An Unintuitive Coin Flip Problem (With Secret Markov Chains)

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An Unintuitive Coin Flip Problem (With Secret Markov Chains)

Рет қаралды 10,978

Professor Peter

Күн бұрын

Пікірлер: 23

@johnhaber3254 4 жыл бұрын

The probabilities that the most recent two tosses are either HT or HH are the same. Each will lead to success or failure. If HH fails then it is in the same position to win on the next toss but if HT fails then it stands at TH and cannot win on the next toss. It needs an extra toss to put it in a possible winning position again (with probability 0.5) and is, therefore, half as likely to win as HH. In the long run, HH is twice as likely to win as HT so it should be favored at 2:1 odds. Good presentation.

@ProfessorPeterMath 4 жыл бұрын

Definitely. I love doing this demonstration in person with students, because you can see a couple of students notice the HH trap while they're flipping coins initially, and start to put together what's going to happen.

@koolitsch Жыл бұрын

@John Haber, and @Prof, very interesting video and comment. but i dont get i quite, can you explain me more further why HH appears in the "long" run 2/3. I tried it and counted it and it seems to be 50 50%. Cause after f.e. HHH it needs to stop somewhere with a T at the and, so you would get in this example HHHT so the last 2 tosses are HT. I counted manually several time in 100 = n tosses and it appears to the same amount to me. Can you explain me how in practise HH appears 2/3 to HT? Regards, cool comment and cool video

@lairdofgarscaddon 2 жыл бұрын

Going to use this in my math class I teach. Ty!

@Ovechkin8484 2 жыл бұрын

So cool. This is the first time I've been introduced to Markov chains.

@samarkand_nights 3 ай бұрын

No need to write down a matrix to get the conclusion. Probability of absorption in HHT can be recursively calculated: HHT: 1 HHH: 1 THH: 1 HTH: 2/3 THT: 1/3 HTT: 0 TTH: 2/3 TTT: 2/3 Sum: 16/3, which is 8*2/3. Hence HHT with probability 2/3.

@rachelgilyard3430 3 ай бұрын

I really appreciate this

@safihsoufian5956 10 ай бұрын

We need the matrix resolution

@CertifiedSlamboy 3 жыл бұрын

Haven't watched it yet, but I assume Heads, Heads, Tails is more likely to occur. As it's not just 3 flips, it's flipping until that pattern emerges in the chain. Even if you flip Heads, Heads, Heads, then you need to get one Tails to make it complete. But you need 2 tails. I can't explain my thinking, but thats roughly it.. lol. Now I'll watch and see how wrong I am.

@GodwynDi 2 жыл бұрын

You were right

@bellapoarch4621 Жыл бұрын

What about HHT & TTH... I don't think probability is tilted on one side, it's just that you're trying to find the outcome of a condition vs a whole different condition, not the opposite condition

@isaacAdam 4 жыл бұрын

You should have more subscribers, I really enjoyed watching your cours, you have a good voice too, I wish if you can recommend an easy markov chain introduction book, Thank you 🙏.

@ProfessorPeterMath 4 жыл бұрын

Thanks for the kind words! My first text for Markov Chains was a book called "Markov Processes for Stochastic Modelling" by Oliver Ibe. I found it to be a good one for reading independently.

@edwardmacnab354 2 жыл бұрын

Statistics was bad enough as it is then Markov joined the chat . Now we all realize just how stupid we really are .

@user-np3oh7yy5j Жыл бұрын

Hi Professor Peter, appreciate this video. which phyton program do you use. I tried running your code and keep getting the error missing parentheses in call to 'print".

@riyatyagi1271 3 жыл бұрын

Great vid! I'm just a bit confused on one thing: Don't you have to empty the fliplist (in the code) after receiving one of the patterns?

@ProfessorPeterMath 3 жыл бұрын

Yah, notice that we set the fliplist to be empty at the beginning of the for-loop counting out trials. So once we find a pattern and add 1 to the corresponding counter, the code runs back to the beginning of that for-loop which starts off with blanking out the fliplist.

@egorsemevskiy285 4 жыл бұрын

New sub! Now I know how to win a coinflip

@cupyucchinno 4 жыл бұрын

Appreciated it. Keep it up!

@dhanush5247 3 жыл бұрын

thank you sir

@saravanarallapalli8565 2 жыл бұрын

I understood why probability is (2/3):(1/3), but I don't understand how to proceed after constructing transition matrix. Could you please let me know?

@benedictus5657 2 жыл бұрын

you need to solve the system of state * transition_matrix = state to find the limit, ie the state where applying the matrix one more time does not change anything. Alternatively you can simply compute some initial state * transition_matrix ^ n, the bigger n the better it approximates the true limit