Absurd fares pricing

[hairyhandedfool]

....Obviously all the numbers are completely arbitrary and it's not to say that you shouldn't pay more than £40 Advance for a £50 walk-up ticket,....

With all due respect, it's all just cost vs risk.

....and there will be scenarios where Advances make more sense at higher prices,....

Which makes the point nicely.

....and scenarios where they make less sense, it does however show the process, and illustrates hopefully that £2 off a £10 ticket is more significant than £2 off a £100 ticket....

If the chances I won't make the train are high, spending more than £10 on an Advance could be considered 'insane'. If the chance of not getting the train is small then why spend the extra? Does it really matter what the difference actually is?

....Well no, the point is that any of us who has done a weekly trip for a long period can probably point to problems in that time, so the £2 saving is not accurate, it's like saying that if you cover 34 numbers on the roulette wheel with £1 then you win £2 each time, well yes you do, but when your numbers don't come up, you lose £34, and in the long run if you continued playing roulette, it is a mathematical certainty that you will lose all your money....

I have, in the past, travelled regularly on the same trains five days a week for more than five years, the number of times I missed the train, or couldn't travel, could probably be counted on one hand. If I save more during my travels than any extra spend I make because of missed trains, is the risk not justified by the saving?

My understanding of Roulette is somewhat limited, but I believe there are 36 numbers plus a 0 and maybe a 00, depending which version of the game you play. Thus it would cost £36 to play every number. Every spin has a 1 in 37/38 chance of walking away with nothing and a 36 in 37/38 chance of walking away with £36. I couldn't 'win £2'. However, the possibility remains that I could spin the wheel 1,000 times and not lose once, it is just a relatively small chance.

....Indeed. However these fares do not appear to be in the customer's interests overall, given for instance that the return was only a small % more than the Advance,...

In your opinion. Something which makes the journey cheaper could be in many people's interest.

....and we have got to assume that a high proportion of people buying tickets are not experts and do not understand the rules, and therefore they will work out worse off, net, for the sake of a small saving.

It would be an assumption, but not necessarily a correct one. If we say it's a correct assumption, they would only work out worse off if they failed to make the train. If they made it they would be better off.

 

[orpine]

If the chances I won't make the train are high, spending more than £10 on an Advance could be considered 'insane'. If the chance of not getting the train is small then why spend the extra? Does it really matter what the difference actually is?

Yes. You're failing to do the risk analysis.
Using your logic you'll take an advance at £99.99 instead of an anytime at £100. No-one sane would do that if aware of both tickets and their restrictions.
Obviously a price difference of 0.01% isn't enough to justify the extreme restrictions of an Advance. BUt what price is? That differs per person. You may be happy to make a 1% saving, most people wouldn't because as soil's analysis shows, it's a false economy - in the long term you'll lose out.
Personally I'd hope for at least a 10% saving; ideally a lot more.

I have, in the past, travelled regularly on the same trains five days a week for more than five years, the number of times I missed the train, or couldn't travel, could probably be counted on one hand. If I save more during my travels than any extra spend I make because of missed trains, is the risk not justified by the saving?

Yes, but these numbers vary for different people. Some people are rubbish at catching trains. Others have circumstances that may mean they're more likely to miss a train (using the Tube for instance).

However, the possibility remains that I could spin the wheel 1,000 times and not lose once, it is just a relatively small chance.

Correct. A simpler example - you can flip a coin 10 times in a row to be on the same side, but it'll take about a full day of coin flipping to manage it.

 

[OLJR]

Well I don't think many people would feel that way, I do have to wonder how many journeys you've actually made on Advance tickets. You do realise that if you were to buy a London Terminals to wherever Advance ticket and you are delayed on the tube from Pimlico, you're not covered, don't you?

Final answer?

This year I have bought 20 Advance singles, 16 on East Coast, 2 on Virgin and 2 on East Midlands. I know that I am not the most frequent of rail travellers!

It takes just under 30 minutes to get from my front door to platform 0 at King's Cross if the tube is working as normal. But I always leave about 50-60 minutes ahead of travel to allow for delays.

Boarding is normally called about 15 minutes ahead of departure so if all goes well I have a not unreasonable 5-15 minutes of people watching at King's Cross. If all does not go well I should have time to exit the tube system somewhere on the Victoria line and take a cab.

