I've written a program to simulate benchmark and other rules, but the results consistently result in a player advantage of $18, rather than the $16 indicated in the book.
Is there a realistic method for verifying simulator results?
Joe,
Post the parameters you used: decks, rules, penetration, number of players, count system, indexes used, and bet schedule. I (and/or others) will sim it and post results.
Dog Hand
Thanks, that's a nice offer.
What I had in mind was detail that will help me locate the discrepancy(s) in my results. For example, a while ago I discovered an error in my simulator where the first hand of a split pair would not split a second time, resulting in a slightly lower than normal EV. I was able to discover the error by using an input file of shuffled decks. This provides reliable, repeatable results when program changes do not produce logic errors.
Will your simulator accept shoes of cards from an input file, or does it accept only the output of an on-the-fly generator of shuffled cards? If only the latter, then the best you can do (or so I suspect) is to provide an EV. I welcome any feedback you can offer.
Having said that, here are some recent results for 6 decks at 5/6 penetration and 1 deck at 26 card penetration, natural payoff 3:2, 1 player, 25 billion hands.
The first section begins with High-Low count using benchmark rules described in Professional Blackjack pp. 18. Insurance is taken with a true count (TC) of 3 or higher. Play decisions are as defined in Tables 9 and 10.
The Halves count section uses the same betting rules as for High-Low and insurance is taken at TC 3.3 or higher. Play decisions as defined in Tables 69 and 70.
The Basic section uses flat bets, no insurance, and play decisions as described in The Theory of Blackjack pp. 174-177.
The first group is 6 decks and the second is 1 deck.
SYSTEM S17 DAS % VALUE
------ --- ---- -------
HILO S17 nDAS 1.8117
HILO S17 DAS 2.2948
HILO H17 nDAS 1.3308
HILO H17 DAS 1.8136
HALVES S17 nDAS 2.0092
HALVES S17 DAS 2.5043
HALVES H17 nDAS 1.5155
HALVES H17 DAS 2.0283
BASIC S17 nDAS -0.5701
BASIC S17 DAS -0.4100
BASIC H17 nDAS -0.7844
BASIC H17 DAS -0.6202
HILO S17 nDAS 5.1036
HILO S17 DAS 5.6590
HILO H17 nDAS 4.6427
HILO H17 DAS 5.2069
HALVES S17 nDAS 5.4402
HALVES S17 DAS 6.0236
HALVES H17 nDAS 4.9972
HALVES H17 DAS 5.5883
BASIC S17 nDAS -0.0918
BASIC S17 DAS 0.0709
BASIC H17 nDAS -0.2806
BASIC H17 DAS -0.1139
Joe,
First, sorry about not replying sooner... it's been a crazy week!
Below I've reproduced part of your post, along with some of the output I obtained from CVCX (a commercial BJ simulator) and the values given by Stanford Wong in the 1994 version of Professional Blackjack.
For each CVCX run, I used a heads-up player playing 100 rounds per hour using complete HiLo or Halves, as indicated. The bet schedule is that given by Wong: $10 for TC<0, $25 at 0 & +1, $50 at +2, $75 at +3, and $100 at +4 and higher. The WR (Win Rate) and SD (Standard Deviation) numbers are in $/hr, while the IBA (Initial Bet Advantage) is in percent. Note, though, that Wong's numbers assume the table has two players, rather than heads up, and that, for HiLo, the counter uses only indexes in the range of -10 to +10.
As you can see, the CVCX WR's and SD's are similar to but somewhat larger than those given by Wong, probably due to using more indexes and having fewer spots in play.
However, your "% Value" values are approximately three times the IBA's I found using CVCX. How, precisely, did you calculate your % Values, and what do they represent?
Dog Hand
.
