TSB cutting rates again from 3% to 1.5%

Marcus is cutting its basic rate from 1.35% to 1.30% on 10th March. Bonus rates unaffected.

it's a bad decline...

"The odds of any £1 bond number winning any prize will decrease from 24,500/1 to 26,000/1 from the May 2020 draw onwards. Around 173,718 fewer premium bond prizes will be handed out in May, compared with February.

It means, for example, that there will be five £100,000 prizes up for grabs in the May draw, down from six in February. And there will be around 13,448 £100 prizes on offer in May, down from 27,221 in February, NS&I said."

www.theguardian.com/money/2020/feb/17/nsi-announce-interest-rate-reductions-for-25m-customers

That's the size of the prize fund, but a lot of the prize fund is used to pay the small number of large prizes, leaving most people to get nothing at all. The amount you can expect to actually receive is much less than 1.3% of the amount you invest -- MoneySavingExpert goes into detail on this: www.moneysavingexpert.com/savings/premium-bonds/

That's my belief too. 
As far as I remember, £2 fee on 1|2|3 was there at the beginning, later increased to £5.   I've opened 2 accounts as soon the product was launched, it was great - £100 p/m for a safe storage.  When they've dropped the rate to 1.5% I reduced to one account.  Now I'm planning to ditch Santander all together at the beginning of March.  No point having it at 1%. My bills are small, so I only have about £2.50 reimbursed. This will be covered if I carry on with monthly saver (next available issue is 2%), but I'll still be left with 1% profit.  I have 1.5% ISA with Santander, but that runs out in March... there's no incentive for me to have any accounts with this bank. There're plenty of easy access accounts that pay better interest.

There are few good products for those with children under 16 on FSCS market:
Nationwide "Future Saver 3" - 3% on 5k.
Halifax "Kids' Saver" - 2% on 5k. + you can open 4.5% "Kids' monthly saver" (only £100 p/m allowance, but every little helps). 
Few more building societies offer children's accounts at decent rates... they come and go and some are only available in branch.

Not really. 5% of the prize fund goes into the top prizes (£5k+, including the two £1M prizes), another 5% into the middle band (£500 - £1k) and 90% goes into the lower value (£25-£100), almost all of that into the £25 wins. www.nsandi.com/prize-checker 

You could legitimately model this as being a 1.3 * 0.9 = 1.17% return that you would reasonably expect to see if you have a reasonable number of bonds (at least £10k, say), with the tiny chance of a big prize as a bonus on top.

And with your second para I think you have finally got the point!

The thing that Lottery Tickets and Premium Bonds have in common is that what you're really buying is a Licence To Dream: the opportunity to fantasise, for a moment, about what you'd do with all that dosh. The odds of it actually coming off are pretty irrelevant - once they get over, say, 1:1,000,000 then it really stops mattering.  In this sense the £100 of PBs is a much better bet than one Lottery Ticket (whatever the maths might say) because you have twelve draws in the year instead of one.

They also both operate in the same way as insurance policies - you expect to lose money on those, too, but every sensible person has some. Insurance policies pool risk: lotteries pool reward. 

Anyhoo, the point of my first post stands - the cut in rates has been hugely overstated by sensationalist reporting (in the Guardian of all places!). The overall payout at 1.3% is at the top end of current instant cash rates (tax free, risk free), and holders are choosing to get a bit less than that in exchange for said Licence To Dream.

Hardly worth it when you are only allowed to save £100 for 24 months at 1%.