I've done some searching, but can't seem to find the formula or equation for calculating a player's advantage. If I remember correctly, the one I saw incorporated the players # of wins and losses and perhaps also bet sizes?
Can someone please post a reply containing at least one method of calculating player advantage?
The first thing to do is to find out the advantage off the top which depends very much on the rule variations. In fact it is almost systematically a disadvantage for the player ranging from -0.2 to -1.5 %, typically it's -0.5%. Now if you have any idea about card counting, it's quite easy to roughly figure out the advantage situation for the following round. Just figure half a percent of ev in favour of the player for every TC-unit. That's all you need to know to get started.
Francis Salmon
is the basic strategy expectation if he plays perfect basic strategy. If he plays less than perfect he can define the alternative strategy he plans to use and then look up the cost of each error (deviation from basic strategy) in a book like Professional Blackjack or Blackjack Attack. Add up the errors and add that to the basic strategy house advantage and that is his disadvantage without counting.
Google: BJ advantage calculator.
Does it sound like OK is lookIng for the empirical calculation, which I think would be net $ won/loss divided by total $ placed in action, expressed as a percentage? Other than a short term personal performance metric, using his personal history wouldn't be very useful unless you were totaling up what, about a million hands, and the data was for a specific set of game conditions.
Yes, Intermediate, that's what I was looking for - the kind of equation you provided. But I am confused, which isn't surprising:). Did I incorrectly apply said formula below?
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 am simply looking for a method to gauge the efficaciousness or power or effectiveness of my strategy - in part so I can reference The Wizards of Odd's computer sim to see how long it might take my strategy to reach a profit of $1,000,000 (see above).
Does "Intermediate's" (please see above) formula look correct, and, if so, did I apply it correctly (to my short-term results) to obtain my advantage figures in my post "Please check out this example..." above?
It seems to me that we are confusing advantage with the win rate. The win rate will be influenced by the bet sizes that are place at various TCs. The advantage is a result of TC.
Your calculation is correct in your example, but be careful about calling it your advantage. If you were simulating a particular combination of rules, penetration, betting schedule, and statistically driven outcomes for different hands, and ran a gazillion hands to similate the long run, then you could say playing in that situation has that advantage. Tallying that figure over a small number of hands just tells you the performance of the short term sample, like saying your stock find grew by 6% over the last 12 months.
The difference between what you bet in winning situations and what you bet in losing situations is a strong driver of performance, so your observation about the impact of varying your bets is directionally correct. Others have already simulated how bet spread affects your expectation. I would reccommend you pick up Blackjack Attack v3 or software like CVCX to really understand your advantage.
"So, then, is player advantage a function of the amount of spread between bets?"
Advantage. Generally used to describe a player's expected value in a game, it can also be used to describe the casino's expected value as well. It is most often expressed in terms of percentage. A player may be said to have a 1% advantage in a certain game. This means that the player can expect to have a 1% return on all of the money bet in that game.
Win rate. The speed at which one is expected to win, commonly expressed as a percentage (in which case it is identical to the theoretical player's advantage), or in dollars per hour or per a specified number of hands. Distinction must always be made between theoretical Win Rate (which is derived through calculation) and actual win Rate, which is obtained from the data of actual play. From the casino's perspective, Win Rate can mean, depending upon the context, the theoretical House Edge, which is expressed in percentage terms, or it can mean the amount of dollars that the house expects (theoretical WR) or actually wins (actual WR) per unit of time.
I think you should look at it as win rate. The more you spread the bets the higher the return. Refer to charts in BJA3. He shows hourly return on various betting strategies and bet spreads. In your first example you showed a spread of 1-100. In your second example you showed a spread of 1-2. However more trials would be in order.