Joe Joe Joe Joe Joe CVCX CVCX CVCX SW SW
SYSTEM DECKS S17 DAS % VAL IBA% WR SD WR SD
HILO 6 S17 nDAS 1.8117 0.684 $18.51 $430.00 $16 $415
HILO 6 S17 DAS 2.2948 0.830 $22.47 $436.18 $20 $421
HILO 6 H17 nDAS 1.3308 0.496 $13.42 $430.43 $11 $416
HILO 6 H17 DAS 1.8136 0.645 $17.45 $436.62
HALVES 6 S17 nDAS 2.0092 0.750 $20.33 $434.45 $17 $426
HALVES 6 S17 DAS 2.5043 0.906 $24.54 $441.01
HALVES 6 H17 nDAS 1.5155 0.566 $15.33 $436.10
HALVES 6 H17 DAS 2.0283 0.724 $19.60 $442.81
HILO 1 S17 nDAS 5.1036 1.624 $52.30 $506.41 $48 $482
HILO 1 S17 DAS 5.6590 1.763 $56.72 $511.17 $51
HILO 1 H17 nDAS 4.6427 1.475 $47.51 $506.87 $42
HILO 1 H17 DAS 5.2069 1.618 $52.08 $511.73
HALVES 1 S17 nDAS 5.4402 1.720 $55.66 $512.49
HALVES 1 S17 DAS 6.0236 1.867 $60.33 $517.94
HALVES 1 H17 nDAS 4.9972 1.571 $50.83 $513.37
HALVES 1 H17 DAS 5.5883 1.719 $55.56 $518.88
Thank you for the information you provided and for your time.
The values I posted under the heading "% VALUE" reflect my misunderstanding of Wong's win rate. When multiplied by 1,000%, each of my numbers represents win rate in dollars and is within +3.9/-2.4% of the numbers you posted.
Also, as you politely noted, my numbers reflect heads up play, rather than the two players in Wong's benchmark.
I have more work to do on my simulator and, thanks to you, I am aware of some areas that need attention.
Dog Hand,
Thank you once again for providing simulation results that I have been unable to find elsewhere. As noted in another post, after multiplying my results by 1,000%, they represent an hourly (100 hands) win rate in dollars that is within a few percentage points of the numbers that you posted, leading me to believe that I�m on the right track.
I modified my simulator to allow from one to seven players and tested the new code. I then ran simulations with two players using the bet, insurance, and play rule combinations that I posted previously.
To keep a long story short, my two player results are similar to my heads up results. I compute the hourly win rate for Wong�s benchmark rules to be $18.27, which is more than 15% higher than the $15.78 he indicates in Professional Blackjack (pp. 19). This difference is significant and cannot be attributed to sampling error, so I have some specific questions for you:
Does your simulator approximate the win rate indicated for Wong�s benchmark (pp. 18)?
Can you direct me to published sources of simulation results and play indexes?
Do you know of an Internet forum that focuses on the development of Blackjack simulators?
Joe
Joe,
I ran a new CVCX sim for a HiLo player playing 100 rounds per hour at a 6D table with one other player (so 2 players total) and using indexes from -10 to +10. The penetration was 5/6, the players played all, and the HiLo counter spread according to Wong's schedule: $10 for TC<0, $25 at 0 & +1, $50 at +2, $75 at +3, and $100 at +4 and higher.
For S17 nDAS, the WR was $16.50 and the SD was $441.07; Wong's numbers were $16 and $415.
For S17 DAS, the WR was $20.97 and the SD was $447.82; Wong's numbers were $20 and $421.
For H17 nDAS, the WR was $11.10 and the SD was $442.15; Wong's numbers were $11 and $416.
As you can see, in each case the CVCX WR & SD results are both higher than those Wong found, but the WR for the S17 nDAS game is much less than the $18.27 you found.
As for published sources for simulations and a forum to discuss simulators... that's a toughie. Norm W. (the author of the CVCX software I used) has some information at the link shown below.
I also ran the S17 nDAS version in CVData. Below is some of the output: note that I used $5 units (so all the bet amounts would be integers). Thus, the SD of 88.15 units is $440.75.
Perhaps you can check the Initial Bet Advantage for the various starting hands to see if one or more of the hands differs markedly from the values I obtained. Pay particular attention to the hands where the player has a BJ ("AT") and the dealer's upcard is a 10 or an Ace.
