Wimbledon Draw

First topic message reminder :

Wimbledon is just around the corner and the draw is announced in the next few minutes.
How do you see things going?

Wimbledon Mens Draw Click Here

Wimbledon Womans Draw Click Here

Nadal will cruise to the final as usual. No real dangers. The only two players who can beat him on grass may have to play each other i.e Federer and Djokovic and there is no guarantee either will make it that far. I think its potentially going to be a Nadal v Djoko final. Grass is basically green clay now so I do not think Nadal will struggle at all. I hope it won't be like last years final which was really poor quality from what we have become accustomed to in the last few years with those amazing 5 set matches.

The ideal scenario would be Fed for Wimbledon and Murray for USO. That way each of the top 4 would have won a slam this year.

FedsFan wrote:... The ideal scenario would be Fed for Wimbledon and Murray for USO. ...

Ideal for whom? Roanic supporters might not think this ideal etc. May the best man win ...

Nore Staat wrote:

FedsFan wrote:... The ideal scenario would be Fed for Wimbledon and Murray for USO. ...

Ideal for whom? Roanic supporters might not think this ideal etc. May the best man win ...

Anyone who thinks Raonic could win Wimbledon or think he will be a tricky opponent for Nadal is clearly deluded. Sorry to offend his fans but lets not lose touch with reality. If he does, good on him and I will be the first to applaud his achievements.

Tom_____ wrote:

letigre wrote:

Tom_____ wrote:

letigre wrote:

Tom_____ wrote:It worth noting that all slams follow the 1/2 seeds opposite sides of the draw and then the 3/4 are randomised etc. So given nadal and Fed have been 1 and 2 or vice versa for years, you would statistically expect to see roughly a 50/50 split where Murray and Djoko land in either the top half or the bottom half (even where these two were lower ranked). I.e there should be an approximately equal chance of Murray or Djoko being in Federer or Nadal's half of the draw at any given slam.

Yet out of 18 slams listed. Murray and Nadal have been on collision course 13 times, as have Federer and Djoko.

You shouldn't really expect a near 50/50 split out of 18 draws, that would actually be quite unusual. Try flipping a coin 18 times, it's unlikely you'll get 9 heads and 9 tails or even 10 of one and 8 of the other. I just used a random number generator to generate either a 1 or a 2 eighteen times and I got 14 2's and 4 1's. Even further from the 50/50 split. If there had been 1000 draws and Murray had been drawn in Nadal's half 72% of the time then I might think something funny was going on. But on 18 draws it is really not surprising at all.

I didn't say it was statistically surprising, however the consecutive nature over the last 3 years at slams off clay is very unlikely and for example the Aus open 5 years in a row has a very low chance.

Being drawn in Nadal's half in the Aus open 5 years in a row is a 1 in 32 chance. I guess it's pretty low, but not that low, and it's just as likely as any other unique sequence.

yes except the majority of these sequences contain 2 or 3 times in opposite sides of the draw

I accept that. If it had been a nice alternating sequence of 2 of one and 3 of the other like 1,2,1,2,1 no one would raise an eyebrow though. Despite the fact that specific sequence is just as unlikely as 1,1,1,1,1. And an alternating sequence in general (either 1,2,1,2,1 or 2,1,2,1,2) is still only a 1 in 16 chance. The same chance as 4 of one in a row (1,1,1,1).

I don't know if you are just saying it's unusual or unlucky, or if you are suspicious of the draw. If you are just saying it is unusual or unlucky then I agree to a certain extent. It's certainly not anywhere near unusual enough to be suspicious though, and it is definitely not evidence of seeds 2 and 3 deliberately being drawn in one half and 1 and 4 in the other, or of Nadal and Federer deliberately being drawn to meet in the final.

letigre wrote:

Tom_____ wrote:

letigre wrote:

Tom_____ wrote:

letigre wrote:

Tom_____ wrote:It worth noting that all slams follow the 1/2 seeds opposite sides of the draw and then the 3/4 are randomised etc. So given nadal and Fed have been 1 and 2 or vice versa for years, you would statistically expect to see roughly a 50/50 split where Murray and Djoko land in either the top half or the bottom half (even where these two were lower ranked). I.e there should be an approximately equal chance of Murray or Djoko being in Federer or Nadal's half of the draw at any given slam.

