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Sep 98 Prog Challenge

Volume Number: 14 (1998)
Issue Number: 9
Column Tag: Programmer's Challenge

Sep 98 Programmer's Challenge

by Bob Boonstra, Westford, MA

Big Baby

Fifty years ago this past June, the Manchester Mark I prototype computer, also known as "Baby", became operational. Baby was the first computer to store a program electronically, and was also the first computer to store instructions and data in the same memory. Because vacuum tube technology was too immature to store memory reliably, Baby was designed to test memory based on a cathode ray tube. Not much memory, mind you. Baby boasted a full 1K bits of memory, organized as 32 words (or lines) of 32 bits each.

In celebration of the birth of the first stored program computer on June 21, 1948, the Department of Computer Science at the University of Manchester recently reconstructed Baby and ran a programming contest to write the most imaginative program for Baby. Inspired by that contest, your Challenge is to write an assembler and an emulator for an extended ("Big") version of Baby. The prototype for the code you should write is:

#if defined(__cplusplus)
pragma extern "C" {
#endif

#define kMaxInstructions 32

typedef UInt32 CRT_memory[kMaxInstructions];

pascal void AssembleBabyProgram(
   char *program,
   CRT_memory memory,
   UInt32 address_bits
);

pascal void ExecuteBabyProgram(
   CRT_memory memory,
   UInt32 address_bits
);

#if defined(__cplusplus)
}
#endif

Baby has a single general-purpose register, called the Accumulator. The program counter is called the Control Instruction, or CI. The CI is incremented just before the next instruction is fetched, which means that a jump instruction, for example, is coded with a value one less than the actual target address. Baby also has a red light that indicates the program has halted. One interesting thing about Baby is that it lacks an addition instruction - addition is done by subtraction.

Baby's instruction repertoire is listed below. The function bits (or opcode) associated with each instruction is listed in parentheses after the mnemonic.

STO (110)
Store the contents of the Accumulator in the store line.
SUB (001 or 101)
Subtract the contents of the store line from the Accumulator. There is no ADD instruction; addition is done indirectly by combining the SUB and the LDN instruction.
LDN (010)
Copy the contents of the store line, negated, to the accumulator.
JMP (000)
Copy the contents of the store line to the CI (so the store line holds the number of the line one before we want to jump to). In modern terms, this an indirect jump, which uses up an extra store line compared to a direct jump.
JRP (100)
Add the contents of the store line to the CI. This looks forward to larger machines, where it would be important to be able to load the same code in different places, and hence would need relative jumps.
CMP (011)
Skip the next instruction if the contents of the Accumulator are negative, i.e. a conditional branch.
STOP (111)
Stop the machine and turn the red light on
NUM (N/A)
An assembler mnemonic to initialize a store line to a data value.

For example, the following program computes the greatest common divisor of the number in locations 30 and 31:

22
0000 NUM 0
0001 LDN 30
0002 STO 29
0003 LDN 31
0004 STO 31
0005 LDN 31
0006 STO 30
0007 LDN 29
0008 SUB 30
0009 CMP
0010 JRP 27
0011 SUB 31
0012 STO 31
0013 SUB 28
0014 CMP
0015 JMP 00
0016 STP
0027 NUM -3
0028 NUM 2
0029 NUM 0
0030 NUM 3141593
0031 NUM 5214

Baby's instructions are assembled into a 32 bit word by placing the function code associated with the mnemonic into bits 13-15 (numbered with bit 0 as the most significant bit). In the original Baby, the store line associated with the instruction is placed in bits 0-4. Bits 5-12 and 16-31 are not used as part of the instruction, although they can be used as data. The program listed above assembles to the following:

22
0000:00000000000000000000000000000000
0001:01111000000000100000000000000000
0002:10111000000001100000000000000000
0003:11111000000000100000000000000000
0004:11111000000001100000000000000000
0005:11111000000000100000000000000000
0006:01111000000001100000000000000000
0007:10111000000000100000000000000000
0008:01111000000000010000000000000000
0009:00000000000000110000000000000000
0010:11011000000001000000000000000000
0011:11111000000000010000000000000000
0012:11111000000001100000000000000000
0013:00111000000000010000000000000000
0014:00000000000000110000000000000000
0015:00000000000000000000000000000000
0016:00000000000001110000000000000000
0027:10111111111111111111111111111111
0028:01000000000000000000000000000000
0029:00000000000000000000000000000000
0030:10011011111101111111010000000000
0031:01111010001010000000000000000000

Our contest will make one change to the original Baby: in our extended, Big Baby, machine, the store line is extended from 5 bits (0-4) to address_bits bits (0 - address_bits-1). This allows more than 32 words of memory and therefore larger programs.