| Hands | $/Hour | Units
W/L | Advan. | Std Dev | Performance | ||||||||||||
| Seat | Played | Skip | % | Action | WinRate | Units
W/L | TBA% | IBA% | SE | Round | Hour | 100 | Shoe | DI | SCORE | N0 | Factor |
| 1 | 410,416,968 | $3,359.22 | $16.38 | 1.3107e7 | 0.488 | 0.558 | 0.04 | 8.82 | 88.15 | 88.15 | 49.7 | 3.72 | 13.82 | 72,374 | .553 | ||
| 2 | |||||||||||||||||
| 3 | |||||||||||||||||
| 4 | |||||||||||||||||
| 5 | |||||||||||||||||
| 6 | |||||||||||||||||
| 7 | |||||||||||||||||
| Seat | Playing Strategy | Betting Strategy |
| 1 | Complete High-Low | Wong's Benchmark Spread |
| 2 | ||
| 3 | ||
| 4 | ||
| 5 | ||
| 6 | ||
| 7 |
| Rounds: 400,000,000 |
| Hands: 410,416,968 |
| Shoes: 12,559,659 |
| Hours: 4,000,000 |
| Player #1: Advantages for each Dealt Hand (IBA) | |||||||||||
| Dealer Up Card | |||||||||||
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Ace | Totals | |
| 2 | See AA | See AA | See AA | See AA | See AA | See AA | See AA | See AA | See AA | See AA | See AA |
| 3 | See A2 | See A2 | See A2 | See A2 | See A2 | See A2 | See A2 | See A2 | See A2 | See A2 | See A2 |
| 4 | See A3 and 22 | See A3 and 22 | See A3 and 22 | See A3 and 22 | See A3 and 22 | See A3 and 22 | See A3 and 22 | See A3 and 22 | See A3 and 22 | See A3 and 22 | See A3 and 22 |
| 5 | -11.83 | -7.94 | -3.54 | 0.64 | 1.66 | -13.34 | -20.60 | -28.69 | -38.63 | -52.00 | -23.02 |
| 6 | -13.04 | -9.24 | -4.79 | 0.07 | 1.18 | -16.60 | -23.73 | -31.32 | -40.76 | -53.49 | -24.91 |
| 7 | -9.06 | -5.74 | -1.41 | 3.08 | 5.72 | -6.58 | -22.34 | -30.01 | -38.73 | -53.18 | -21.92 |
| 8 | -0.39 | 3.45 | 7.72 | 12.43 | 17.40 | 9.71 | -5.86 | -22.06 | -32.07 | -45.03 | -12.45 |
| 9 | 12.26 | 18.33 | 25.46 | 32.70 | 38.73 | 20.62 | 11.49 | -4.89 | -22.48 | -35.54 | 1.23 |
| 10 | 41.88 | 48.05 | 53.13 | 59.66 | 64.51 | 45.72 | 34.03 | 18.77 | -4.69 | -23.94 | 23.63 |
| 11 | 53.28 | 58.03 | 63.86 | 69.06 | 73.02 | 51.19 | 38.96 | 25.74 | 10.74 | -18.04 | 34.09 |
| 12 | -24.87 | -21.72 | -17.80 | -13.14 | -12.90 | -22.82 | -29.05 | -35.99 | -44.44 | -56.11 | -32.22 |
| 13 | -27.28 | -22.53 | -17.98 | -13.27 | -13.16 | -28.78 | -34.43 | -40.23 | -48.58 | -59.30 | -35.29 |
| 14 | -27.30 | -22.82 | -18.05 | -13.23 | -13.32 | -34.43 | -39.08 | -44.85 | -52.58 | -62.63 | -38.03 |
| 15 | -27.39 | -22.89 | -18.13 | -13.32 | -13.29 | -38.89 | -43.88 | -49.46 | -56.19 | -65.40 | -40.51 |
| 16 | -27.44 | -23.11 | -18.27 | -13.22 | -13.67 | -42.45 | -47.19 | -52.24 | -58.04 | -67.53 | -42.06 |
| 17 | -13.79 | -9.88 | -5.56 | -1.66 | 3.15 | -10.15 | -39.15 | -43.15 | -47.36 | -63.08 | -29.43 |
| 18 | 12.80 | 15.98 | 18.92 | 22.03 | 30.08 | 41.69 | 10.52 | -20.07 | -25.48 | -37.88 | -1.39 |