Yet out of 18 slams listed. Murray and Nadal have been on collision course 13 times, as have Federer and Djoko.

You shouldn't really expect a near 50/50 split out of 18 draws, that would actually be quite unusual. Try flipping a coin 18 times, it's unlikely you'll get 9 heads and 9 tails or even 10 of one and 8 of the other. I just used a random number generator to generate either a 1 or a 2 eighteen times and I got 14 2's and 4 1's. Even further from the 50/50 split. If there had been 1000 draws and Murray had been drawn in Nadal's half 72% of the time then I might think something funny was going on. But on 18 draws it is really not surprising at all.

I didn't say it was statistically surprising, however the consecutive nature over the last 3 years at slams off clay is very unlikely and for example the Aus open 5 years in a row has a very low chance.

Being drawn in Nadal's half in the Aus open 5 years in a row is a 1 in 32 chance. I guess it's pretty low, but not that low, and it's just as likely as any other unique sequence.

yes except the majority of these sequences contain 2 or 3 times in opposite sides of the draw

I accept that. If it had been a nice alternating sequence of 2 of one and 3 of the other like 1,2,1,2,1 no one would raise an eyebrow though. Despite the fact that specific sequence is just as unlikely as 1,1,1,1,1. And an alternating sequence in general (either 1,2,1,2,1 or 2,1,2,1,2) is still only a 1 in 16 chance. The same chance as 4 of one in a row (1,1,1,1).

I don't know if you are just saying it's unusual or unlucky, or if you are suspicious of the draw. If you are just saying it is unusual or unlucky then I agree to a certain extent. It's certainly not anywhere near unusual enough to be suspicious though, and it is definitely not evidence of seeds 2 and 3 deliberately being drawn in one half and 1 and 4 in the other, or of Nadal and Federer deliberately being drawn to meet in the final.

there's 20 of 32 combinations that contain 2 or 3 turns on opposite sides of the draw, 10 more that contain at least one opposite and 1 each of either 5 same side or 5 opposite side.

I'm just saying its unlucky really, but that due to the finite nature of the top rankings, we are unlikely to see the trend reverse before one of the players drops out of contention.

Don't think the draw is manipulated, its not as if Mahut is playing Isner again at wimbledon is it?

The law of averages will kick in at some point. No-one can say when that is.

But like rules, laws are subject to not being followed.

It is "strange" how Djokovic keeps meeting Federer though...I'm sure the inequity of keeping in the same half of draws must be something they think about too.

The only way they can certainly avoid this is to become #1 and #2! Djokovic can, but can Roger?

Just posted this on my "Thankyou Tennis Gods" topic and see that it might be relevant here.


"Did you know that if you throw a coin... say 10 times the chances of predicting any sequence is 1 in 1024. It doesn't matter what the sequence is. It could be HHHHHHHHHH or TTTTTTTTTT or HTHTHTHTHT or HHHTTHTHTT or any other sequence. Also say by some freak occurrence you throw a coin 1,OOO times and get Tails every time. The chance of getting a Tail next time you throw the coin is 1 in 2 (exactly the same chance as getting a Head). Sorry if this is obvious to some but I'm always surprised at how often people are surprised by this.

As for Isner v Mahut. Thats just the Tennis Gods having a laugh! Ha ha!"

its FO 2005 the last time nadal met fed in sF in major
now fed is 3rd,,after 2 majors of this year (+ us open 2009 when nadals 3rd),,theyre destined to meet in final only. such a coincidence

though,,tbh,,im always hoping for fedal final

hawkeye wrote:Just posted this on my "Thankyou Tennis Gods" topic and see that it might be relevant here.


"Did you know that if you throw a coin... say 10 times the chances of predicting any sequence is 1 in 1024. It doesn't matter what the sequence is. It could be HHHHHHHHHH or TTTTTTTTTT or HTHTHTHTHT or HHHTTHTHTT or any other sequence. Also say by some freak occurrence you throw a coin 1,OOO times and get Tails every time. The chance of getting a Tail next time you throw the coin is 1 in 2 (exactly the same chance as getting a Head). Sorry if this is obvious to some but I'm always surprised at how often people are surprised by this.

As for Isner v Mahut. Thats just the Tennis Gods having a laugh! Ha ha!"

