the OP doesnt have access to a friend with $2m..
he is just trying to up his rep so he can go on a money grab by asking for bitcoin off people.
(i presume he wants to use this topic to explan starting a server farm and later offer (vapour) cloud mining contracts to people)

many have noted his failed attempts in the past.

but the short answer to everyone speculating about mining,
unless you can buy a rig at 25% or less than the retail prices of a rig, it wont matter if you have free electric or not.
the difference between 20cnt/kwh and 5cent/kwh is only about $700 per rig over 6 months.
bitmain S9=$1600
electric in UK for 6 months= $900
electric in US for 6 months=$450
electric in asia for 6 months= $225

however if your paying retail price($1600) for a rig your already 5x worse off compared to the mining competitors who actually make their own rigs
bitmain/antpool make the rig for under $400.. in actual fact for every $1600 rig they sell to people, bitmain create atleast 4 rigs and hand out 1 to the customer and happily keep atleast 3 for themselves(for free essentially).

so even if you can get free electric. your still $1200-$1400 behind antpool before you even started.

trying to get your $1600(+free electric) back is not possible, based on difficulty and competitor hash power adjustments that slowing decline your rewards
trying to get your $1800(+asian electric) back is not possible, based on difficulty and competitor hash power adjustments that slowing decline your rewards
trying to get your $2000(+US electric) back is not possible, based on difficulty and competitor hash power adjustments that slowing decline your rewards
trying to get your $2500(+UK electric) back is not possible, based on difficulty and competitor hash power adjustments that slowing decline your rewards

non ASIC manufacturing people will not break even, the hope they have is just to mine bitcoin. not to pay off costs. but to hoard and hope one day the fiat price value doubles, triples and quadruples to then break even on the fiat price.

in short
if your spending bitcoin in hopes of mining more bitcoin, forget it.
if your spending fiat, to mine bitcoin in hopes waiting for bitcoin fiat value to give you more fiat, its possible. but you might aswell just buy bitcoin and hoard

wrong on so many levels

payment channels (lightening network) are multisigs.

say you want to spend funds regularly with a merchant.
you set up a multisig with the merchant, by both sides giving a public key to create a multisig address. they doublecheck the multisig is correct and matches to the same 3Bl4ahBlahBlahBlahBlah address before funding it.

both sides put funds in and lock them for X blocks (onchain)
onchain shows 2 deposits
eg person 1btc, merchant 1btc making so both sides have collateral and incentive to not mess around, because they both have something to lose

now without broadcasting to the network(offchain) person and merchant agree on who owes what amount of the funds in the multisig to each other and both sign the transaction (but dont transmit it onchain). it just sits in each others individual mempool, not random nodes.
making it a private transaction at this point
day 0 both parties agree merchant gets 0.1btc person gets 0.1btc, both sign
EG

the first day (offchain) both parties agree that when person buys a coffee merchant gets 0.11 person gets 0.09, both sign
the next day (offchain) both parties agree that when person buys another coffee merchant 0.12 person gets 0.08, both sign
the next day (offchain) both parties agree that when person buys another coffee merchant 0.13 person gets 0.07, both sign
and so on and so on.. untill the locktime has expired and both sides decide its time to settle the transaction by closing the channel and broadcast the most upto date transaction ONCHAIN.

carlton. please research harder

payment channels can be useful. but we should not rely on them for every transaction. just the ones where you would regularly spend and happy to and X funds over upfront so you dont have 10mins+ at the cashiers aisle.
signing the transaction of who owes what is a split second activity. thus allowing fast "spending"
the reasons we should not rely on merchants holding all the coin is that places like walmart and starbucks could become the new banks, by being the middleman required to authorise payments with people begging those middle men permission(to close channel) to pull out money to spend elsewhere..

we still need onchain scaling too, otherwise bitcoin becomes middlemen controlled by hub hoarding all the coins and we needing their signature to move our money

0.0002 is $0.12 at this moment
which is the equivalent to over 1hour minimum wage for atleast half a dozen countries.

