A new table leads us to learn why $5 blackjack tables are rare (1 Viewer)

dennis63

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Getting a new blackjack table with "Key West" on the layout was a great conversation starter. The other day, while sitting at the table, my father -- who is 88 -- asked an intriguing question about the game.

He goes to the casinos regularly, and could not understand why he sees a waiting line at a $10 blackjack table, and a dealer standing idly at a $25 table.

"Why don't they just open another $10 table and let people play?" he asked.

I assured him that the casinos have already "done the math" and had a good reason for not opening that second $10 table. I also know that they've certainly calculated the exact time that needs to pass before some of the people standing in the $10 table line break down and walk over to the $25 table.

He was not satisfied with this answer. At 88, he is rarely satisfied with why anyone does anything these days. So I decided to look into it a bit further.

Clearly, it has something to do with the table limits and the house advantage -- the percentage of hands (and money) the casino is likely to win over time.

What we know:

Table dealers are paid by the hour. The casino also has to pay the "floor," and a pit boss.
The casino advantage on a standard eight-deck shoe is 0.430 % to 0.446% (from The Wizard of Odds). That means they'll win less than one-half of one percent more of the games played, and presumably, the total amount bet in all the hands by all the players, than they lose.
Professional dealers are required to deal between 200 and 300 hands per hour, including the dealer's hand, and shuffling.

If we assume most people will place the minimum bet, we can calculate the house "win' over the course of an average hour.

For a $5 table
$5 x 200 hands x (house advantage - 0.00430) = $4.30
$5 x 300 hands x (house advantage - 0.00430) = $6.45
$5 x 200 hands x (house advantage - 0.00446) = $4.46
$5 x 300 hands x (house advantage - 0.00446) = $6.69

For a $10 table:
$10 x 200 hands x (house advantage - 0.00430) = $8.60
$10 x 300 hands x (house advantage - 0.00430) = $12.90
$10 x 200 hands x (house advantage - 0.00446) = $8.92
$10 x 300 hands x (house advantage - 0.00446) = $13.38

For a $25 table:
$25 x 200 hands x (house advantage - 0.00430) = $21.50
$25 x 300 hands x (house advantage - 0.00430) = $32.25
$25 x $200 hands x (house advantage - 0.00446) = $22.30
$25 x 300 hands x (house advantage - 0.00446) = $33.45

So, on a $5 table, the casino can expect an average hourly "win" of between $4.30 and $6.69 -- not even the minimum wage paid to the dealer.

And on a $10 table, the average hourly win for the casino will be only $8.60 to $13.38. I can understand why some casinos would hesitate to even wager for such a small win.

To me, this explains why I see more $25 tables these days.

For the record, I've assumed that people play according to basic strategy. One maniac can be a bonanza for the casino. And the Wizard of Odds says the more likely and "realistic" number is the higher house advantage. And I'm sure we've all bet $10 or $20 or even $50 at a $10 table, so the actual average bet per hand is probably higher than the low limit.

Now, convincing my dad will be more difficult than algebra.
 
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Psypher1000

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I'm not sure if your hands/hour takes into account all the time when there's no action on the table. If so, very well. If not, then the dealer w/no action at the $25 table is even further upside down than the dealer with full action at the $5 table (since he would be making 0 revenue instead of "more than nothing"), and the rates/edges/takes listed above wouldn't necessarily account for the decision.

That being said, I'm sure that math plays a heavy factor in the decision, regardless of the specific numbers involved. I'm sure there's a psychological element that comes into play somewhere, too. Ultimately it's one of those things where your dad would have to trust that the casinos know what they're doing because I'm *sure* that someone on a casino staff has asked that question before and has either done the math or actively experimented with it. It's not like the casinos just started 10-20 years ago and it's their business to maximize sustained profit on the floor, so if there's something they thought could make them extra money, the merits would absolutely be weighed and the idea actioned accordingly.
 

trever

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Casinos want you to play up. $5 players will play for $10. Simple as that.
 