Thats true, however if you carry out probability distribution on the 1000 tail coin, you are likley to find that while its theoretically possible the coin is still fair, the chances of that are remote. Theres also a much higher probability that the coin flip isn't fair and is producing a bias result, with very little likelihood of error.

I did a few calcs and for the 14 out of 19 times for Murray to be in same half, when the true probability is 50% then we would need to be accepting an error margin of over 23% based on the results so far. You could use the same stats (14 of 19 slams) to say with 90% confidence that the real odds of Murray and Nadal being in the same half is between 59% and 88%.

Each coin toss does not have a memory of the prior toss, nor can it be used predict or summise the outcome of the next one. Each coin toss outcome is INDEPENDENT of every other, regardless of it's place in a sequence of coin tosses.
Statistically, you are just as likely to toss HHHHHHHHHHH as you are any other combination.

Heads and tails have the same value, it doesn't become imbalanced whilst a run of any side does not make the odds of the next one being the opposite any more likely.

The chances are ALWAYS 1 in 2. regardless of what came before or came after.
Similarly, when playing the lottery you are just as likely to get a run of consecutive numbers e.g. 1,2,3,4,5,6 as you are any other combination.

super_realist
With the lottery the only problem is that it is essentially 14 million to one against any particular 6 number combination. However, the fact that the draws are independent means that there is as high a possibility of two consecutive draws giving the same number combination as it producing any other combination.

It is true though that a run of 4 or 5 consecutive 'heads' in a coin flip is not particularly likely within one batch of 4 or 5 flips, if you continue the sequence for say 100 or 1000 flips you will find a number of occasions where such sequences (and longer) occur.

The possibility that the draw is not genuinely random is fairly remote (although I have sometimes had my suspicions about the FA Cup draw - both that the 3rd round often produces Man u v Aston Villa, and that the SF draw usually keeps the bigger clubs apart)

Precisely Dummy_Half, the point i'm making is that no number or face value of a coin is dependent or linked to any other, any sequences are purely the result of random occurance. Each number (or face) has the same value, and none can be drawn or flipped with any favour, therefore such events, coin tosses or lotteries have exactly the same chance of occuring every time you do one.
1 in 2 for a coin toss, 1 in 14 million for any combination of winning numbers in the lottery.

super_realist wrote: Each coin toss does not have a memory of the prior toss, nor can it be used predict or summise the outcome of the next one. Each coin toss outcome is INDEPENDENT of every other, regardless of it's place in a sequence of coin tosses.
Statistically, you are just as likely to toss HHHHHHHHHHH as you are any other combination.


Heads and tails have the same value, it doesn't become imbalanced whilst a run of any side does not make the odds of the next one being the opposite any more likely.

The chances are ALWAYS 1 in 2. regardless of what came before or came after.
Similarly, when playing the lottery you are just as likely to get a run of consecutive numbers e.g. 1,2,3,4,5,6 as you are any other combination.

Yes but as i mentioned above there are far more conbinations that contain multiple results of H and T.

for example, as above throw a coin 5 times, there are 32 sequences.

1 HHHHH (all same half of draw)
1 TTTTT (all opposite side of draw)
5 x mixture of THHHH
5 x mixture of HTTTT
10 x mixture of TTHHH
10 x mixture of TTTHH

So for the last five years at the AO, there 20 combinations out of 32 that would have seen Murray an Nadal in the same half 2 or 3 times out of 5. The fact the they have been in the same half on all occasions is simply very lucky, a 1 in 32 chance. Next year, it still a 50/50 on the draw day, given we have already had a 5 streak, but to go down that road of 6 consecutive clashes the probability of the whole sequence drops to 1 in 64.

Now separately, the next flip always being a 50/50 is true, but only if you know the coin toss is fair. You would normally do statistical testing on any kind of randomised test to make sure the results match what you consider the correct probability to be. A coin toss is considered fair, but if you do 100s of tosses and get heavily bias looking data, the likelihood of bias increases. At a certain tipping point a coin becomes more likely to be a biased coin than an unbiased coin that happens to have produced a run of biased looking results - thats where confidence intervals come in.

Finally believe it or not, most production coins are not absolutely 50/50, but the discrepancy is so minimal that it makes little difference, like 0.499999 vs. 0.500001

I would concur that the difference in weight of each side of the coin would be considered irrelevant due to the inertia of the coin movement, but each toss is on it's own is a separate entity, it is not dependent on the prior one or the future one, and any sequence that results is purely coincidental. You are just as likely to get a long run of either heads or tails as you are a mixture.

