What's the difference between doubling A2 and A3 compared to doubling A4 and A5?

You're supposed to double A2 and A3 against a dealer 5 or 6, and you're supposed to double A4 and A5 against a dealer 4,5, or 6. Why don't you double A2 and A3 against a dealer 4? It seems to me that A2, A3, A4, and A5 are basically the same hand. They all have the same number of cards that make totals of 17-21. What is the difference?

They are not the same hands, although they are very similar in nature on a "continuum" of hand types.

Those hands are right at the cut-off point to double or not, and since strategy must have these "yes or no" cut-off points to define the strategy, they are put at their closest points of accuracy.

It's a "49% versus 51%" grey-area type of thing, not 100% and 0%, so where the player's return is mathematically higher than a competing option, then that side is declared the action to take - even if it is only Infintessimally superior.

If you're an agressive player, then you're breaking no laws if you double A4 against a dealer's 2.
It's just that your return would be mathematically or statistically less, and therefore "the lesser play."

Quote: DelbertCoogan

You're supposed to double A2 and A3 against a dealer 5 or 6, and you're supposed to double A4 and A5 against a dealer 4,5, or 6. Why don't you double A2 and A3 against a dealer 4? It seems to me that A2, A3, A4, and A5 are basically the same hand. They all have the same number of cards that make totals of 17-21. What is the difference?

While doubling A3 against a 4 has the same expected valuse as A4 against a 4, the value of hitting the A3 is higher than hitting an A4. The EV of doubling falls in between the two, thus the reason you should hit A3 and double A4.

Your reasoning it correct. The difference comes from the fact that your double gets only one card, while hit doesn't.

When you hit A2 against 4, there is a higher chance that you want to hit again. Say you get 1-4
When you hit A6 against 4, there is lowerchance that you want to hit again. only if you get an ace.

Thus EV(double) may be considered equal for infinite decks.
But EV(hit) will increase with smaller soft totals. Thus
Ev(hit) at A2 >Ev(double) at a2-a5> Ev(hit) at A5 ...

Thanks Wizard, I've been wracking my brain over that one.