Your AssembleBabyProgram routine should accept the mnemonic input listed above, pointed to by the program parameter, and assemble them into 32-bit Baby instructions in memory. Your ExecuteBabyProgram routine will be called to execute the program one or more times. Both of your routines will be provided an address_bits parameter that describes the size of memory. You will be asked to assemble more than one program, your assembled programs may be executed more than one time each, and you may be asked to execute a program that has been hand-assembled.

More information about the University of Manchester Baby programming contest can be found at http://www.cs.man.ac.uk/prog98/. Programming reference documentation for Baby can be found at http://www.cs.man.ac.uk/prog98/ssemref.html and at ftp://ftp.cs.man.ac.uk/pub/CCS-Archive/misc/progref1.doc.

The winner will be the solution that assembles and executes a set of test programs in the minimum amount of time.

This will be a native PowerPC Challenge, using the latest CodeWarrior environment. Solutions may be coded in C, C++, Pascal or, as is our tradition in the month of September, in assembly language. Thanks to Eric Shapiro for suggesting this Challenge.

Three Months Ago Winner

Congratulations to Tom Saxton for writing the most successful simulated gambler at the blackjack table of our June Programmer's Challenge Casino. Tom beat out four other entries and was one of only two entries to actually come out ahead at the blackjack table.

Tom precomputed the expected winnings for each situation and created tables with the action that led to the best result. He uses the Hi-Lo card counting method to determine whether the remaining cards contain a disproportionate number of high-valued cards, and then uses that estimate to adjust his wager. Tom's solution is also not too greedy; it contains heuristics to quit when it has won a reasonable amount or played long enough, ensuring that it has wagered enough credits to avoid the "freeloader" penalty imposed by the problem.

A few words about our other gamblers are in order. The second-place solution, by Kevin Hewitt, also used precomputed tables, but his were based only on the initial pair of cards dealt. Kevin also spent more time at the table, quitting only when winnings or losses exceeded a threshold. JG Heithcock's solution spent the least amount of time at the table. He quit soon after the minimum total bet criterion was met. Ken Slezak kept playing until he lost 75% of his bankroll (or quadrupled his money) and Randy Boring played until he ran out of money or, as it turned out, until the house threw him out of the casino. Both of those players left with not much more than the shirts on their backs.

Here are the statistics for the entries to the Blackjack Challenge. Each player played a series of five games where the house varied the number of decks of cards used. Players were given the same number of credits at the start of each game, totaling 21000 credits for all of the games. The table below lists the total number of credits wagered by the player, the number of credits left when the player decided to quit, the number of hands played, total execution time, and the overall player score. Also listed are the code and data sizes for the entries, along with the programming language used. As usual, the number in parentheses after the entrant's name is the total number of Challenge points earned in all Challenges to date prior to this one.

Name Credits Wagered Credits Left Hands Played Exec. Time Score Code Size Data Size Lang
Tom Saxton (19) 47451 25199 327 7169 25194 1496 1924 C
Kevin Hewitt 438700 23800 1833 37923 23766 996 2156 C
JG Heithcock (20) 22616 20484 769 17950 20470 1304 232 C
Ken Slezak (20) 91760 9140 1701 36911 9106 1240 172 C
Randy Boring (81) 437230 8670 15425 460099 8213 4920 353 C

Top Contestants

Here are the Top Contestants for the Programmer's Challenge, including everyone who has accumulated more than 20 points during the past two years. The numbers below include points awarded over the 24 most recent contests, including points earned by this month's entrants.

