I have an interesting puzzle 2

[chessplayer]

Nvm. Deleted. Perhaps it does not work. For the rest go to the first puzzle: http://www.blackjackinfo.com/bb/showthread.php?t=17874

 

[Sucker]

If you were to play in a casino where they used a pinochle deck, you would obviously bankrupt the house in rather short order. I'm going with option 2); HH vs. H.

 

[chessplayer]

And in http://www.blackjackinfo.com/bb/showthread.php?t=17874 you chose HM vs M as the one you thought correct llol

If you were to play in a casino where they used a pinochle deck, you would obviously bankrupt the house in rather short order. I'm going with option 2); HH vs. H.

 

[Sucker]

In that thread I chose High+UNKNOWN vs. UNKNOWN, not High+Middle cards Vs. Middle card; or so I thought. I was allowed an increased chance of having a high first card only, and the other cards were "normal" (TC=0).
In that case I interpreted "normal" as meaning "random"; and not "medium".

In THIS case I'm interpreting "high card" as meaning 10 or Ace, "medium card" as 7, 8, or 9; and "small card" as 2 - 6.
If you meant something else, then I apologize for misunderstanding you, but to be fair; you really didn't make it all that clear.

I actually wrote a software program about 15 years ago that can give the EXACT answer to ANY deck composition, including these questions in particular. I still use it quite often for my S game.

 

[chessplayer]

Ermm..

In general,but not always, if the actualisation of the goal is good, it means something which increases our chance of getting it is good.

For instance, a dealer Ace or 10 is bad. You can tell that "an increased chance of a dealer ACE or 10, other factors remaining the same", is bad.

Similarly, if having a higher chance of HM vs M is better than HH vs H is good , as was indicated by you in the other thread, it naturally follows that an actual case of HM vs M ivs is superior to HH vs H. Not always, but generally so.

I could have added in the part about TC here in the OP, but the post
might have been too lengthy and confusing.

In that thread I chose High+UNKNOWN vs. UNKNOWN, not High+Middle cards Vs. Middle card; or so I thought. I was allowed an increased chance of having a high first card only, and the other cards were "normal" (TC=0).
In that case I interpreted "normal" as meaning "random"; and not "medium".

In THIS case I'm interpreting "high card" as meaning 10 or Ace, "medium card" as 7, 8, or 9; and "small card" as 2 - 6.
If you meant something else, then I apologize for misunderstanding you, but to be fair; you really didn't make it all that clear.

I actually wrote a software program about 15 years ago that can give the EXACT answer to ANY deck composition, including these questions in particular. I still use it quite often for my S game.

 

[chessplayer]

BTW, I appreciate your comments and have altered the OP.

 

[k_c]

Nvm. Deleted. Perhaps it does not work. For the rest go to the first puzzle: http://www.blackjackinfo.com/bb/showthread.php?t=17874

I get these approx EVs for the puzzle 1 question:

I used a program I have written to compute the probabilities of drawing each rank from a 6 deck shoe with 156 cards remaining and a HiLo RC=+12
Cards in deck=156 (TC=04.0)
p(2) = 0.06923
p(3) = 0.06923
p(4) = 0.06923
p(5) = 0.06923
p(6) = 0.06923
p(7) = 0.07692
p(8) = 0.07692
p(9) = 0.07692
p(10) = 0.33846
p(1) = 0.08462

[u]Case 2)[/u]
6 decks at pen level of 156 cards (1/2 shoe dealt), s17, NDAS ...... :
HiLo RC = +12, TC = +4
Both of player's cards and dealer's up card come from a shoe that starts
with HiLo RC=+12, TC=+4
EV (total dependent bs) = ~+1.34%, insurance EV = +.11%

[u]case 1)[/u]
player's first card from HiLo TC =+4, everything else normal
I used above probs for player's first card * ev(given the shoe reverts
to a normal shoe after first card is dealt) and summed the result for
each up card.

EV  = ~+0.92%, optimal insurance EV = 0

I see you deleted your original question for this thread but here's an answer (+ rant) anyway.

HH v H seems to be pretty good. It's even better than a guarantee of a player ace on his initial card versus whatever dealer may randomly be dealt. The reason is player is guaranteed 2 high cards while dealer is guaranteed only 1. Dealer can still have a 'stiff' whereas player is guaranteed a very good hand.

Mathematics below for HH v H (relative to HiLo count) lists all possible hands,
their unconditional ev (which is what we need for calculation,) their ev on
condition dealer has checked for bj and doesn't have it,) their probability of
occurrence, their weight relative to their probability of occurrence, and finally
the ev of each possiblity.

