Posted by Pete Moss on 22 Oct 1997, at 12:01 p.m.
I've just done some research into the costs of cover betting and preferential shuffling. The sims used the count system I use in the casinos, and were done for a single deck game, H17, DOA. Each sim comprised at least 15 million rounds of play. Although the system I use is not available to the public, you may find the results interesting. Be aware though that your mileage may vary. As a basis of comparison, here is how the system does with 65% penetration, and no cover except for the bet spread constraint.
Spread 1 to 5
Bankroll $10000
Optimal unit size 0.5295% of bank = $52.9550
Average bet 0.9305% of bank = $93.05
Return per hand 0.0194% of bank = $1.94
7159 Rounds to double bankSpread 1 to 4
Bankroll $10000
Optimal unit size 0.5634% of bank = $56.34
Average bet 0.9078% of bank = $90.78
Return per hand 0.0165% of bank = $1.65
8423 Rounds to double bankSpread 1 to 3
Bankroll $10000
Optimal unit size 0.5890% of bank = $58.90
Average bet 0.8486% of bank = $84.86
Return per hand 0.0124% of bank = $1.24
11146 Rounds to double bankBy the way, the above numbers are quite good, I blush to say. The decent numbers for the 1-3 spread are due in large part to good playing efficiency.
In another simulation with 65% penetration, I imposed the following betting "cover":
1. Never more than double the bet from previous round.
2. Never more than half the bet from previous round.
3. Do not change bets after pushes.
4. Do not reduce bet coming off the top after a win.I only simulated a 1-5 spread. I had to guess at the optimal unit size,
because with the cover betting, my software is not set up to calculate
it. I put it at .4% of bankroll. I also used a simple betting schedule
that I guessed was about right.The result was...
9508 Rounds to double bank.
Compare that with the 7159 above with no cover.
In the next simulation, the dealer used a preferential shuffle against one player at the table. He would shuffle at 60% penetration or greater if the player had an advantage (based on the count system I use), but deal again if the player was at a disadvantage and at least 13 cards (25%) remained. I guess I should have simmed this for very large bet spreads, given the circumstances, but I didn't. The bet spread constraint was the only cover used. Here are the numbers. I find them surprisingly good. Much better than I expected, and indeed, much better than a typical shoe game with a rather large bet spread. Fifteen million rounds were simulated.
Spread 1 to 5
Bankroll $10000
Optimal unit size 0.4293% of bank = $42.90
Average bet 0.7469% of bank = $74.69
Return per hand 0.0127% of bank = $1.27
10951 Rounds to double bankSpread 1 to 6
Bankroll $10000
Optimal unit size 0.4102% of bank = $41.02
Average bet 0.7638% of bank = $76.38
Return per hand 0.0145% of bank = $1.45
9532 Rounds to double bankNotice that these games have about the same value to the player:
1. 65% pen. no-cover 1-3 spread
2. 65% penetration game with cover betting and a 1-5 spread
3. preferential shuffle game with a 1-5 or 1-6 spread.