  1. Munter, Ernst 190
  2. Boring, Randy 76
  3. Cooper, Greg 54
  4. Mallett, Jeff 50
  5. Rieken, Willeke 47
  6. Nicolle, Ludovic 34
  7. Lewis, Peter 31
  8. Maurer, Sebastian 30
  9. Saxton, Tom 29
  10. Heithcock, JG 27
  11. Gregg, Xan 24
  12. Murphy, ACC 24
  13. Hart, Alan 21
  14. Antoniewicz, Andy 20
  15. Day, Mark 20
  16. Higgins, Charles 20
  17. Hostetter, Mat 20
  18. Studer, Thomas 20

There are three ways to earn points: (1) scoring in the top 5 of any Challenge, (2) being the first person to find a bug in a published winning solution or, (3) being the first person to suggest a Challenge that I use. The points you can win are:

  • 1st place 20 points
  • 2nd place 10 points
  • 3rd place 7 points
  • 4th place 4 points
  • 5th place 2 points
  • Finding bug 2 points
  • Suggesting Challenge 2 points

Here is Tom's winning solution:

Player.c
Copyright © 1998 Tom Saxton

#include "BlackJack.h"

// Naming Conventions:
//
// Without getting into the gory details of the Hungarian naming convention,
// here are some common prefixes and their meanings:
//
//      a       array
//      p       pointer
//      c       count
//      mp      map (one data type to another)
//      i       index
//
// The prefixes modify a base type. So, if FOO is a base type (like a struct,
// or an enum), the following declarations illustrate the above prefixes:
//
//      FOO     foo;
//      FOO *   pfoo;
//      FOO     afoo[10];
//      int     ifoo; // an index into an array of FOOs
//      int     cfoo; // a count of FOOs.
//
//      for (ifoo = 0; ifoo < cfoo; ++ifoo)
//         pfoo = &afoo[ifoo];
//

enum { fFalse = 0, fTrue = 1 };
#define DIM(a) (sizeof(a)/sizeof((a)[0]))

// Be sure to enable this define to pick up a couple of post-deadline bug fixes.
//
// #define BUGFIX

// disable debug code
#define Assert(f)

// The following tables determine the actions for all possible hands,
// divided into three groups: pairs, soft hands and hard hands, considered
// in that order. (A pair of aces is treated as a pair, not as a soft hand.)
//
// The tables were computed by taking the Dealer's up card and assuming
// a huge shoe with an even card distribution finding the probability
// for each of the possible final dealers scores (bust, 17, 18, 19, 20 and 21).
//
// Then, given that table, I computed the expected earnings (win, lose or
// push) for each of the possible actions, and recorded the action with
// the best result.
//
// I found the book "Best Blackjack" by Frank Scoblete (c) 1996 to be
// helpful, and my tables are close to his multi-deck tables.
// I modeled an infinite, evenly distributed shoe, he may have modeled
// a fixed number of decks.

// macros to make these tables manageable...
#define H kHitMe
#define D kDoubleDownAndHitMe
#define S kStandPat
#define X kSplitAndHitMe
#define B kClaimBlackjack

// For "hard" hands (no Aces scored as 11), plug in the dealer's up card
// (minus 1) and the hand's score to find the next action. If this isn't the
// first action of the hand, treat kDoubleDownAndHitMe as kHitMe.
Action mp_spot_score_actionHard[10][22] = 
{
//      0   - 21
   { H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,S,S,S,S,S },   /*  A */
   { H,H,H,H,H,H,H,H,H,D,D,D,H,S,S,S,S,S,S,S,S,S },   /*  2 */
   { H,H,H,H,H,H,H,H,H,D,D,D,H,S,S,S,S,S,S,S,S,S },   /*  3 */
   { H,H,H,H,H,H,H,H,H,D,D,D,S,S,S,S,S,S,S,S,S,S },   /*  4 */
   { H,H,H,H,H,H,H,H,H,D,D,D,S,S,S,S,S,S,S,S,S,S },   /*  5 */
   { H,H,H,H,H,H,H,H,D,D,D,D,S,S,S,S,S,S,S,S,S,S },   /*  6 */
   { H,H,H,H,H,H,H,H,H,D,D,D,H,H,H,H,H,S,S,S,S,S },   /*  7 */
   { H,H,H,H,H,H,H,H,H,H,D,D,H,H,H,H,H,S,S,S,S,S },   /*  8 */
   { H,H,H,H,H,H,H,H,H,H,D,D,H,H,H,H,H,S,S,S,S,S },   /*  9 */
   { H,H,H,H,H,H,H,H,H,H,H,D,H,H,H,H,H,S,S,S,S,S }    /*  10 */
};