Final answer!

 

[yorkie]

OK, so if you were to take the 1903 King's Cross to Peterborough, you'd leave Pimlico between 1803-1813?

In that case, if all goes well, you'd be in time for the 1830 departure. But for the sake of £2.50 you'd then be wasting 33 mins of your time (say you got a 1st anytime advance for £64.50, with a £2.50 difference as in the original example)

But if things do not go well, it is possible for delays on the tube to mean you miss the 1903, and then you would have to buy a whole new £67 ticket. There's no way you could forsee that.

Does that really make sense?

Only if your time is valued at under £5 an hour and there is absolutely no chance of missing that train!

 

[OLJR]

you'd then be wasting 33 mins of your time

I do not mind spending 30 minutes waiting at King's Cross. In fact I quite enjoy the chance to do some people watching and switch off from electronic devices and work projects.

As I am self-employed I find that unless I am on Client site I do a lot of my work late in the night rather than the day. I also often spend 'dead' time planning my next proposal or report in my head. Accordingly I do not consider the time waiting on the concourse wasted.



I think that we both have different appetites for risk! Or maybe I have not travelled by rail enough to get worried yet!

 

[yorkie]

Perhaps a bit of both!

 

[John @ home]

If all does not go well I should have time to exit the tube system somewhere on the Victoria line and take a cab.

My experience is that, when the Victoria line is suspended, a Victoria - Kings X cab struggles to reach walking pace.

 

[hairyhandedfool]

Yes. You're failing to do the risk analysis.
Using your logic you'll take an advance at £99.99 instead of an anytime at £100. No-one sane would do that if aware of both tickets and their restrictions.
Obviously a price difference of 0.01% isn't enough to justify the extreme restrictions of an Advance. BUt what price is? That differs per person. You may be happy to make a 1% saving, most people wouldn't because as soil's analysis shows, it's a false economy - in the long term you'll lose out.
Personally I'd hope for at least a 10% saving; ideally a lot more....

Am I? Sure I might have missed the odd train here and there, but if I really did manage five missed trains over five years (I honestly couldn't give you a definitive figure, but in any case let's say 220 return trips a year as a very approximate figure), then the risk is minimal and so the value of that risk is very low. If I say the value of those return journeys was £50 and I paid £48 on the Advance tickets for each return journey (as an average if you prefer), I might have spent out £50 extra one day, but saved £438 over all the rest, so I haven't really lost out in the long term, have I?

Okay, let's ignore my experiences for now, and those of OLJR too, and let's say I analyze the chances of me missing the train, things like the time it takes to get to the station, the time I have to make that journey, the number of Pelican and Toucan crossings I encounter on the way, the chance of me being delayed in some way and so on, and lets assume that the percentage chance of me missing each train is 40%, 4 in 10. Let's say I justify that risk as 1% of the ticket price per percentage point of risk. I'd be looking for Advance ticket £20 below our £50 walk up price in order to justify it or 'break even'.

Let's assume I manage to get Advance tickets at £25 for ten trips, below the target figure, now I have breathing room, but that 40% chance is on each trip so it is entirely possible to miss every single one and if that happens then I am £250 out of pocket. On the other hand I might make all of them and be £250 better off.

If it is the former I probably won't ever buy an Advance again, even if the next ten trips are made on time. For the latter I am more likely to risk the Advance fares because I didn't have a problem. So if I make ten more trips, and the Advance fares are £45, am I insane for risking a £50 saving? or am I insane for overspending by £50?

....Yes, but these numbers vary for different people. Some people are rubbish at catching trains. Others have circumstances that may mean they're more likely to miss a train (using the Tube for instance)....

Exactly, but if OLJR, or myself, chooses to risk a small saving because we make 99.9% of the trains, it doesn't make the fares pointless or us 'insane', we have experience to work from, rather than a seemingly random set of figures.

 

[soil]

Well no, the point is that any of us who has done a weekly trip for a long period can probably point to problems in that time, so the £2 saving is not accurate, it's like saying that if you cover 34 numbers on the roulette wheel with £1 then you win £2 each time, well yes you do, but when your numbers don't come up, you lose £34, and in the long run if you continued playing roulette, it is a mathematical certainty that you will lose all your money.

My understanding of Roulette is somewhat limited, but I believe there are 36 numbers plus a 0 and maybe a 00, depending which version of the game you play. Thus it would cost £36 to play every number. Every spin has a 1 in 37/38 chance of walking away with nothing and a 36 in 37/38 chance of walking away with £36. I couldn't 'win £2'. However, the possibility remains that I could spin the wheel 1,000 times and not lose once, it is just a relatively small chance.

I've done quite a bit of work on probability.

In Europe there is typically one zero on a roulette rule, in the US two, plus the numbers 1-36 inclusive, so 37 or 38 possibilities

For a £/$1 bet on a single number, in either country, if the number comes up then you get back £/$36 (35 to 1 odds, sometimes expressed as 36 for 1)

As per my example, if you bet £1 on numbers 1-34, then your stake would be £34, and you would get £36, which is indeed winning £2. If 35, 36, or 0 come up, then you lose £34.

Your example would never take place in reality: if you cover numbers one to thirty six, then you cannot win, you can only lose - your stake is £36 and you win £36 on each of 1-36, so the net win is £0 if 1-36 come up (a 36/37 or 36/38 probability), and the net loss is £36 if zero (or double zero) comes (a 1/37 or 2/38 probability).

The chance of spinning the wheel 1,000 times and not coming up with any zeroes is in fact zero. Well, to be more accurate it is 0.00000000000126, which is sufficiently small that it would be normally be displayed as zero. On a double zero wheel, it is even less likely, 0.00000000000000000000000330.

Just to get some idea of how unlikely that is, Sally Clark was convicted of murdering her two infant children on the basis of evidence from Sir Roy Meadow, who claimed, quite wrongly, that the chance of two cot deaths in the same family was 0.000000014; this number (far more likely than 1000 roulette spins) was deemed sufficiently small to send Mrs. Clark to prison, and in normal circumstances that would be more than reasonable - the problem was that the probability given by Sir Roy was a load of b***locks, because he failed, so to speak, Statistics 101.

Anyway, it IS possible to get no zero 1000 times in a row, but if that happened, we'd conclude that the wheel is broken and pull it from service (and in reality in any casino, they'd do it much earlier than that).

Just as you will get a zero (the expected numbers of spins is 37), so too will you eventually miss a train (will vary from individual to individual: me - very frequently, someone else - rather seldom).

 

[OLJR]

The chance of spinning the wheel 1,000 times and not coming up with any zeroes is in fact zero

Quite so. An always-win strategy with roulette is to bet red every time and double up on your stake for as long as red does not appear. Since the return is 2:1 as long as you do not run out of money you are always guaranteed to win one over your cumulative bets when red finally appears.

Red will surely come up sooner or later. The question is, do you run out of money before it appears?

At ten blacks or zeroes in a row you have spent 1,023, at 20 in a row you have spent 1,048,875!

 

[hairyhandedfool]

.....As per my example, if you bet £1 on numbers 1-34, then your stake would be £34, and you would get £36, which is indeed winning £2. If 35, 36, or 0 come up, then you lose £34.....

Oh, I see what you are saying, I misunderstood that part.

.....Just as you will get a zero (the expected numbers of spins is 37), so too will you eventually miss a train (will vary from individual to individual: me - very frequently, someone else - rather seldom).

So the question is not "Will I miss a train?" but actually "When will I miss a train?".

If probability tells us that a loss (and not just a 0) will occur 3 times in 37 spins, then can we get 17 spins before we spin a loss? If we can then the loss is negated by the £34 already won, we are back to the start but we haven't actually lost anything. Equally, it does't have to be 17 spins before we 'lose' if we have sufficient funds on us, it just has to be 1 'loss' in every 18 spins.

.....The chance of spinning the wheel 1,000 times and not coming up with any zeroes is in fact zero. Well, to be more accurate it is 0.00000000000126, which is sufficiently small that it would be normally be displayed as zero. On a double zero wheel, it is even less likely, 0.00000000000000000000000330....

I realise the the chances were small and I noted that, but if the chances of a 0 not showing up are not zero, but are considered to be zero, because they are so small, could the chances of missing a train be considered zero, if the chances are that small?

If the chances are that small, does it matter if the saving is £2 or £20?

.....Just to get some idea of how unlikely that is, Sally Clark was convicted of murdering her two infant children on the basis of evidence from Sir Roy Meadow, who claimed, quite wrongly, that the chance of two cot deaths in the same family was 0.000000014; this number (far more likely than 1000 roulette spins) was deemed sufficiently small to send Mrs. Clark to prison, and in normal circumstances that would be more than reasonable - the problem was that the probability given by Sir Roy was a load of b***locks, because he failed, so to speak, Statistics 101....

I just used it as an example of a very small chance being possible, rather than likely, I guess it works both ways.

Just on a statistics theme (I am digressing but I think it's interesting), a BBC programme broadcast in 2003 called The Day Britain Stopped noted that NATS (National Air Traffic Services) commissioned a report in 1993 that stated that there was a chance that a 'missed approach collision' would occur at Heathrow every twenty years. Apparently the report was not endorsed as Heathrow (at that point) had 'been operating for more than fifty years without a single collision'. I have no idea what those odds were, but they'd have to be pretty small.

.....Anyway, it IS possible to get no zero 1000 times in a row, but if that happened, we'd conclude that the wheel is broken and pull it from service (and in reality in any casino, they'd do it much earlier than that)....

Tbf 'Luck' with missed trains isn't as loaded as Roulette, so if you catch the train 100% of the time for 100 trips, the TOC aren't going to try to change your odds by hijacking a bus and running you over on the way to the station or perform a rain dance in the hope that you get struck by lightning, or whatever, and they won't run a train early just to catch you out.

 

[soil]

Quite so. An always-win strategy with roulette is to bet red every time and double up on your stake for as long as red does not appear. Since the return is 2:1 as long as you do not run out of money you are always guaranteed to win one over your cumulative bets when red finally appears.

Red will surely come up sooner or later. The question is, do you run out of money before it appears?

At ten blacks or zeroes in a row you have spent 1,023, at 20 in a row you have spent 1,048,875!

This is called the Martingale, and it is very bad indeed, the problem being that you can throw very large sums of money after a small loss.
--- old post above --- --- new post below ---

If probability tells us that a loss (and not just a 0) will occur 3 times in 37 spins, then can we get 17 spins before we spin a loss? If we can then the loss is negated by the £34 already won, we are back to the start but we haven't actually lost anything. Equally, it does't have to be 17 spins before we 'lose' if we have sufficient funds on us, it just has to be 1 'loss' in every 18 spins.

Well yes, but the point is that mathematics determines that on average you will lose. The chance of getting to 17 spins without losing is (34/37)^17 = 0.24. Obviously we are likely to come out a loser, the basic problem being that there are 37 numbers but only £36 paid for a winner. If £37 was paid, then it would be a wash - if you are risk-seeking then it's fun, if risk-adverse than no reason to play, and if £38 was paid for a winner (on a single zero wheel) then even the risk-adverse should play, subject to sensible bankroll management - e.g., if you are poor you might risk 10p/spin, if wealthy you might risk £1000/spin.

I realise the the chances were small and I noted that, but if the chances of a 0 not showing up are not zero, but are considered to be zero, because they are so small, could the chances of missing a train be considered zero, if the chances are that small?

Well the point is not so much that the chance of missing a train can be considered zero, but that the cumulative chance of ever missing a train is in fact 100%.

Just on a statistics theme (I am digressing but I think it's interesting), a BBC programme broadcast in 2003 called The Day Britain Stopped noted that NATS (National Air Traffic Services) commissioned a report in 1993 that stated that there was a chance that a 'missed approach collision' would occur at Heathrow every twenty years. Apparently the report was not endorsed as Heathrow (at that point) had 'been operating for more than fifty years without a single collision'. I have no idea what those odds were, but they'd have to be pretty small.

I guess this is the sort of Concorde 'safest to most dangerous plane with one crash' kind of model.

Tbf 'Luck' with missed trains isn't as loaded as Roulette, so if you catch the train 100% of the time for 100 trips, the TOC aren't going to try to change your odds by hijacking a bus and running you over on the way to the station or perform a rain dance in the hope that you get struck by lightning, or whatever, and they won't run a train early just to catch you out.

Yes, if you catch the train every time then that's probably true.

Personally speaking I often don't even check the timetable, since trains are so frequent here, so the concept for me of catching or missing a train is absent. If you live on the Heart of Wales line or something that you might well have a different perspective.