HH v H (p3+p4+p5+p6+p7+p8) = 0.05601876591 = tot weight = sum(probs below)
A-A v A, -.2230, +.1271 (no dbj), p = p3 = .00040372448, w = .0072, w*ev = -.00161
A-A v T, +.0978, +.1820 (no dbj), p = p4 = .00176170681, w = .0314, w*ev = +.00307
A-T v A, +1.039, +1.500 (no dbj), p = p5 = .00352341363, w = .0629, w*ev = +.06535
A-T v T, +1.388, +1.500 (no dbj), p = p6 = .01455323019, w = .2598, w*ev = +.36060
T-T v A, +.1512, +.6546 (no dbj), p = p7 = .00727661510, w = .1299, w*ev = +.01964
T-T v T, +.4380, +.5591 (no dbj), p = p8 = .02850007580, w = .5088, w*ev = +.22285

HH v H ev = .6699 = 66.99% = sum(last column)

LM v L, HM v M, and LL v L could be similarly computed, although there would be more data.

My programs, which have been hiding in plain sight for over 2 years, can answer problems like this if someone is industrious enough to do some math. Even someone that can't deal with the math or chooses to not want the problem of dealing with the math can get a lot of the same information right out of the box from the programs that comes from other alternatives, both more and less expensive.

When I started developing these I was hoping to do well enough financially to justify putting in the time to add other functionality, but that is not the case. Although I've added a couple of things, for the most part I don't work on them.

The main thing I've done recently is to create a .dll library that can port
composition dependent calculation data to other programs, such as Excel. To use it requires some programming skills, but ev data like the above would be available to a programmer to use as he/she saw fit. The .dll is capable of simming comp dependent basic strategy or optimal comp dependent strategy using a shuffle that is supplied by the programmer. At this point the sims output only end results and do not record any intermediate results such as ev(s) for each player decision in an optimal sim.

 

[chessplayer]

I get your case. Wow, it gets so precise. BTW, then we seem to be able to conclude that in the case of HH vs H, it is the same as if it is in an ordinary case where the count is positive at the count of the H. For in stance, you had a +4 TC with each of the H cards in HH vs H, and the advantage you calculated is +1.34. In a normal BJ game, at +4 the advantage would be about +1.5(-0.5 for HA).

I

[u]Case 2)[/u]
6 decks at pen level of 156 cards (1/2 shoe dealt), s17, NDAS ...... :
HiLo RC = +12, TC = +4
Both of player's cards and dealer's up card come from a shoe that starts
with HiLo RC=+12, TC=+4
EV (total dependent bs) = ~+1.34%, insurance EV = +.11%

[u]case 1)[/u]
player's first card from HiLo TC =+4, everything else normal
I used above probs for player's first card * ev(given the shoe reverts
to a normal shoe after first card is dealt) and summed the result for
each up card.

EV  = ~+0.92%, optimal insurance EV = 0

sim.

 

[Sucker]

Case 2)
6 decks at pen level of 156 cards (1/2 shoe dealt), s17, NDAS ...... :
HiLo RC = +12, TC = +4
Both of player's cards and dealer's up card come from a shoe that starts
with HiLo RC=+12, TC=+4
EV (total dependent bs) = ~+1.34%, insurance EV = +.11%

This intuitively doesn't seem right. If the dealers hole card is at a count of 0 then that means that when the hand is dealt out, instead of having HH vs. H you'll actually HAVE HH vs. HM.

In a normal situation with a count of +4 you'll end up having HH vs. HH. How can HH vs. HH possibly be better than HH vs. HM? Also; if the count for the dealers' hole card is zero, how can you be gaining equity from insurance? With a count of 0, you'll NEVER take insurance.

I believe that if you re-run this hand you'll find an error, and will come up with a number that's closer to the +2.38% advantage that MY program gets.

 

[chessplayer]

Perhaps it is due to him including the HA. For instance, he writes :"EV (total dependent bs) = ~+1.34%"

He wrote total dependent bs which presumably included 0.5% HA. If he adds it, he gets 1.84, which is not too far from your 2.38. Unless of course you included the HA in your 2.38%.

This intuitively doesn't seem right. If the dealers hole card is at a count of 0 then that means that when the hand is dealt out, instead of having HH vs. H you'll actually HAVE HH vs. HM.

In a normal situation with a count of +4 you'll end up having HH vs. HH. How can HH vs. HH possibly be better than HH vs. HM? Also; if the count for the dealers' hole card is zero, how can you be gaining equity from insurance? With a count of 0, you'll NEVER take insurance.

I believe that if you re-run this hand you'll find an error, and will come up with a number that's closer to the +2.38% advantage that MY program gets.

 

[k_c]

This intuitively doesn't seem right. If the dealers hole card is at a count of 0 then that means that when the hand is dealt out, instead of having HH vs. H you'll actually HAVE HH vs. HM.