// For "soft" hands (at least one Ace used as an 11), plug in the dealer's up card
// (minus 1) and the hand's "other" card (or combined score without the ace)
// to find the next action.
Action mp_spot_spot_actionSoft[10][10] = 
{
   { H, H, H, H, H, H, S, S, S, B },   /*  A */
   { H, H, H, H, H, D, S, S, S, B },   /*  2 */
   { H, H, H, H, H, D, D, S, S, B },   /*  3 */
   { H, H, H, H, D, D, D, S, S, B },   /*  4 */
   { H, H, H, D, D, D, D, S, S, B },   /*  5 */
   { H, H, H, D, D, D, D, S, S, B },   /*  6 */
   { H, H, H, H, H, D, S, S, S, B },   /*  7 */
   { H, H, H, H, H, H, S, S, S, B },   /*  8 */
   { H, H, H, H, H, H, H, S, S, B },   /*  9 */
   { H, H, H, H, H, H, H, S, S, B }    /* 10 */
};

// If dealt a pair, plug in the dealer's up card (minus 1) and the spot
// value of the pair (minus 1) to find the suggested action.
Action mp_spot_spot_actionPair[10][10] = 
{
   { X, H, H, H, H, H, H, H, S, S },   /*  A */
   { X, X, X, H, D, H, X, X, X, S },   /*  2 */
   { X, X, X, H, D, H, X, X, X, S },   /*  3 */
   { X, X, X, H, D, X, X, X, X, S },   /*  4 */
   { X, X, X, H, D, X, X, X, X, S },   /*  5 */
   { X, X, X, D, D, X, X, X, X, S },   /*  6 */
   { X, X, X, H, D, H, X, X, S, S },   /*  7 */
   { X, X, X, H, D, H, H, X, X, S },   /*  8 */
   { X, X, H, H, D, H, H, X, X, S },   /*  9 */
   { X, H, H, H, H, H, H, H, S, S }    /*  10 */
};

// undefine shortcuts used in the above tables
#undef H
#undef D
#undef S
#undef X
#undef B

// Score bust as zero.
#define scoreBust            0
// The Player's hand is limited to five cards.
#define ccardMaxPlayer       5
// The dealer can never draw more than nine cards
// (nine 2's for example).
#define ccardMaxDealer      10

// Entry in the SPOT table, used for scoring and printing card values
typedef struct ESPOT
{
   char   score;
   char   sz[3];
} ESPOT;

static const ESPOT s_dnspot[kKing+1] = 
{
   {  0, "?" },
   {  1, "A" },
   {  2, "2" },
   {  3, "3" },
   {  4, "4" },
   {  5, "5" },
   {  6, "6" },
   {  7, "7" },
   {  8, "8" },
   {  9, "9" },
   { 10, "10" },
   { 10, "J" },
   { 10, "Q" },
   { 10, "K" },
};

// game statistics...
static int s_cdeck;
static int s_ccreditStart;
static int s_ccreditMinBet;
static int s_ccreditMidBet;
static int s_ccreditMaxBet;
static int s_ccreditBalance;
static int s_ccreditTotalBet;

// callback functions
static BetProc *s_pfnMakeABet;
static HitProc *s_pfnHitMe;

// function to score a hand
static int _ScoreHand(const Card acard[], int ccard,
                              int *pcAce);

// struct for counting cards...
typedef struct DECK
{
   int acspot[10+1];
   int cspotStart;
   int cspotRemain;
   int dcount;
   int fInfinite;
} DECK;
static DECK s_deck;
// calls to reset card counters and count the cards in a hand
void _InitDeck(int cdeck, int fInfinite);
void _CountCards(const Card acard[], int ccard);
// call to compute the proper action given the player's hand and
// the dealer's up card, and whether or not this is the first action
static Action _ActionLookupHand(Spot spotDealer, Card acard[], int ccard, int fFirst);

InitBlackjack
// Call to start a game
void InitBlackjack(
   int numDecks,       /* number of decks used by the dealer, 2..10*/
   int yourBankroll,   /* number of credits you have to start */
   int minBet,         /* minimum bet for each hand */
   int maxBet,         /* maximum bet for each hand */
   BetProc pfnMakeABet,/* callback to place a wager */
   HitProc pfnHitMe    /* callback to get a card */
)
{
   s_cdeck             = numDecks;
   s_ccreditStart      = yourBankroll;
   s_ccreditMinBet     = minBet;
   s_ccreditMaxBet     = maxBet;
   s_pfnMakeABet       = pfnMakeABet;
   s_pfnHitMe          = pfnHitMe;

   s_ccreditTotalBet   = 0;
   s_ccreditBalance    = s_ccreditStart;
}

Blackjack
// Call to play a hand
Boolean Blackjack(Boolean fNewDeck)
{
   int      ccreditBet;
   Card     acardPlayer[ccardMaxPlayer], acardDealer[ccardMaxDealer];
   int      ccardPlayer, ccardDealer;
   Action   actionFirst;
   int      ccreditWin;
   Spot     spotDealer;
   int      ihand, chand;
   int      count;
   Result   result;
   
   if (fNewDeck)
      _InitDeck(s_cdeck, fFalse /*fInfinite*/);
   // normalize the card count. A positive count means that the shoe is
   // heavy in large cards, which makes it more likely for the dealer to
   // bust. A negative count means that the shoe is heavy in small cards,
   // which makes it less likely that the dealer with bust.
   count = (s_deck.dcount*52)/s_deck.cspotRemain;
   // Make a bet that is proportional to our current balance, so that losing
   // streaks don't clean us out, and winning streaks rake in extra chips.
   // Bet more when the count is high, less when it's low, but stay within
   // the stated betting limits.
   ccreditBet = (count+2)*s_ccreditBalance/50;
   if (ccreditBet < s_ccreditMinBet)
      ccreditBet = s_ccreditMinBet;
   else if (ccreditBet > s_ccreditMaxBet)
      ccreditBet = s_ccreditMaxBet;
   // Place bet, get some cards
   (*s_pfnMakeABet)(ccreditBet, acardPlayer, acardDealer);
   ccardPlayer = ccardDealer = 2;
   // store and normalize the dealer's up card
   spotDealer = acardDealer[1].spot;
   if (spotDealer > k10)
      spotDealer = k10;
   // get the first action for the hand
   actionFirst = 
            _ActionLookupHand(spotDealer, acardPlayer, 2, fTrue);
   if (actionFirst == kDoubleDownAndHitMe)
      ccreditBet *= 2;
   chand = (actionFirst == kSplitAndHitMe) ? 2 : 1;
   // play out the hand(s) (there are two hands if we kSplitAndHitMe)
   for (ihand = 0; ihand < chand; ++ihand)
   {
      Boolean   fInsurance;
      Action action = actionFirst;
      // take the "insurance" side bet when the dealer shows an Ace and there is
      // a better than one third chance of the dealer having a 10 for the other card.
      fInsurance = (spotDealer == kAce) && 
                        (3*s_deck.acspot[k10] > s_deck.cspotRemain);
      for(;;)
      {
         // play out an action
         result = 
               (*s_pfnHitMe)(action, fInsurance, acardPlayer, 
                           &ccardPlayer, acardDealer, &ccardDealer, 
                                 &ccreditWin);
         if (result != kNoResult)
            break;
         
         // If we didn't kStandPat or bust, calculate the next action
         action = _
         ActionLookupHand(spotDealer, acardPlayer, ccardPlayer, 
                                                fFalse);
      }
      
      // count the cards shown in this hand
      _CountCards(acardPlayer, ccardPlayer);
      if (ihand == chand-1)
         _CountCards(acardDealer, ccardDealer);
      
      // tally our win/loss
      s_ccreditBalance += ccreditWin;
      s_ccreditTotalBet += ccreditBet;
   }

   // If we have lost most of our money, quit
   if (s_ccreditBalance < s_ccreditStart/3)
   {
      return fFalse;
   }
   // If we have won a lot, and will avoid the freeloader penalty, quit
   if (s_ccreditBalance > 7*s_ccreditStart/4 && 
            s_ccreditTotalBet > s_ccreditStart)
   {
      return fFalse;
   }
   // If we have won some, and played for twice the freeloader requirement, quit
   if (s_ccreditBalance > 5*s_ccreditStart/4 && 
            s_ccreditTotalBet > 2*s_ccreditStart)
   {
      return fFalse;
   }
   // If we haven't lost, and played for five times the freeloader requirement, quit
   if (s_ccreditBalance > s_ccreditStart && 
            s_ccreditTotalBet > 5*s_ccreditStart)
   {
      return fFalse;
   }
   // If we've played 10 times the freeloader penalty, quit before the time penalty
   // takes it all away...
   if (s_ccreditTotalBet > 10*s_ccreditStart)
   {
      return fFalse;
   }
   return fTrue;
}

_ActionLookupHand
// Call to get the next action for this hand
static Action _ActionLookupHand(Spot spotDealer, Card acard[], int ccard, int fFirst)
{
   int score, cAce;
   Spot spot;
   Action action;
   
   // get the hand's score, and the count of Aces scored as 11
   score = _ScoreHand(acard, ccard, &cace);
   Assert(kAce <= spotDealer && spotDealer <= k10);
   if (fFirst && ccard == 2 && acard[0].spot == acard[1].spot)
   {
      // first action on a pair, check the pair's table
      if ((spot = acard[0].spot) > k10)
         spot = k10;
      action = 
         (Action)mp_spot_spot_actionPair[spotDealer-1][spot-1];
   }
   else if (cAce > 0)
   {
      // "soft" hand, check the soft table
      spot = (Spot)(score - 11);
      Assert(kAce <= spot && spot <= k10);
#ifdef DEBUG
      if (ccard == 2)
      {
         int icard = acard[0].spot == kAce ? 1 : 0;
         Assert(spot == acard[icard].spot || 
                        (spot == k10 && acard[icard].spot > k10));
      }
#endif
      action = 
         (Action)mp_spot_spot_actionSoft[spotDealer-1][spot-1];
   }
   else
   {
      // "hard" hand, chech the hard table
      action = 
         (Action)mp_spot_score_actionHard[spotDealer-1][score];
   }
   
   // If it's not the first play of the hand, we can only kStandPat or kHitMe
#ifdef BUGFIX
   // Another Bug Fix: be careful trying to catch illegal actions...
   if (action == kClaimBlackjack && ccard != 2)
      action = kStandPat;
   if (!fFirst && (action == kDoubleDownAndHitMe || 
                                    action == kSplitAndHitMe))
      action = kHitMe;
#else
   // This code is wrong, it incorrectly returns kHitMe in two cases:
   //  1. If a pair of 10s or Aces is split, then one of them turned into a blackjack
   //  2. A score of 21 is reached with an Ace and two or more cards.
   if (!fFirst && action != kStandPat)
      action = kHitMe;
#endif
   return action;
}

_InitDeck
// reset the counts for a fresh set of decks
static void _InitDeck(int cdeck, int fInfinite)
{
   Spot spot;
   int cspot = 4*cdeck;
   for (spot = kAce; spot < k10; ++spot)
      s_deck.acspot[spot] = cspot;
   Assert(spot == k10);
   s_deck.acspot[k10] = 4*cspot;
   s_deck.cspotRemain = s_deck.cspotStart = 52*cdeck;
   s_deck.dcount = 0;
   s_deck.fInfinite = fInfinite;
}

_CountCards
// This is the counting method used by the couple of people I've talked
// who have actually counted cards playing Blackjack. It's call "Hi-Lo"
// in "Best Blackjack". I tried several other counting models listed
// in that book, and this performed the best. It gives a simple assessment
// of how far off balance the shoe is with respect to small and large cards.
static const int s_mp_spot_dcount[k10+1] =
//    A  2  3  4  5  6  7  8  9  10
{ 0, -1, 1, 1, 1, 1, 1, 0, 0, 0, -1 };

// Remove the specified set of cards from the shoe
void _CountCards(const Card acard[], int ccard)
{
   if (s_deck.fInfinite)
      return;
      
   while (ccard- > 0)
   {
      Spot spot = acard[ccard].spot;
// Bug Fix: we shouldn't count hidden cards...
#ifdef BUGFIX
      if (spot == kHiddenSpot)
         continue;
#endif
      if (spot > k10)
         spot = k10;
      -s_deck.acspot[spot];
      -s_deck.cspotRemain;
      
      s_deck.dcount += s_mp_spot_dcount[spot];
   }
}

_ScoreHand
// Determine the score for the given cards. When possible, score
// Aces at 11, and return the number of aces thusly scored.
static int _ScoreHand(const Card acard[], int ccard, int *pcAce)
{
   int cAceDummy;
   int score = 0;
   int cAce = 0;

   if (pcAce == NULL)
      pcAce = &cAceDummy;
   *pcAce = 0;
   while (ccard- > 0)
   {
      if (acard[ccard].spot == kAce)
         ++cAce;
      score += s_dnspot[acard[ccard].spot].score;
   }
   
   if (score > 21)
      return scoreBust;
   while (score + 10 <= 21 && cAce > 0)
   {
      score += 10;
      -cAce;
      ++*pcAce;
   }

   return score;
}
 

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Never Gone (Games)
Never Gone 1.0.2 Device: iOS Universal Category: Games Price: $2.99, Version: 1.0.2 (iTunes) Description: ###IMPPORTANT### Never Gone's HD art resources require devices with more than 1GB RAM, so please note that iPhone 4/4s, iPad 2/... | Read more »
INKS. (Games)
INKS. 1.0 Device: iOS Universal Category: Games Price: $1.99, Version: 1.0 (iTunes) Description: From the makers of BAFTA-winning Lumino City comes INKS. INKS updates pinball for a new generation. It combines the joy of pinball with... | Read more »
How to maximise your profits in Bakery B...
Running a bakery can be an expensive venture. You’ll need to continuously upgrade your oven, your kitchen supplies, and even your ingredients to keep customers happy. Most of these renovations in Bakery Blitz cost a pretty penny, but we have a few... | Read more »
How to manage your time in Bakery Blitz
It can be tricky, especially when you risk burning your kitchen to the ground if you forget a cake in the oven, so make sure to use these time management tricks to keep your bakery running smoothly. Don’t collect the money right away [Read more] | Read more »
Model 15 (Music)
Model 15 1.0 Device: iOS iPhone Category: Music Price: $29.99, Version: 1.0 (iTunes) Description: The Moog Model 15 App is the first Moog modular synthesizer and synthesis educational tool created exclusively for iPad, iPhone and... | Read more »
How to deal with wind in Angry Birds Act...
Angry Birds Action! is a physics-based puzzler in which you're tasked with dragging and launching birds around an obstacle-littered field to achieve a set objective. It's simple enough at first, but when wind gets introduced things can get pretty... | Read more »
How to get three stars in every level of...
Angry Birds Action! is, essentially, a pinball-style take on the pull-and-fling action of the original games. When you first boot it up, you'll likely be wondering exactly what it is you have to do to get a good score. Well, never fear as 148Apps... | Read more »
The beginner's guide to Warbits
Warbits is a turn-based strategy that's clearly inspired by Nintendo's Advance Wars series. Since turn-based strategy games can be kind of tricky to dive into, see below for a few tips to help you in the beginning. Positioning is crucial [Read... | Read more »
How to upgrade your character in Spellsp...
So you’ve mastered the basics of Spellspire. By which I mean you’ve realised it’s all about spelling things in a spire. What next? Well you’re going to need to figure out how to toughen up your character. It’s all well and good being able to spell... | Read more »
5 slither.io mash-ups we'd love to...
If there's one thing that slither.io has proved, it's that the addictive gameplay of Agar.io can be transplanted onto basically anything and it will still be good fun. It wouldn't be surprising if we saw other developers jumping on the bandwagon,... | Read more »