To clarify my view, i am not for one minute saying that the draw method is biased or unfair. however what i am saying is that statistically we have landed in a streaking sequencing that is relatively rare compared to more random looking draws. Now this would not be a point for discussion if the top 4 were around for 15 years, but considering the top 4 are not likely to be competitive long enough for the current streak to fully right itself, its worth noting that till this point in slam the number of potential Fed /Djoko and Nadal/Murray slam clashes vastly outnumber the potential Fed/Murray and Nadal Djoko clashes. Its a worthy point of discussion for some (not me) who may believe that Djoko not being on course to play Nadal before slam finals has stopped him reaching more finals, or perhaps some people might have an opposite view etc etc.

All i'm saying it that even though there doesn't have to be biased in the draw, the fact the were have seen so many occasions where the draws have been a particular way is potentially worth discussing in terms of any effect it may have had on results of slams.

I see what you mean Tom, but as there is only a 1 in 2 chance of a player being in either half of the draw, it's not too much of a stretch to imagine how it might happen frequently as each draw bears no relevance to what comes before or after. Each draw stands on it's own, and it's only when you look at other years it appears that draws are maybe being made favourable until you realise that statisitical likelihood is dependent ONLY on th eyear that it is made.
I'd personally rather see Nadal and Federer knock each other out as I hate Nadal's coin biting of the trophy and I think Federer is smug and smarmy and fairly disingenuous. Time for either Murray or Djokovic to make their mark in this tourney.

super_realist wrote:I would concur that the difference in weight of each side of the coin would be considered irrelevant due to the inertia of the coin movement, but each toss is on it's own is a separate entity, it is not dependent on the prior one or the future one, and any sequence that results is purely coincidental. You are just as likely to get a long run of either heads or tails as you are a mixture.

None of what i have written suggests otherwise


"You are just as likely to get a long run of either heads or tails as you are a mixture."

There are however a far greater number of separate series that contain mixtures than contain streaks, so series of mixtures are far more likely than a series of streaks.

E.g 5 tails = 1 in 32
Any combination of 2 Heads or tails and 3 tails or heads = 20/32

Tom_____ wrote:

super_realist wrote:I would concur that the difference in weight of each side of the coin would be considered irrelevant due to the inertia of the coin movement, but each toss is on it's own is a separate entity, it is not dependent on the prior one or the future one, and any sequence that results is purely coincidental. You are just as likely to get a long run of either heads or tails as you are a mixture.

None of what i have written suggests otherwise


"You are just as likely to get a long run of either heads or tails as you are a mixture."

There are however a far greater number of separate series that contain mixtures than contain streaks, so series of mixtures are far more likely than a series of streaks.

E.g 5 tails = 1 in 32
Any combination of 2 Heads or tails and 3 tails or heads = 20/32

Tom, you are right about the number of sequences, but each coin toss is an independent entity, and any sequence created from a succession of coin tosses is purely incidental.

The fact that more sequences exist is actually is not related to the odds a toss being a head or a tail, it does not mean that any sequence is any more likely than any other when the odds of it being heads OR tail is 1in2.

super_realist wrote:

Tom_____ wrote:

super_realist wrote:I would concur that the difference in weight of each side of the coin would be considered irrelevant due to the inertia of the coin movement, but each toss is on it's own is a separate entity, it is not dependent on the prior one or the future one, and any sequence that results is purely coincidental. You are just as likely to get a long run of either heads or tails as you are a mixture.

None of what i have written suggests otherwise


"You are just as likely to get a long run of either heads or tails as you are a mixture."

There are however a far greater number of separate series that contain mixtures than contain streaks, so series of mixtures are far more likely than a series of streaks.

E.g 5 tails = 1 in 32
Any combination of 2 Heads or tails and 3 tails or heads = 20/32

Tom, you are right about the number of sequences, but each coin toss is an independent entity, and any sequence created from a succession of coin tosses is purely incidental.

The fact that more sequences exist is actually is not related to the odds a toss being a head or a tail, it does not mean that any sequence is any more likely than any other when the odds of it being heads OR tail is 1in2.

I am not contesting the odds of a single independent 50/50 event, i don't know why you think i am? All sequences have the same probability as you say, but there are simply MORE sequences available where a mixture of results occur and therefore the occurrence of a mixed sequence is far more likely than than a streaked sequence.

Thats exactly the same reason throwing 7 with two dice is far more likely than throwing 12. (theres six ways to do it vs. one)

It would be possable to forget about probability and statistics if the number 1 seed was matched with the number 4 seed and the number 2 seed with the number 3 seed automatically.

I'm not going to spell it out anymore than this

Imagine H - drawn same half, T- drawn opposite half
Always a 50/50 toss and independent of other throws

32 possible sequences over 5 events, each of these sequences has a 1 in 32 chance:

1. HHHHH

2. HHHHT
3. HHHTH
4. HHTHH
5. HTHHH
6. THHHH

7. HHHTT
8. HHTTH
9. HTTHH
10. TTHHH
11. HHTHT
12. HTHTH
13. THTHH
14. THHHT
15. THHTH
16. HTHHT


17. HHTTT
18. HTHTT
19. HTTHT
20. HTTTH
21. THTTH
22. TTHTH
23. TTTHH
24. THHTT
25. THTHT
26. TTHHT

27. HTTTT
28. THTTT
29. TTHTT
30. TTTHT
31. TTTTH

32. TTTTT

Note that what we got for the Aus open was HHHHH

An even looking result would have been either (two T's and three H's) or (two H's and three T's) - if you look above at combos no.7 - no.26 there are 20 ways this could have happened and only one way the HHHHH can occur. Therefore a fair looking mixture was 20 times more likely to occur than the 5H streak we ended up getting.

hawkeye wrote:It would be possable to forget about probability and statistics if the number 1 seed was matched with the number 4 seed and the number 2 seed with the number 3 seed automatically.

thats true, but then if say the no.1 could always beat the no.4 then the no.4 would be more likely to stay lower ranked. If the No.4 could always beat the No.2, but never gets a chance to play him it would be considered unfair. Thats why we have the random system.

Tom___

Of course if the top 4 remains stable there might be some repeated matches but how often does that occur. The way the seeding is at the moment can also potentially protect players from difficult match ups. For ages I wanted to see a Djokovic Murray match but their seeding prevented it. Admittedly when it did happen it was dissapointing.

Nothings perfect but IMO automatic placements would be fairer. Hasn't the number 1 seed earned the right to face a lower ranked opponant in the semi's?

Hi All - Please don't forget to visit this thread if you haven't do so....I can see a few new posters out there.

https://www.606v2.com/t7357-606-index

hawkeye wrote:Tom___

Of course if the top 4 remains stable there might be some repeated matches but how often does that occur. The way the seeding is at the moment can also potentially protect players from difficult match ups. For ages I wanted to see a Djokovic Murray match but their seeding prevented it. Admittedly when it did happen it was dissapointing.

Nothings perfect but IMO automatic placements would be fairer. Hasn't the number 1 seed earned the right to face a lower ranked opponant in the semi's?

its been on the cards to occur 14 out of the last 19 slams in Fed and Djokos case

Also as i said above automatic placements might falsely benefit some. E.g if one players always loses to another, but never gets to play another player they themselves could beat, because they are always on the other side of the draw, then they don't get a chance to push to finals and move up the rankings.

E.g Jeff, Ralph, Dave, and Josh are all awesome tennis players who always get to semi finals

lets say:-

Ralph can always beat Dave
Dave can always beats Jeff and Josh
Josh can always beats Jeff
Jeff can always beats Ralph and Dave
Josh always beats Ralph.

Josh is number 1, Ralph is number 2, Jeff 4, Dave 3.

Fixed draw in SF 1vs4, 2 vs3

SF Josh beats Jeff
SF Ralph beats Dave

F Josh beats Ralph

This would always happen and the seeds would remain identical

Randomise it, you could have 1 vs 4 and 2 vs 3 as above

or you could have 1 vs. 3 and 2 vs 4:-

SF: Dave beats Josh
SF: Jeff beats ralph

F: Dave beats Jeff

In this scenario Dave has made the final and won, therefore his ranking may go up. the other way Dave is always locked into losing his SF.

Now, obviously this isn't real life, but we do have matchups on tour where one player normally beats another. Its would be unfair to that beaten player not to have the chance to play some one in the draw to potentially improve and move up the rankings

Tenez wrote:Hi All - Please don't forget to visit this thread if you haven't do so....I can see a few new posters out there.

https://www.606v2.com/t7357-606-index

Tenez, not everyone here is from 606.
We are also advertising on twitter and other various means.

