Soft doubling -- BS doesn't make sense? ??

[PinkChip]

Thanks for this great link! It contains some results I anyway wanted to have a look at but had not found them elsewhere.

[roliin]

The point is, for the player who hesitates to double down, the correct decision (according to Basic Strategy) would be to hit rather than double down. This is because both plays have a positive expectation, but to hit gains more on average (in the long run). But the player (erroneously from his perspective) wants to double down but has too little money, so he tries to double for less (for half in this case).

Now that the player has decided, the question for you is just, should you participate in this double play and lay down the rest of the money till it is a doubling for the full amount. The answer is yes, because from your perspective, the double down play is still advantageous (it will win more than 50 percent of the time, yielding a positive expectation for the double down wager, thus also for your share). Basic Strategy is optimal for the player who makes the playing decisions, but not necessarily for the bystander who was the option to bet on, but not to play the hand.

I'm still a little lost. If 9 vs 7 is gonna win better than 50% of the time, how come the index # is +3? In other words, I wouldn't double 9 vs 3 on my own hand unless the count was +3 or better. So why would I double down at a count of 0 just because it's someone elses hand?

[Renzey]

I'm still a little lost. If 9 vs 7 is gonna win better than 50% of the time, how come the index # is +3? So why would I double down at a count of 0 just because it's someone elses hand?

Roliin,
Here it is. When you have 9 vs 7 for $100 at a neutral count, if you hit 100 times you'll go 59 and 41 for an $1800 gain.
If you double down, you'll go 53 and 47 at $200 apiece for a $1200 gain.
So -- hitting is the best play -- for you.

Now if somebody else has that hand and doubles for just another $50, he'll go 53 and 47. You can either sit there and watch him do it -- or you can jump in on a 53% shot with your own $50 to fill up the double.

So when you have the hand, your options are 59% or 53%.
When somebody else doubles that hand for less, your options are 53% or nothing.

[RS]

Here's another way to think of it (easier for me).

Let's say someone gets dealt a ten, ten and the dealer is showing a 6 up. He wants to split, for whatever reason, but doesn't want to split for the full amount, so you top the bet for the split so he can do it. For him, this is bad, because he used to have 20. For you, however, this is good, because it's like playing a (new/separate) hand where you know the dealer has a 6 and you know your first card is a 10. You aren't giving up anything "good", you are only getting "good" out of it Kind of like how doubling a 9v7 is bad for that player, because he is giving up the chance to hit again (in case he draws a 2 or 3 or 4 or whatever).


On the opposite spectrum, let's say you are playing a $10 free-play coupon. You get a pair of 8's against a dealer ten. Basic strategy says to split, right? However, this is a -EV play, because that free-play coupon has no value. It doesn't hurt you if it loses. It only helps you if you win. In this situation, you would not split those 8's. If another player had 8's against a dealer 10, same scenario. Would you give money to split, because it's "proper BS"? Of course not, because splitting 8's against a 10 still has -EV....it's just that hitting or staying is more -EV than splitting.


This is all because Basic Strategy is based on the outcome of hitting vs staying vs doubling down -- your money is already on the line. However with other things (like doubling 9v7), you have the option of doubling down or not doubling down, whereas the player with the hand has the option of doubling down OR hitting.



Question for the gurus, if you have a FP coupon out and are dealt a 9v7, I'm assuming you would not treat that as a different player's hand (ie: You wouldn't double it), just because you can get more value for yourself if you hit it? Because that FP coupon is actually "worth" something to you, if it wins...and you have a higher chance of it winning if you hit instead of double.

[roliin]

Just got around to reading the replies. Good stuff. Thx