Interesting Puzzle

[chessplayer]

Hi all,

I have an interesting puzzle.

Case 1) You are allowed an increased chance of having a high card for your first card only(Say, +4 TC for the first card ONLY). Your other card's chance and dealer's card's chance is normal(AT TC =0)

Case 2) You are allowed an increased chance of having high cards for both of your cards(+4TC). However, in this case, the dealer's upcard also has the same increased chance of having a high card(+4).

The rest of the cards delt(Such as the dealer's remaining cards and cards if you hit) have the normal chance of being a high or low card (Count =0)

The Puzzle is which will a good player choose.

This is for those interested only.

 

[muppet]

2

 

[winr_winr_chicken_dinner!]

2, I want a BJ please.

 

[Polarbearsolvent]

Indeed 2. My blackjack pays 3 to 2, and dealer only takes my initial bet if he gets blackjack. (And I suppose the player always is taking insurance if the dealer spikes an ace heh)

 

[Sucker]

The Puzzle is which will a good player choose.

A GOOD player will probably choose the second choice.
The person that knows the correct answer to this problem will choose the first choice, without any hesitation.

This thread begins to venture into top secret territory, and I would hope that the mods at least move it into the category of "advanced strategies".

 

[Automatic Monkey]

A GOOD player will probably choose the second choice.
The person that knows the correct answer to this problem will choose the first choice, without any hesitation.

This thread begins to venture into top secret territory, and I would hope that the mods at least move it into the category of "advanced strategies".

The problem with it all is that the higher incidence of high cards with TC = +4 isn't really enough to do anything drastic.

 

[muppet]

why 1?

 

[Blue Efficacy]

But the dealer still has a neutral count chance of having junk in the hole with option 2. I am curious why 1 is better.

 

[MAZ]

But the dealer still has a neutral count chance of having junk in the hole with option 2. I am curious why 1 is better.

Alright I'll pose you a few questions than. If you were to get an ace or even a 10 as your first card what type of advantage do you start with? At a TC of +4 TC without any cards dealt yet, what is your advantage here? What is known and what is unknown? Which play gives you the most information to make a decision? What would you rather do play every hand at an advantage of +4 TC, or every hand with an ace as your starting card in a neutral count?

 

[creeping panther]

Maz

Alright I'll pose you a few questions than. If you were to get an ace or even a 10 as your first card what type of advantage do you start with? At a TC of +4 TC without any cards dealt yet, what is your advantage here? What is known and what is unknown? Which play gives you the most information to make a decision? What would you rather do play every hand at an advantage of +4 TC, or every hand with an ace as your starting card in a neutral count?

Ace.

CP

 

[Blue Efficacy]

Alright I'll pose you a few questions than. If you were to get an ace or even a 10 as your first card what type of advantage do you start with? At a TC of +4 TC without any cards dealt yet, what is your advantage here? What is known and what is unknown? Which play gives you the most information to make a decision? What would you rather do play every hand at an advantage of +4 TC, or every hand with an ace as your starting card in a neutral count?

Of course you'd want the ace or the ten.

But that wasn't the question. Option 1 isn't a sure T or A, it's +4 chance of the first card being one. Option 2 is a +4 chance of both your cards and the dealer's being a big card. I know you know this, just explaining why I am confused.

Why is having one card having increased odds of being big beat the odds of both cards being big, even at increased chances of a strong dealer upcard? Again because this +4 count doesn't affect the dealer holecard I am not sold. Perhaps I am stuck thinking in the box here?

 

[assume_R]

So it seems a combinatorial approach would yield the correct answer. I didn't do one (I don't know all the information), but here's how I would go about it:

There are 4 cards we are considering: your 2 cards, the dealer's up card, and the dealer's hole card.

Each card has 10 possible values (A through X), which means there are 10^4 = 10,000 (non-unique) combinations. Each of those 10,000 combinations has an EV associated with it.

In case 1, only your first card has the probability of getting each card not equal to 1/13 (or 4/13 for the X), while the other 3 cards (your second card and the dealer's 2 cards) have a 1/13 chance for each value (or 4/13 for the X). So all you would need to do is multiply the probabilities with the EV's for each of the 10,000 outcomes.

Case 2 has the first 3 cards (your 2 plus the dealer's up) with non-even probabilities of having each value.

Now the only question would be what are the EV's of each outcome given your 2 cards and the dealer's 2 cards. Perhaps this is in a book I simply don't own.

Is there an easier way to figure this out mathematically?

 

[Dyepaintball12]

Alright I'll pose you a few questions than. If you were to get an ace or even a 10 as your first card what type of advantage do you start with? At a TC of +4 TC without any cards dealt yet, what is your advantage here? What is known and what is unknown? Which play gives you the most information to make a decision? What would you rather do play every hand at an advantage of +4 TC, or every hand with an ace as your starting card in a neutral count?

I read the book Busting Vegas and it said dealt a 10 as your first card you have a 10% advantage, with an Ace its 50%.

 

[nottooshabby]

I read the book Busting Vegas and it said dealt a 10 as your first card you have a 10% advantage, with an Ace its 50%.

Very close . . . 13% player advantage when his first card is a 10, 52% when it's an A. (Griffin, 6th ed., pp 146)

 

[bjcount]

Hi all,

I have an interesting puzzle.

Case 1) You are allowed an increased chance of having a high card for your first card only(Say, +4 TC for the first card ONLY). Your other card's chance and dealer's card's chance is normal(AT TC =0)

Case 2) You are allowed an increased chance of having high cards for both of your cards(+4TC). However, in this case, the dealer's upcard also has the same increased chance of having a high card(+4).

The rest of the cards delt(Such as the dealer's remaining cards and cards if you hit) have the normal chance of being a high or low card (Count =0)

The Puzzle is which will a good player choose.

This is for those interested only.

I would say case 1 is better for a few reasons:

1) Because the remaining cards to be dealt are coming from a neutral shoe the standard thought of dealers breaking because of more 10's in the remaining cards doesn't apply.
2) At TC+4 there are more high cards, but some counting strategies don't consider the 7,8, and 9's and since 17 is a loser, 18 is not much better, your stuck while the dealer can hit in a neutral deck instead of a TC+4 deck(shoe) where you are expecting more breaks.
3) receiving 17,18,19,20's, and the 1 in 20.8 hand snappers never gives you the opportunity to DD, split, etc.. because in case 2 your not going to have many opportunities to split due to the increased chances of a dealers high up card (10 or A)
4) Case 2 may present more surrender hands while case 1 may deal you more stiffs but with a dealers low card you'll surrender/bust less while the dealer may bust more. Just many more variables in case 1 vs case 2 which can work in your favor.

of course how the cards come out is not ever set in stone but you dd and split less when the dealer shows a high card and the remaining decks are neutral.

just my thought.

BJC

 

[ycming]

Case 2 always, but in reality Case 1 will happen more often.

Ming

 

[muppet]

A GOOD player will probably choose the second choice.
The person that knows the correct answer to this problem will choose the first choice, without any hesitation.

This thread begins to venture into top secret territory, and I would hope that the mods at least move it into the category of "advanced strategies".

?