In a normal situation with a count of +4 you'll end up having HH vs. HH. How can HH vs. HH possibly be better than HH vs. HM? Also; if the count for the dealers' hole card is zero, how can you be gaining equity from insurance? With a count of 0, you'll NEVER take insurance.

I believe that if you re-run this hand you'll find an error, and will come up with a number that's closer to the +2.38% advantage that MY program gets.

I may have misinterpreted the question. I assumed the only condition was that both player cards and delaer up card came from a +4 HiLo TC and whatever came after that was normal in that the deal proceeded from that same shoe composition for case 2.

Player's EV would probably increase if dealer's cards would be dealt from a 0 HiLo TC shoe, as you have suggested. Dealer would have more stiffs and less pat hands.

 

[chessplayer]

I may have misinterpreted the question. I assumed the only condition was that both player cards and delaer up card came from a +4 HiLo TC and whatever came after that was normal in that the deal proceeded from that same shoe composition for case 2.

You mean the cards AFter the HH vs H came from the same +4 shoe, so it is basically HHHH... vs HHHH.... . No then, since this will merely mean we are calculating the Advantage at Tc +4 since ALL the cards are from+4.

The puzzle is only for HH vs H as the beginning cards. The rest of the cards will be drawn from a shoe with TC= 0

 

[Sucker]

I get these approx EVs for the puzzle 1 question:

I used a program I have written to compute the probabilities of drawing each rank from a 6 deck shoe with 156 cards remaining and a HiLo RC=+12
Cards in deck=156 (TC=04.0)
p(2) = 0.06923
p(3) = 0.06923
p(4) = 0.06923
p(5) = 0.06923
p(6) = 0.06923
p(7) = 0.07692
p(8) = 0.07692
p(9) = 0.07692
p(10) = 0.33846
p(1) = 0.08462

These are the EXACT figures that I came up with. I then inputted these numbers into the players' first card, second card; and then the dealers' up card.
I then switched the count to 0 for the rest of the hand. This meets the conditions of the problem; HHMM vs. HMMM. After running one million hands, my simulator came up with a players' advantage of +2.38%.

I'm wondering if maybe you ran it as HHHH vs. HHHH. This would explain the insurance EV that you came up with. If you run it as HMMM; when the dealers' up card is an ace, the chance of BJ is only 0.30768; not enough to EVER take insurance.

 

[k_c]

This intuitively doesn't seem right. If the dealers hole card is at a count of 0 then that means that when the hand is dealt out, instead of having HH vs. H you'll actually HAVE HH vs. HM.

In a normal situation with a count of +4 you'll end up having HH vs. HH. How can HH vs. HH possibly be better than HH vs. HM? Also; if the count for the dealers' hole card is zero, how can you be gaining equity from insurance? With a count of 0, you'll NEVER take insurance.

I believe that if you re-run this hand you'll find an error, and will come up with a number that's closer to the +2.38% advantage that MY program gets.

I guess case 2 is saying that players's first 2 cards and dealer's up card will be drawn from a HiLo TC=+4 and after that shoe probabilies revert to the same as they would be if the resulting 3 cards had come from a full shoe.

Assuming this, the process to compute case 2 would be to compute full shoe EV as would be normally done except the probabilities of each of the 550 possibilities (55 possible player 2 card hands versus 10 possible dealer up cards) would be replaced by the probabilities of each of the 550 possibilities drawn from a +4 HiLo TC shoe. These probs will vary depending upon remaining cards. The example I used started with a HiLo RC=+12 with 156 cards remaining dealt from 6 decks and assumes nothing has been specifically removed and only the HiLo RC=+12.

After player's first card is given, to compute the prob of the next card then the first card needs to be specifically removed. For example after an ace is drawn the new condition relative to HiLo is RC=+11 with 155 cards remaining dealt from 6 decks with 1 ace specifically removed. That would lead to these probs for the next card:
Cards in deck=155 (TC=03.7)
p(2) = 0.06975
p(3) = 0.06975
p(4) = 0.06975
p(5) = 0.06975
p(6) = 0.06975
p(7) = 0.07719
p(8) = 0.07719
p(9) = 0.07719
p(10) = 0.33858
p(1) = 0.08112

Successive cards would be similarly removed. In this way it may be possible to program a CA that is based upon a count.

Anyway, back to the original problem. Using the above method to compute the probabilities of each of the 550 possibilities for RC=+12, 156 cards remain from 6 decks multiplied by the full shoe ev for each possibility and summing all this up would give an answer based on the condition that the starting point is a HiLo RC=+12 dealt from 6 decks with 156 cards remaining.

The only difference from a normal full shoe calculation would be that the probabilities of all 550 possibilities would not necessarily be the same as the full shoe probabilities.

I'm not about to do this by hand. :grin: