Attempting a Fair Comparison with OPP

The Easy OPP Count vs. Other Card Counting Systems

by ETFan
[From Blackjack Forum Vol. XXV #1, Winter 2005/06]
© 2005 ETFan

Carlos Zilzer has done a fine job putting forth an idea for a new blackjack card counting system and running preliminary sims to test different approaches. He is not selling a book; he is not charging hundreds of dollars for a seminar. He set forth an idea in its formative stages to allow others to aid in its development.

I feel it’s grossly unfair to compare the easy OPP card counting system for recreational players to a full blown professional card counting system with indices, true count conversions and optimal betting ramps that took months and often years to develop for other systems. In particular, it’s well known that indices play a crucial role in one and two deck games with good penetration. There hasn’t even been time to develop indices for the OPP, yet this is the comparison repeatedly urged by one expert who certainly knows better.

Carlos Zilzer is working on developing indices for the OPP. In particular, I think the Counters Basic Strategy would be a good addition to OPP, well suited to the spirit of the count, along with the insurance index.  But to compare apples to apples, I decided to sim Hi-Lo with no indices, no true count conversions, and a bet ramp similar to the one MathProf used in his OPP sim. Here are the results:

The -20 bucket includes all results below RC = -20; the +20 bocket includes all results above +20. There is 1 player. Bet = 1 unit at RC = +1 and below, then 2, 4, 6, 8, and finally 10 units at RC = +6 and above. 1,000,000,000 rounds were simmed.

Bankroll? (default = $10,000)
1: $.0298882/$2.41872 = 1.235701%  var = 16.8634  score = 52.9728  ROR = 4.031056e-16

The SCORE of about 53 is naturally a far cry from the 107 you get with indices. However, bending over backwards to be fair, let’s note that Hi-Lo has a definite 0.45% positive advantage at RC = +1, whereas OPP doesn’t really kick in until +2. So let’s give Hi-Lo a ramp that moves up quicker, even though this is slightly weaker from a cover standpoint. Let’s try 1 unit at 0 and below, then 2, 4, 6, 8 and finally 10 units at +5 and above. Same 10:1 bet ratio, different distribution. This returns the following:

Bankroll? (default = $10,000)
1: $.0367128/$2.97817 = 1.232727%  var = 23.7286  score = 56.8018  ROR = 3.641082e-14

The SCORE MathProf reported for his OPP sim was 42.8, giving an OPP/Hi-Lo SCORE ratio of 80.8% in the first case, and 75.4% in the second case. Pretty darn close to the 70-75% reported by the promoters of Speed Count.

But there’s more to the story. A basic strategist gives 0.256% to the house in this game. Clearly, part of the work Hi-Lo and OPP do is used just to overcome that house edge! After some thought, I came to the conclusion the fairest way to incorporate this factor is to use the negative win rate of a basic strategist using the same ramp needed to obtain each SCORE — but uncorrelated to the count — as a negative SCORE. To do this you pick a unit size equal to the average bet of a player whose win rate per 100 rounds equals his SCORE and input that as a flat bet at all running counts.

For the 1, 2, 4, 6, 8, 10 ramp, under Hi-Lo the average bet works out to be $42.87, and for the 2, 4, 6, 8, 10 ramp, it’s $46.08. The first uncorrelated ramp loses $10.98 per 100 rounds, the second loses $11.81 per 100 rounds.

With MathProf’s figures, the OPP average bet will be $40.44, which loses $10.36 per 100 when uncorrelated.

So my best guess at a fair OPP/Hi-Lo power ratio is: [42.8 – (-10.36)] / [52.97 – (-10.98)] = 83% or [42.8 – (-10.36)] / [56.80 – (-11.81)] = 77%, depending on which ramp you allow for Hi-Lo.

People can disagree on precisely what constitutes a “fair” comparison, but one thing is clear: 40% isn’t in the ballpark.

Another Comparison of the Easy OPP Count

I was curious to see how much of the drop in Hi-Lo SCORE was due to lack of indices, and how much to lack of TC conversions. So I ran another sim with TC conversion, which came out like this:

1 player. Ramp: 1, 2, 4, 6, 8, 10 (at TC = +6), 1,000,000,000 rounds simmed.

Bankroll? (default = $10,000)
1: $.0268089/$2.07617 = 1.291269% var = 13.17492 score = 54.552 ROR = 2.116262e-18

And for the 2, 4, 6, 8, 10 (at TC = +5) ramp:

Bankroll? (default = $10,000)
1: $.0331026/$2.5196 = 1.313804%  var = 18.1565  score = 60.352  ROR = 1.458947e-16

So even if you add TC conversion to Hi-Lo, and not to OPP (and I can’t imagine why you would) you get a OPP/Hi-Lo power ratio of 71% to 81% depending on which ramp and methodology you choose.

Finally, I was surprised enough at the low SCOREs for Hi-Lo without indices that I ran a short 100,000,000 round sim with Hi-Lo plus indices and TC conversions. I got a SCORE of 111, in good agreement (for the small sample) with the 107 reported by some other guy. ♠