6 sides, there are only 6 possible outcomes. Where does this idea of yours about infinite possibilities exist when there are only 6 sides on that cube?

Unless you bet on all 50 turns in advance at the beginning to turn out in that specific sequence, nothing will change the odds of that last roll, it's still 1 in 6 as there are only 6 possible outcomes of that single roll. There are no infinity dice, or coins, or cards.

The probability of getting four heads in a row is about 6.25%, while that for getting five heads in a row is 3.125%, when the possibility is limited to two (head or tails). When you have either head or tail out of infinite number of possibilities, then it's 50% either head or tails, not dependent on past outcomes of having three heads in a row.

 

[chad86tsi]

Consider that there are two players playing Texas Hold'em Poker, one player has Q-K, while the other player has 3-4. People would assume that the person with the Q-K has the stronger hand, though if one considers that the Q-K player has already won the last three hands, then his probability of winning this hand is actually less than 50%.

The probability of getting four heads in a row is about 6.25%, while that for getting five heads in a row is 3.125%, when the possibility is limited to two (head or tails). When you have either head or tail out of infinite number of possibilities, then it's 50% either head or tails, not dependent on past outcomes of having three heads in a row.

Are you correcting yourself, or contradicting yourself?

Please tell me is the former and not the latter.