FedsFan wrote:

Nore Staat wrote:

FedsFan wrote:... The ideal scenario would be Fed for Wimbledon and Murray for USO. ...

Ideal for whom? Roanic supporters might not think this ideal etc. May the best man win ...

Anyone who thinks Raonic could win Wimbledon or think he will be a tricky opponent for Nadal is clearly deluded. Sorry to offend his fans but lets not lose touch with reality. If he does, good on him and I will be the first to applaud his achievements.

What has delusional thinking got to do with it? You were referring to "ideals", so rather than responding to a straw man it would have been better to address the actual point being raised

Hawkeye, it might sound unfair but the top ranked player can't always face the lower seeds. Any attempt to make draws that way will be chaotic.

[quote="Simple_Analyst"]Hawkeye, it might sound unfair but the top ranked player can't always face the lower seeds. Any attempt to make draws that way will be chaotic.

Tom I don't think anyone is denying that a mixed sequence is more LIKELY than one of 5 straight heads given that there are only two sequences in any possible sequence where it can be all head or all tail, however after the first toss in any sequence there is an equal chance of it being any sequence, straight or mixed until the second coin is tossed. That is to say that every possible sequence has a 1 in 32 chance of occuring.
Probability and likelihood are two different things, and until the second coin is tossed it cannot be commented on.

I just think it is rather convenient that the Federer and Nadal always get put in the other half of the draw eventhough Fed should with the #3 ranking be forced to play Nadal in the semi half of the time. We all understand the basic math. But to me this is real fishy that this is the 5th time in a row Djokovic and Fed have been in the same draw and they have been 2 or 3 everytime (or vice versa). Djokovic is seen as a bigger threat to Nadal, Murray is seen as a bigger threat to Fed, and the tournaments want a Fed/ Nadal final. And murray doesn't get put into Roger's half (has a winning h2h against Roger) and Novak (who Rafa admits is his toughest matchup and beaten him 4 times in a row gets put into the Fed half). When is murray going to be put into Novak's half? Murray could certainly beat him but as the #2 player why does he keep getting #3?

I don't think Murray is seen as a bigger threat to Fed, Socal. They don't want a Fed-Nad semi, they just want a Fed-Nad final. And this is favoring Nadal as it ends up Fed to do the dirty work for him, by either sending Djoko home or sending him exhausted to the final.

super_realist wrote:Tom I don't think anyone is denying that a mixed sequence is more LIKELY than one of 5 straight heads given that there are only two sequences in any possible sequence where it can be all head or all tail, however after the first toss in any sequence there is an equal chance of it being any sequence, straight or mixed until the second coin is tossed. That is to say that every possible sequence has a 1 in 32 chance of occuring.
Probability and likelihood are two different things, and until the second coin is tossed it cannot be commented on.

Of course each sequence has a 1 in 32 chance of occurring, surely we have already established that. Also until the second coin toss there are of course only 2 possible sequence H or T, hence 50/50.

I am not saying that the sequence should be specifically HHTTH or any of the other 20 mixed sequences, only that for a mixed sequence to occur, there are 20 sequences to choose from, so the probability of a mixed sequence is 20/32 = 0.625 = 62.5% (i.e the most likely occurrence). The probability of HHHHH is 1/32 = 0.03125 = 3.1%

over a period of five tosses, the relative likelihood of a mixed sequence compared to a streak of HHHHH is 0.625/0.03125 = 20 times more likely. Hence it is far more probable for any single set of 5 coin tosses.

likelihood is inherently linked to probability as it is commonly used to describe the relative size of two probabilities - i hope i have explained that sufficiently to you above.

The point here is that the whole sequence of 5 is considered as one event, given that we know there are 5 coin tosses and so probabilities are calculated as such. The 50/50 per toss is only relevant in determining the number of possible sequences, being 'n' to the power of 'r' (n^r) where n is the number of things to choose from (2 in this case) and r is the number of events (5 in this case) 2^5 = 32 sequences as above all with equal chance. Instead of tossing a coin multiple times we are effectively having one roll of a 32 sided dice, 20 of which give mixed sequences, only one of which gives the HHHHH streak.