Calculating Non-Card Counting Player Advantage from Wins, Losses

I asked the following on the free message boards of Dr. Wong's BJ21.com, and I have not yet obtained a good answer.

I am interested in calculating player advantage for my blackjack 'system,' which involves no card counting and no kind of progression whatsoever. Is the following a valid method: net $ won or lost divided by total $ placed in action, expressed as a percentage.

For example, if I play, say, 574 hands, and I hypothetically bet the table maximum (say, $5,000 - what I actually saw in Tunica this weekend at Harrah's High Limit, for example) on 287 of those hands that I thought I would win and, for the other 287 hands (the ones that I predicted I would lose), I bet the table minimum: $50.

Let's say I did well and came up with these results: For the $5,000 bets, I won 19 units = +$95,000. For the $50 bets, I lost 16.5 units = -$825.

So, is the following correct to calculate advantage: $95,000-$825/(287 X $5,000 + 287 X $50) = $94,175/1449350=0.0649774, or 6.50% player advantage?

Assuming the above is correct, won't player advantage vary based on bet size? I mean, let's say we keep the minimum bet ($50) the same for those hands we predict we are going to lose, but instead of betting $5,000 on the 'good' hands, we bet $100 instead. Won't our player advantage go way down (to about 2.50%) even though we were still correct with our predictions but using a much smaller bankroll? So, then, is player advantage a function of the amount of spread between bets?

I ask the above in part due to the Wizard's neat post about advantage and reaching $1,000,000. Within the context of discussing shady 'system' sellers, the Wizard of Odds posted the results of a fascinating computer sim whereby the player had a 1% advantage with a starting bankroll of $100 and another player with the same 1% advantage but starting with a bankroll of $1000. He did the same sims for a player with a 2% advantage and a starting bankroll of $100 and another player with a 2% advantage and a starting bankroll of $1000. Here is part of the text from Wizard of Oddsregarding the results in terms of "grinding" your way to $1,000,000:

"System salesmen usually promise ridiculous advantages. For example, even with just a 1% advantage on an even money bet, it would not be difficult to parlay $100 into $1,000,000 by betting in proportion to bankroll. I was asked to prove this claim so I wrote a computer simulation based on the toss of a biased coin, with a 50.5% chance of winning. At all times the player bet 1% of his bankroll, rounded down to the nearest dollar. However, if a winning bet would put the player over $1,000,000 then he only bet as much as he needed to get to exactly $1,000,000. In addition, I ran simulations with a 2% advantage and for a starting bankroll of $1,000. Following are the results of all four tests.

$100 Bankroll, 1% Advantage

Bets won = 7,182,811,698 (50.4999%)
Bets lost = 7,040,599,544 (49.5001%)
Player achieved $1,000,000 first = 79,438 (83.019%)
Player went bust first = 16,249 (16.981%)
Average number of bets to reach $1,000,000 = 174,972 (364.5 days at 8 hours per day, 60 bets per hour)

$100 Bankroll, 2% Advantage

Bets won = 7,027,117,205 (51.0000%)
Bets lost = 6,751,539,769 (49.0000%)
Player achieved $1,000,000 first = 215,702 (98.099%)
Player went bust first = 4,180 (1.901%)
Average number of bets to reach $1,000,000 = 63,775 (132.9 days at 8 hours per day, 60 bets per hour)

$1,000 Bankroll, 1% Advantage

Bets won = 5,213,026,190 (50.4999%)
Bets lost = 5,109,817,544 (49.5001%)
Player achieved $1,000,000 first = 74,818 (99.0285%)
Player went bust first = 734 (0.9715%)
Average number of bets to reach $1,000,000 = 137,208 (285.8 days at 8 hours per day, 60 bets per hour)

$1,000 Bankroll, 2% Advantage

Bets won = 6,332,837,070 (50.9996%)
Bets lost = 6,084,596,671 (49.0004%)
Player achieved $1,000,000 first = 267,445 (99.9996%)
Player went bust first = 1 (0.0004%)
Average number of bets to reach $1,000,000 = 46,428 (96.7 days at 8 hours per day, 60 bets per hour)
These simulations prove that with just a small advantage of as little as 1% and a bankroll of as little as $100 you can grind your way to a million dollars through the gambling equivalent of compound interest. Yet you never hear of this actually happening. Could it be that these gambling systems don’t work after all?!"

player's advantage shouldn't involve bet size.
just count the number of hands win or lose, flat bet.

If you measure your edge in expectation, then it does depend on bet size. That's most of the point of card-counting. You make more money by betting more money when you have a stronger advantage.

If you want to measure your player advantage as a % over all your action, feel free. However, I don't really see the point... what could you compare it to?

I like to measure my edges in $/hr, so I know whether it's worth it to pursue, versus, say, working.

deleted

OK, and how does one "measure your edge in expectation?"

" I mean, let's say we keep the minimum bet ($50) the same for those hands we predict we are going to lose,"

I suggest we bet nothing on the hands we predict we are going to lose !

Quote: Overkill

For example, if I play, say, 574 hands, and I hypothetically bet the table maximum (say, $5,000 - what I actually saw in Tunica this weekend at Harrah's High Limit, for example) on 287 of those hands that I thought I would win and, for the other 287 hands (the ones that I predicted I would lose), I bet the table minimum: $50.

Let's say I did well and came up with these results: For the $5,000 bets, I won 19 units = +$95,000. For the $50 bets, I lost 16.5 units = -$825.

A simple way of calculating your sample expectation is to take your profit $94175, and divide by the number of hands. Your sample expectation is $164.07 per hand. If you bet less, it would be less.

When we talk about actual player advantage, it is a theoretical expectation based on knowledge of the distribution of cards and outcomes based on those distributions. Then our profit depends on how much we bet in those situations.

Since you are not actually claiming to use or alter the house edge inherent to BJ, your true advantage is negative... the house still has the edge.

Advantage % on one hand is a function of the distribution of the cards and rules of the game. Advantage % on MANY hands is a function of those two things, plus how much you bet is various situations.

I too bet more when I think I am going to win and less or nothing when I think I am going to lose. That is the basis of card counting. But those times that I 'think' I am going to win or lose are based on something....the remaining make up of the deck, which I know if it is or isn't in my favor by card counting. There are other methods for determining the remaining make-up of cards yet to be played, shuffle-tracking among others. (which I have not mastered), but you have to have some method of knowing the makeup of the remaining cards. You claim, your method is not card counting but offer no such clue as to what it might be. That is your right, but it is hard to take you seriously without more information. What is it that determines whether you are betting big or small?

Now, as I said on the other site, 576 trials is completely meaningless. To have any kind of significant meaning you need to have a million trials. That is what computer simulations are for. But you say you are unable to run computer simulation of your system. Without that you have insignificant short-term positive variance. Completely meaningless.

The difficulty you are having on the other site, comes from your terminology. Your advantage or disadvantage is determined by the rules of the game. What you are trying to figure out is NOT your advantage but your win rate or expected win, which is how you overcome this initial dis-advantage by wagering more in advantageous situations and less or nothing in dis-advantageous situations, which again, you haven't disclosed. ??