| 19 | 38.88 | 40.60 | 42.68 | 45.31 | 50.87 | 62.99 | 60.20 | 27.50 | -3.59 | -12.19 | 25.58 |
| 20 | See A9 and TT | See A9 and TT | See A9 and TT | See A9 and TT | See A9 and TT | See A9 and TT | See A9 and TT | See A9 and TT | See A9 and TT | See A9 and TT | See A9 and TT |
| 21 | See AT | See AT | See AT | See AT | See AT | See AT | See AT | See AT | See AT | See AT | See AT |
| A2 | 4.66 | 8.28 | 12.79 | 17.65 | 21.85 | 10.07 | 3.39 | -5.91 | -19.21 | -36.73 | -3.66 |
| A3 | 2.34 | 5.49 | 10.04 | 16.58 | 21.14 | 5.48 | -0.78 | -9.76 | -22.74 | -39.54 | -6.75 |
| A4 | 0.06 | 3.14 | 8.02 | 16.45 | 19.73 | 1.29 | -5.41 | -14.14 | -26.32 | -42.40 | -9.73 |
| A5 | -1.82 | 1.63 | 7.44 | 15.90 | 20.26 | -3.09 | -9.46 | -17.70 | -29.36 | -44.77 | -12.18 |
| A6 | 1.47 | 7.90 | 15.14 | 23.02 | 29.09 | 4.50 | -9.28 | -16.83 | -27.69 | -44.80 | -8.53 |
| A7 | 15.17 | 21.24 | 28.74 | 34.48 | 42.36 | 42.18 | 10.78 | -11.09 | -22.59 | -38.09 | 3.35 |
| A8 | 38.97 | 41.55 | 43.79 | 48.87 | 54.24 | 62.95 | 60.60 | 27.71 | -3.71 | -12.63 | 26.15 |
| A9 | 64.16 | 65.03 | 66.88 | 68.95 | 72.38 | 78.11 | 79.98 | 76.56 | 42.49 | 12.98 | 57.62 |
| AT | 150.00 | 150.00 | 150.00 | 150.00 | 150.00 | 150.00 | 150.00 | 150.00 | 138.32 | 102.52 | 142.58 |
| AA | 53.93 | 59.20 | 63.93 | 70.12 | 74.56 | 52.31 | 39.96 | 27.16 | 12.26 | -18.37 | 35.66 |
| 22 | -10.22 | -5.21 | 0.88 | 11.54 | 14.81 | -5.67 | -17.75 | -25.37 | -35.89 | -49.53 | -18.47 |
| 33 | -13.32 | -8.25 | -1.21 | 7.57 | 10.12 | -13.38 | -23.79 | -31.76 | -40.51 | -53.40 | -23.07 |
| 44 | -0.51 | 3.49 | 6.47 | 11.84 | 18.62 | 9.76 | -5.57 | -22.20 | -31.76 | -44.45 | -12.35 |
| 55 | 42.23 | 46.33 | 53.79 | 60.37 | 65.49 | 45.76 | 34.75 | 18.97 | -4.42 | -23.38 | 23.79 |
| 66 | -21.91 | -15.82 | -7.52 | 1.73 | 2.76 | -23.24 | -29.53 | -36.47 | -44.68 | -56.63 | -28.98 |
| 77 | -15.83 | -7.78 | 0.27 | 7.92 | 14.43 | -9.93 | -40.19 | -45.47 | -53.50 | -63.51 | -29.83 |
| 88 | 5.51 | 12.33 | 18.07 | 26.35 | 35.14 | 29.47 | -6.72 | -42.84 | -54.79 | -55.81 | -16.58 |
| 99 | 19.99 | 25.28 | 34.21 | 41.65 | 47.72 | 41.56 | 22.90 | -8.66 | -25.42 | -37.50 | 5.55 |
| TT | 63.86 | 65.08 | 66.80 | 69.38 | 72.67 | 77.95 | 79.77 | 75.96 | 42.44 | 13.41 | 57.61 |
| Tot | 12.07 | 15.69 | 19.78 | 24.26 | 27.02 | 16.08 | 7.04 | -3.27 | -17.20 | -33.57 | 0.56 |
Hope this helps!
Dog Hand
"As for published sources for simulations and a forum to discuss simulators... that's a toughie."
No, not so tough. Advantageplayer.com has a free forum at "Computers for Counters," and Don's Domain, housed at the same site, and which is also free for those who have BJA3, has "Software & Simulations," where Norm is the primary contributor.
Don