Price Scanner via MacPrices.net

Global Tablet Sales Slump Continues, iPad’s F...
Another miserable showing for the global slate tablet category in calendar Q1/16, with global tablet shipments falling another 1ten percent to 46.5 million units during the according to Strategy... Read more
Revel Systems to Showcase iPad POS Platform w...
Revel Systems, specialists in iPad Point of Sale management solution for brick-and-mortar retail, food businesses and more, today announced that it will showcase its innovative iPad Point of Sale... Read more
13-inch 2.5GHz MacBook Pro on sale for $999,...
B&H Photo has the 13″ 2.5GHz MacBook Pro on sale for $999 including free shipping plus NY sales tax only. Their price is $100 off MSRP. Read more
Apple refurbished 2015 iMacs available for up...
Apple now has a full line of Certified Refurbished 2015 21″ & 27″ iMacs available for up to $350 off MSRP. Apple’s one-year warranty is standard, and shipping is free. The following models are... Read more
Indian Smartphone Market Grows Annually by 12...
India’s smartphone market grew by 12 percent year-over-year, with 24.4 million units shipping in Q1 2016. The top five vendors stayed the same, with Samsung in the lead, followed by Micromax, Intex... Read more
Get Notifications When Your Friend’s Phone Ba...
Calgary, Canada based Stonelight Pictures has announced the release of Battery Share 1.0.1, its new utility for iOS 9 supported devices. The company notes that people are spending more time on their... Read more
11-inch 1.6GHz/128GB MacBook Air on sale for...
Amazon has the current-generation 11″ 1.6GHz/128GB MacBook Air (sku MJVM2LL/A) on sale for $749.99 for a limited time. Their price is $150 off MSRP, and it’s the lowest price available for this model... Read more
Price drops on clearance 2015 13-inch MacBook...
B&H Photo has dropped prices on clearance 2015 13″ MacBook Airs by up to $250. Shipping is free, and B&H charges NY sales tax only: - 13″ 1.6GHz/4GB/128GB MacBook Air (MJVE2LL/A): $799, $200... Read more
Mac minis on sale for up to $100 off MSRP
B&H Photo has Mac minis on sale for up to $100 off MSRP including free shipping plus NY sales tax only: - 1.4GHz Mac mini: $449 $50 off MSRP - 2.6GHz Mac mini: $649 $50 off MSRP - 2.8GHz Mac mini... Read more
13-inch Retina MacBook Pros on sale for up to...
B&H Photo has 13″ Retina MacBook Pros on sale for $130-$200 off MSRP. Shipping is free, and B&H charges NY tax only: - 13″ 2.7GHz/128GB Retina MacBook Pro: $1169 $130 off MSRP - 13″ 2.7GHz/... Read more

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Automotive Sales Consultant - Apple Ford Linc...
…you. The best candidates are smart, technologically savvy and are customer focused. Apple Ford Lincoln Apple Valley is different, because: $30,000 annual salary Read more
Restaurant Manager (Neighborhood Captain) - A...
…in every aspect of daily operation. WHY YOU'LL LIKE IT: You'll be the Big Apple . You'll solve problems. You'll get to show your ability to handle the stress and Read more
Simply Mac *Apple* Specialist- Service Repa...
Simply Mac is the largest premier retailer of Apple products in the nation. In order to support our growing customer base, we are currently looking for a driven Read more
Restaurant Manager (Neighborhood Captain) - A...
…in every aspect of daily operation WHY YOU LL LIKE IT You ll be the Big Apple You ll solve problems You ll get to show your ability to handle the stress and Read more
*Apple* Retail - Multiple Positions (US) - A...
Job Description:SalesSpecialist - Retail Customer Service and SalesTransform Apple Store visitors into loyal Apple customers. When customers enter the store, Read more
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