Using the detailed information provided in the links, please answer the questions below:
Which scratchcard offers the "best chance to win" a prize of £25?
Does the cost of the scratchcard make any difference and if so why? The £250,000 Birthday scratchcard costs £2 and the Bingo Doubler White scratchcard costs £3.
What do you consider the phrase "best chance to win" to mean in the context of purchasing a scratchcard.
Links:
£250,000 Birthday scratchcard game procedures
Bingo Doubler White scratchcard game procedures
Update - My thoughts:
On Bingo Doubler White, the odds of winning a prize of £25 could either be 1 in 359 or 1 in 860. The odds of winning on £250,000 Birthday are detailed as 1 in 450 or 1 in 451. The different ways of winning a prize are not comparable with the odds of winning a prize.
According to the relevant game procedures I would need to purchase either 450 or 451 of £250,000 Birthday to statistically win one prize of £25. That appears to be a worse chance than that afforded by Bingo Doubler White as I would only need to purchase 359 scratchcards to statistically win one prize of £25.
Is that right and do you have any thoughts about my other points listed above?
Thank you for reading.
Actually, it would be very laborious to reproduce the calculations printed on the descriptions, and I'm not sure there is enough information to do so. I, for one, don't understand the description well enough to undertake such a calculation (which I would have to do by writing a computer program, if I were to have any confidence in the result.)
This is not necessary, however, if you are prepared to trust the printed information, as I must say I would be. The relevant information is printed at the end, under the caption, "Prize Value in the Game." For the Big Doubler White, it says, "The total value of Prizes in the print run of Scratchcards for the Game represents $66.86\%$ of the total face value of Scratchcards." This means you can expect to lose $33.14\%$ of the money you spend on this game.
For the £$250,000$ Birthday game, the corresponding number is $67.96\%$ so you lose $32.04\%$ on average. There is very little to choose between them, but the Birthday game is a slightly better deal.
EDIT
In answer to the OP's comment. You can add up all the tickets providing the £$25$ prize in the table on the fourth page, and divide by the number of tickets at the top of the table. This gives the probability of winning a £$25$ prize, and perhaps other prizes. It's not particularly meaningful to compare these two probabilities, because one pays different prices for the tickets. You might try to adjust by multiplying the probability in the £$2$ game by 1.5, but this ignores the fact that the £$25$ prize is often awarded in combination with different prizes.
In short, I don't see a meaningful way to single out a particular prize in this game, other than perhaps the grand prize.