knowing people complain about visa/mastercards 2% fee, means that people are kind of happy with 1% fee(preferably less). thus spending anything below $12 is treated as having more than a 1% fee, which makes bitcoin not a good/useful tool for transmitting value, where people actually wants to buy things for less than $12

in short trying to buy things up to a value of 100 hours minimum wage in a number of countries can be seen as expensive to use bitcoin in developing countries

but developed countries treat this with ignorance by saying they dont want people making small payments, thus making things that may be 1-100 hours of minimum wage in developing countries, be treated as annoying spam by developed countries.

its the same mindset of a richguy in a suit thinking he has divine right to not wait in a shopping queue, purely because his $200 bottle of champagne means more to him then a poor mother counting out a handful of change to buy food for her starving child, and has the mindset to argue with the the shop to enforce a $100 minimum spend to sort out the riffraff/underclass so he can buy champagne without waiting. rather than suggest the shop opens up another cashiers aisle

one solution is supposed to be, when bitcoin fiat value goes up, the fee goes down (fee used to cost a tenth of an american cent, now 12cent) so that solution has gone..
another solution is supposed to be, to increase capacity over many years (20-30+) where instead of having a block with 2500 tx's for 0.0002individual fee, capacity grows so that 5000 tx blocks have a 0.0001 individual tx fee (which totals the same 'income bonus' for pools so no loss)

after all pools main income is from rewards, not fee's and the flip where fee's become more important and rewards become less important wont occur for atleast a predicted 20-30 years, and fee's dont become the sole income stream for well over 120 years, so forcing fee wars right now is not 'needed' by pools

in short, delaying capacity growth, forcing a fee war are not good for bitcoin. it does not help users and does not help bitcoin as a whole
slowly bitcoin has/is reduced in its utility and many bitcoiners are stupidly happy for this to continue while they twist bitcoin out of the open currency for the world to use without borders and restrictions, and into a more centralized reserve currency for altcoiners to hop in and out of.

pwc:
segwit, to blind old nodes
no witness mode to not even verify data because they dont ask for signatures
pruned to not have copies of historic data to help newbies start up.

in short segwit code results in LESS fully validating nodes.

have a nice day

thats like saying R3 organisation is not a bank..(because its just an organization)
PwC is just an organisation of partners.. look at the partners of Pwc, just like the partners of R3

R3 and PwC are the same thing.. banker money used to sway programmers to do certain things to get what bankers want. and programmers doing it to release a second tranche of investment by achieving what bankers want.

i look forward to seeing greg and adam get too excited about their next tranche of investment release, as their egos are too big to hide such a milestone. and then they have to start admitting what was required and needed to be achieved to get that tranche of funds

the hypocrisy is amazing when it comes to carlton trying to defend core while attacking anything not core.
carlton, hows the prep work going to REKT luke JR before he releases real capacity buffer increase version of core?

look at carlton with all the propaganda.

but where is carlton when it comes to the bankers investment of $55m that went to adam back and greg maxwell..
oops i struck a nerve.. i mentioned a banker relationship with the ones trying to slow down bitcoin capacity growth..

now i expect more trolling from him not talking about cores funding.. instead of admitting even his beloved chums have been bought out
now i expect more 3 shell game of "everyone look to the left while the bankers attack on the right" to pretend core are innocent and no one should investigate or judge the funding of holy religious order of core control.

in simple laymans

nodes have a mempool.
when they receive or create a new tx, they put it into their mempool and send it out.

when a node sends a TX to someone else, who sends it to someone else, who sends it to someone else, and so on until one of those people have a connection to any of the original nodes, it doesnt cause the original node to automatically re-transmit the same transaction simply because it received it by someone else.. other wise it would trigger a endless loop.

they notice its already in the mempool and just leave it.

in short if the transaction is not already in the mempool its sent out. if it is in the mempool(already sent) its not re-sent out

adam james cornwell linked via companies house details is actually is only 24yo and drives a Skoda.
https://beta.companieshouse.gov.uk/officers/Ibew_mtbD8dKCPmTJza1EHQti4k/appointments
date of birth: 1992

anyway im still laughing at the mobile massage masturbation service the contact telephone number offers

would you kindly realise that many people have done better due diligence to have found the name Mr. Adam James cornwell to see there is a connection

would you kindly refrain from asking people to search your lame insecure website for some free 'clickbait' to get better alexa stats.

