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Is This Game Rigged? Part 3

Many casinos that run on Unified Gaming software have a great single-deck Blackjack game where the player who uses only Basic Strategy can get a small (about 0.14%) edge over the 'house'. It used to be a lot bigger, but the rules were changed some time ago, yet despite that, the question has lingered: Is this an honest game?

I was contacted by a reader who has recently (May, 2001) played over 144,000 hands of single-deck Blackjack for real $$$ at several U.G.-powered casinos and s/he wanted to share the data with all of you to help put this issue to rest. Now you need to bear in mind that 144,000 hands of Blackjack is too small a sample to allow us to draw any absolute conclusions, but this is the first sample of real-money play, to my knowledge, of this size and it tells a very interesting story. Ideally, a sample like this would show the frequency of the cards, show the dealer's ending hands, etc., like I outlined in the first part of this series, but we'll go with what we've got. And what we've got is 144,000 hands of Blackjack, played for real $$$, with a net win for the player. From a percentage point of view, based upon the total initial bets, the player's edge was 0.30% which is somewhat above the expected 0.14% and, while that's not conclusive proof of an honest game, if these guys are cheating, they're doing a lousy job of it.

While I'm at it, let me address another topic that has generated a lot of discussion and that's robot players. The data you see here was generated by a *gasp* robot! Yes, Viriginia...there is a Santa Claus and there is such a thing as robot Blackjack players. I have seen it, used it (in the play-money mode only) and have been completely enthralled by the experience. I have said many times that the technology of the Web and computers in general fascinates me to no end and I'm completely amazed that there are people out there that can create stuff like this. This 'bot (in very hip techno-speak) is one of the slickest things I've ever seen. Comparing this with the crude computers some counters used back in the early '80s is like comparing the Space Shuttle to Flash Gordon. My hands were literally shaking as I fired this baby up and watched it do its "thing." I sat here with my chin on the ground, rapt in amazement, as it dutifully went to work. In case you're wondering: no, it's not for sale, and, no, I won't send you a copy of it.

I'm sure the casinos that have hosted this 'bot would freak out if they knew what has happened to them, but what they should do is thank the reader who created it, and then decided to share the data from its play, because this just might be the device that will prove their game is honest. That ultimately has got to be worth a lot of $$$; far more than what this player will ever make from it.

For those of you who aren't quite up to speed on this situation, let me give you some background information. The Blackjack game we're talking about is, as I mentioned, dealt from a single-deck and the cards are shuffled after every hand, so no advantage can be gained from counting the cards. Any player advantage comes from the very liberal rules: the dealer stands on A-6, you may double on any first two cards, double after splitting pairs and 'late' surrender is available against a dealer's up card of 10. That, and a few other player options, adds up to an advantage for the player who uses perfect Basic Strategy. Well, you don't need a robot to play perfectly, since you can do that at home on your own. But the 'bot does it more quickly. How quickly, I won't say, but fast, accurate play is the way you get samples like the one we're going to discuss here.

The player who created the 'bot played Blackjack only at the $1-$10 table and s/he bet only $1 per hand. That brings us to another part of the argument, which is, you can do pretty good at the $1 table, but it's the $25 games that are rigged. From a personal point of view, I don't think that's the case, although it's possible. Anyone care to finance a test? About $36,000 ought to cover it. In a 100,000-hand trial, you'd expect to make about $3500 and a four standard deviation move to the minus side would basically wipe you out. Yeah, I know...if I'm so sure the game is honest, why don't I do it myself?

Let's move on. What you'll see in the table below is 36 playing sessions that range from 64 to 17,008 hands in length. The player began with $200 and rang up a $439.50 profit, which translates into an edge of 0.30+% on the initial bets and an edge of 0.266% on the total bets made. The "total bets" amount includes the extra bets made for pair splits and doubles. You will see that after session #13, the creator adjusted the 'bot to give a better long-term return by incorporating some of the composition-dependent plays shown in the strategy for the game at www.thewizardofodds.com website, and by surrendering 15 vs. 10.

At the end of session 13, the 'bot had played 37,290 hands, bet a total of $43,244 and was left with a $15 loss. Now, imagine that you had played this game at a rate of 200 hands per hour. You would have played for 186 hours and not made a dime! No wonder people think the game is rigged. But that's how it is at Blackjack and there's nothing you or I can do to change it.

