Blackjack House Edge with standard deviation pertaining to Theoretical Win

I work in a casino that I believe is incorrectly rating players on blackjack. If the formula to calculate the theoretical win goes like this:

Average Bet X Bets Per Hour X Total Time Played X House Edge = Theoretical Win

It would be in the casino's best interest to know the correct numbers for that formula. Average Bet and Time Played are monitored by the floor personnel. It's the Bets Per Hour and House Edge that seem to be kept at the "standard" we've been told. At present, they're using 60 Hands Per Hour and a House Edge of 2%.

My question is, how do I figure the actual house edge including standard deviation?

Blackjack rules here are: Dealer hits soft 17, player can double on any two cards, player can double after split, player can split up to 4 times, player can resplit aces, blackjack pays 3:2, no surrender, no hitting split aces. We use 2, 4, 6, and 8 deck shoes.

I'll tackle the fact that most of the dealers here are not reaching that 60 rounds per hour number at a later time. For now, I'm just trying to show that our edge is not 2%. And maybe I'm wrong. If I am, I'd like to know.

2% sounds way wrong unless you are factoring in realistic, non-basic strategy play

Incidentally, is rating as shoddy in the US as in my UK local, where I see the dealer punch in table min as my betting level, regardless of the fact that my smallest chip is much bigger? Seems to be quantized to 3 levels on the tablet display he enters it on.

I think that 2% is wrong even if we factored in realistic, non-basic strategy play. Which is exactly why I'm asking how to better calculate it. The calculator at WizardOfOdds shows our realistic house edge with basic strategy and a cut card at 0.40% for 2 Deck, 0.53% for 4 Deck, 0.57% for 6 Deck, and 0.59% for 8 Deck.

As far as your question about betting minimum ratings, I can't speak for all US casinos. At this particular casino, the table minimum and maximum are posted at the table and the individual player's bets are monitored by floor personnel and written on a clipboard. That data is later entered into the computer.

I think the player's skill level is also imputed when the floor is closing out the player.

2% sounds sort of reasonable if you're offering 6:5 BJ.

Quote: Donuts

2% sounds sort of reasonable if you're offering 6:5 BJ.

This isn't the first time I've heard this 2% figure. I was shocked at how large it was at first, but if you've spent any considerable amount of time at blackjack tables you'll probably understand that "on average" this is probably about the houses edge. At a full table, how many players actually play perfect basic strategy? 1... if you're lucky? Now how often do you see people standing on every bust hand, hitting 12's-15's to dealer 6's, splitting 10's to anything, doubling hard 6 vs dealer 5, splitting 5's instead of doubling, etc, etc... I can tell you I personally see people do stupid stuff like this at pretty much every table I play at. I believe they're playing at MORE than a 2% house edge, which is why the 2% "on average" doesn't seem all that far off (even though it does have some initial shock value).

The hands per hour is going to vary wildly on the dealer, # of decks, how fast/slow the players play, etc. There's so many calculations that go in to it that you kind of need to take an 'average.' The only better way to calculate this would be to compile data on every dealer and then apply their averages to their shifts (accounting for the breaker/etc). i.e. not worth it.

One problem I see is the hands per hour estimate. I often play over 200 hands per hour but feel that if I were to play rated the 60 hands per hour figure would be used. That's not a problem for the casino but for the player. Of course that doesn't change the house edge but would shortchange comps.

Romes and 1BB bring up good points. 60 hands per hour and a 2% house edge are probably conservative in favor of the house. Realistically the average player can probably play faster than that, but without perfect play. I've never seen a non-counter with perfect basic. They're almost always taking even money and missing key doubles, both of which are pretty detrimental to your advantage.

In short, you're getting comped for less than you deserve based on what you're actually giving the casino, which makes sense if they want a buffer.