im sorry to tell you this but you may have lost out the money you spent this week setting up your scheme.
maybe time you stop with the money grab. and instead get a real job

ill rather call lloyds of london and inform them about you.
have a nice day

PS. i see TX3 is only active for 4 days. i see your pretending it has been active since 2011 (TX MULTIPLEX LIMITED) and i see the £1 earnings of said dormant company.

as for your telephone number. it routes to a mobile phone.
as for your business address. its a virtual office and mail redirection service

meaning. no way to slap you with a wet fish, because all you done was spend maybe £200 to buy up dormant accounts in another persons name.

even your website is patchy and insecure..
i see so many flaws that you are obviously not even trying hard

contact tx3
020 3239 6188

AKA The Mobile Masseuse

need i say more

lauda
you wrote a reply that may have actually helped answer the OP question, kinda respect that your now researching things, but even you have to admit its not a complete answer.. because predictions* cannot be guaranteed when there is a bit of randomness involved.
but atleast you provided an answer
*it lacks all the factors of bitcoin to be termed a reliable probability.

carlton
troll on.. none of your replies helped the OP in anyway. but its funny how you follow lauda around backing each other up.
seems many of your replies on many topics never help the topic and are just trolls. but goodluck in life.

OP
when using predictions its best to get multiple answers that can either back each other up a good answer or dismiss a certain wrong answer.
that way you get a broader opinion and 'guess' of the chances blocks will get solved more often than not.

EG
if you see hashrate drop.. expect the stats from the links provided by others, to shift over to a higher percentage after 10minutes
if you see hashrate rise.. expect the stats from the links provided by others, to shift over to a higher percentage under 10minutes
as it would give you a second opinion to how reliable the maths may be

lets put it simply..
imagine you have got data of 1008 blocks and the majority of them were over 10 minutes..
because things like the difficulty went up so high prior to the 1008 blocks and hashrate dropped
i would not say that there is a probability that the remaining 1008 blocks will be under 10 minutes.

because the difficulty and hashrate have not moved in favor of faster blocks and so all 2016 blocks will be majority over 10 minutes.
unless the hashrate changes drastically or until the difficulty dropped to allow the next fortnight of blocks to be under 10minutes to counter the previous fortnight..

the network doesnt change difficulty hourly or daily to keep the average at 10 minutes.. so there is not much 'probability' within an hour or within the 2 week period. but you could 'probably' (if you factor in enough variables) predict that the following 2 weeks will be faster, due to previous 2 weeks being slower.

its not a simple if 2 blocks are under 10 minutes, then theres 2 blocks over 10 minutes in the same hour
its based on an average over a LONG PERIOD(fortnight)

if your looking for more short term predictions (educated guesses) there are other factors involved
like hashrate,
like spam/dodgy transactions/blocks made to force orphans/delays
like starting a new block attempt before auditing last block ('empty blocks')
which would all need to be factored in along side the time ratio before the last difficulty change, for even a chance to get a somewhat reliable 'probability'

anyway
imagine you have got data of 1008 blocks and the majority of them were over 10 minutes..
if pools decide to continue to cut the hashrate down, blocks will continue to take longer..
if pools decide to ramp up hashrate you can predict that its possible to see more blocks under 10 minutes. but still not probable.

because of other factors mentioned

so unless you can mathematically factor all of that in.. it wont be a probability, but more of just a possibility (guess/prediction)
others say there is a branch of maths that can make probabilities.. (mainly semi accurate from one difficulty adjustment to the next)
short term maths calculations can change faster then you can type it in (due to the other factors)

lol im guessing the authorities are gonna be closely watching those that reply.

kind of like the 1980's lottery 'sting'
authorities want to catch certain people. so pretend they won a car/boat/lottery and need to go to an office to get their prize
then just wait for the vermin to happily walk into the cage

if your starting an exchange with a team of less than 30 people. then expect issues and expect it not to run well.

this is because if you split the day up into 3 shifts of 8 hours work over 7 day. you would have 10 people working at any one time on 56 hour contracts each.