Okay, with no further fuss, here are the stats, but meet me down below, because I want to make some comments:

Session	Hands	Total bets	Win/loss	Return	Ending bal	Cumul. Bets	Cumul. W/L	% return
1.	200	225.00	-15.00	-6.70%	185.00	225.00	-15.00	-6.70%
2.	335	375.00	-15.00	-4.00%	170.00	600.00	-30.00	-5.00%
3.	693	800.00	-26.50	-3.31%	143.50	1400.00	-56.50	-7.06%
4.	69	79.00	+12.00	+15.19%	155.50	1479.00	-44.50	-3.00%
5.	64	73.00	+2.00	+2.74%	157.50	1552.00	-42.50	-2.73%
6.	701	850.00	+47.00	+5.52%	204.50	2402.00	+4.50	+0.18%
7.	17008	19361.00	-100.00	-0.52%	104.50	21763.00	-95.50	-0.493%
8.	621	706.00	+3.00	+0.42%	107.50	22469.00	-92.50	-0.411%
9.	1951	2233.00	-2.00	-0.09%	105.50	24702.00	-94.50	-0.383%
10.	9003	11000.00	+82.50	+0.75%	188.00	35702.00	-12.00	-0.034%
11.	3832	4378.00	+85.50	+1.95%	273.50	40080.00	+73.50	+0.183%
12.	1491	1680.00	-26.00	-1.55%	247.50	41760.00	+47.50	+0.113%
13.	1322	1484.00	-62.50	-4.21%	185.00	43244.00	-15.00	-0.0003%

# Bot logic change from here on out: fixed one of the wiz's critical errors. And now using hand composition exceptions.

# The old logic above was netting only about 0.115% in 20+ separate 50 million hand simulations. New logic should return about 0.14% now.

Session	Hands	Total bets	Win/loss	Return	Ending bal	Cumul. Bets	Cumul. W/L	% return
14.	13007	14779.00	-82.50	-0.56%	102.50	58023.00	-97.50	-0.168%
15.	1708	1991.00	+22.00	+1.10%	124.50	60014.00	-75.50	-0.126%
16.	1083	1253.00	+38.50	+3.07%	163.00	61267.00	-37.00	-0.060%
17.	6083	6903.00	-103.00	-1.49%	60.00	68170.00	-140.00	-0.205%
18.	3001	3421.00	+34.00	+0.99%	94.00	71591.00	-106.00	-0.148%
19.	605	682.00	+17.00	+2.49%	111.00	72273.00	-89.00	-0.123%
20.	11289	12797.00	+15.00	+0.12%	126.00	85070.00	-74.00	-0.086%
21.	15541	17644.00	+46.00	+0.26%	172.00	102,714.00	-28.00	-0.027%
22.	1053	1184.00	+57.50	+4.86%	229.50	103898.00	+29.50	+0.028%
23.	9804	11108.00	+218.00	+1.96%	447.50	115006.00	+247.50	+0.215%
24.	435	487.00	+12.50	+2.57%	460.00	115493.00	+260.00	+0.225%
25.	2645	2993.00	+35.50	+1.19%	495.50	118486.00	+295.50	+0.249%
26.	426	481.00	+13.50	+2.80%	509.00	118967.00	+309.00	+0.260%
27.	7602	8608.00	+206.50	+2.40%	715.50	127575.00	+515.50	+0.404%
28.	9630	10971.00	+28.50	+0.26%	744.00	138546.00	+544.00	+0.393%
29.	293	331.00	-37.00	-11.18%	707.00	138877.00	+507.00	+0.365%
30.	1149	1290.00	+41.50	+3.22%	748.50	140167.00	+548.50	+0.391%
31.	678	776.00	+48.50	+6.25%	797.00	140943.00	+597.00	+0.426%
32.	1060	1202.00	-68.00	-5.65%	729.00	142145.00	+529.00	+0.372%
33.	1298	1469.00	+59.00	+4.02%	788.00	143614.00	+588.00	+0.409%
34.	766	860.00	-13.00	-1.51%	775.00	144474.00	+575.00	+0.398%
35.	16043	18263.00	-197.00	-1.08%	578.00	162737.00	+378.00	+0.232%
36.	2220	2551.00	+61.50	+2.41%	639.50	165288.00	+439.50	+0.266%

I highlighted session #29 because, as I have often said, a "bad" session may find you losing at a rate of 15% of all the $$$ you bet. Now here is a 'machine' that plays perfectly and it lost over 11% at what is, presumably, a fair game. At that point, the 'bot was winning well above expectation, so it shouldn't be a surprise that the gods of expectation got even with our little digital friend. Session #29 is a 2SD result (about a 1 in 20 occurrence), which is quite normal.

Overall, this expectation for this trial was to win $202.50, so the result is about 0.5 SD above that; not at all unusual. Even if the trial had ended with a $600 loss, it could still be said that the game is "fair", but it sure makes a better argument when it ends with a win. But let's not kid ourselves here, because this profit could also be a "positive variance" of a non-random game. However, I want to reiterate what I said earlier: If these guys are cheating, they're doing a lousy job of it.

I also want to repeat something else that I often say: Here at GameMaster Online, we have the best, the smartest and the most generous readers on the 'Net and the person who contributed this information is a prime example. Thanks to...(you know who you are).

See you here next time.

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