which usually doesnt work well because some people dont want to work weekends. so already you will need more relief support for weekends

anyway the daily tasks needed are

things like a decision maker (manager) who needs to over see all the staff and deal with issues outside of individual employees control.

you need finance trained people to promptly handle deposits/withdrawals inline with policies (usually regs)
you need someone who can handle chargebacks and wire reversals(scam attempts/ basic bank processing/account management)
you need network admin monitoring for issues and/or hackers
you need customer support

and then theres the staff not required to work around the clock, like advertising, graphic design, PR, legal, etc
along with the guys that can understand and specialise in the large investments and behind the scenes business VC stuff.

so if you think you can run a long term legit and sustainable exchange with less than 30 employee's then you are skimping (being light handed/running a skeleton crew) somewhere, which will negatively affect business at some point

the network only adjusts itself once every 2 weeks..

the relevance of 2 blocks solved in 10 minutes does not affect the speed of the next couple of blocks..
however hashrate, orphans and starting a new attempt before auditing the previous block has more affects than anything

because the average is 10 minutes.. obviously its a very low chance of being exactly 10minutes 0 seconds..

however lets start with basic maths/logic/common sense.
because its an average there is a automatic assumption that 50% chance of being less than 10 minutes, 50% chance of being more then 10 minutes. all because of common sense that an average is an average

now to go beyond 50:50 average
then you have to add in extra data such as how much the hashrate has risen when you want to predict the next 'chance' compared to the hash rate when the difficulty last changed ,

usually hashrate is on an upward rise, usually difficulty is also in an upward rise which would lead to the chances of a block being solved in under 10 minutes to be much higher then the expectant 50:50
though this is not always the case, sometimes hashrates drop and difficulty drops so its not always a higher chance of faster block production

next you have to look at who is making the blocks. are they fully auditing the blocks received before starting a new attempt or are they starting a new attempt(empty block) before auditing a blocks received.

in short

if you see pools making empty blocks and the hashrate is alot higher then when the difficulty changed.. expect fast blocks production
if you see pools are not making empty blocks and the hashrate is lower then when the difficulty changed.. expect slower blocks production

but with all predictions.. its more guess than science

most localbitcoiners do not do enough trade to meet the thresholds to require a licence.
most localbitcoiners do not make enough profit from the spread to cover the costs of having a licence

but here is the thing. if they are licensed, they will have registration numbers and documents. so ask them for their MSB number and their data protection policy. they cannot refuse it. but if not presenting it, they are obviously not an MSB

secondly some localbitcoiners dont actually need the documents, but ask anyway to scare off scammers trying to do chargeback/wire reversal scams.

thirdly if you are being asked for such documents you might aswell just use a well known more legit service that supplies registration details and an office address, rather than a complete stranger who wants your life story.

after all that stranger might then ID fraud you by scamming someone else but pretending to be you because he now has your info.

in short.
if they are asking for your life history, dont be afraid to ask for their business details

"Those users won't even see the rule-breaking chain no matter how long it is. "
because they blacklist the nodes transmitting the changed rule.. to not even get that changed rule block

without blacklisting rule changed nodes. then "those users" will see the rule changed block but will orphan off the rule changed blocks, because that is how the consensus mechanism works. if a block is seen that doesnt match the rules, its orphaned.

separately if a node blacklists rule changed nodes.. then they wont even talk to each other to use the orphan consensus mechanism.. meaning that both sides are not orphaning each other and instead working as independent chains.

again it requires blacklisting opposing nodes to avoid the consensus mechanism to keep a minority chain alive. other wise orphaning will take care of the "battle" in a thunderdome scenario(2 enter 1 leave). which is exactly how the consensus mechanism works.
its been working every day, an average of 2 blocks a day occur due to them not fitting the rules of the majority

put it this way. if ethereum just done a roll back.. the 'hacked' ether transactions would have got orphaned and everyone would make new blocks ontop of the backdated chain

but instead vatelik actually added a bit more code to intentionally black list nodes against each other to cause a split (controversial fork)

that oppose dao fork. is the flag to cause an intentional split by bypassing the standard orphaning mechanism by not letting the nodes talk to each other to come to a consensus.

so ethereum was an intentional split. rather then changing the rules for everyone to head in a single direction and let orphans take care of the minorty.