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You made a mistake in your calculation - those are the earnings per player, not per table. Multiple by the number of players.

However, you've also missed a bunch of costs - floor security, overhead security, cashiers - utilization goes up for everything.

You also need to consider the potential lost revenue if a couple players walk in who are willing to play $25/hand (or even much more), but who can't find a seat, because the open $25 table has been converted to $10 or $5 and is now full. A single person betting $50/hand (not uncommon) generate more than a full table betting $5/hand.

The casinos are opening up tables in anticipation of the expected crowd in the next hour or two, not always chasing the crowd that's already standing there.
 

beaver

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I alone lose a lot more than $6.69 an hour at a $5 table.... Those are the odds when assuming optimal play, which isn't how most players play. The casino is actually making a lot more than ~.5%.
 

dennis63

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You made a mistake in your calculation - those are the earnings per player, not per table. Multiple by the number of players.

Actually, it's not earnings per player or table. It's the dealing pace expected of a professional dealer -- the "number of hands dealt." (200 hands per hour at a "break-in casino," and 300 hands per hour at a casino on the Las Vegas strip, according to the dealer video from Heather at VegasAces.) The casino advantage should translate into that percentage above 50 percent of hands won by the casino. This should be the same as the percentage (above 50 percent) of all bets placed at the table.

Two hundred hands per hour is pretty quick. Three hundred hands per hour is very, very fast. (See the video, below.)

Using hands per hour makes the number of people at a table at any given time a moot point, unless the number is, as you say, zero. Clearly, the number of hands per hour will drop if you have only a couple of players. With three or four or more players, the dealer will return to their usual pace of hands per hour.

All of this is all really, really theoretical.

And I do agree that people bet more than the minimum. That's why I put $5, $10 and $25 calculations up, as people will vary their bets a bit. So real-life numbers at a $10 table will probably land between the $10 and $25 charts.

Here's a 32-second video that shows a pretty quick pace:

 

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Ah - technically, I believe you're referring to the "hands played per hour" not "hands dealt per hour." The 32-second video is three hands played, one hand dealt.

And to be honest, I don't feel that was a quick dealer, and one of the players was very slow... But I'm pretty demanding, having pumped cards for a living. Not that I ever rushed a player, but when we were dealing, we seriously pumped cards. The goals was that we may wait for them, but they shouldn't have to wait for us. I've had to remind people there's no rush to act; I think it's because I was so fast they felt like they had to hurry!
 

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A brief search for a good, sharp dealer on video leaves me disappointed...

I expected not to find many, since no casinos allow videos to be captured on the floor, but I only found one dealer working a decent pace - and he was a student practicing to learn to deal. I even found bad dealing advice (from my perspective.)

Am surprised to see so many seated blackjack dealers... dealing from seated is more tiring and slower. I've only seen standing dealers in AC, unless I'm mistaken. (In blackjack, I mean.)
 

Psypher1000

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Am surprised to see so many seated blackjack dealers...

Nearly every casino I go to in Vegas has at least one seated blackjack dealer, and if more than one is present, at least one is at the low limit. Bellagio had at least two seated $10 tables last time I was there.
 

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I suspect it may be to ensure there's a low limit table easily accessible to wheelchair-bound patrons.

Since dealers certainly deal more hands per hour standing, casinos prefer standing dealers.

I suppose it's also good for dealers who can't stand for long periods, too.
 

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One other calculation related comment. You calculation is based on the house edge against players playing proper basic strategy. If all players used proper basic strategy... I can guarantee the casino would no longer offer blackjack. I seem to recall reading somewhere (when I was heavy into blackjack and card counting) that the house earns 2%-3% per hand on average.

Here is an article that discusses "hold" and states that my number above is 5%, but the "hold" is much greater. For your calculation, the 5% number is more appropriate.
http://www.betfirm.com/casinos-hold-in-blackjack/
 

dennis63

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One other calculation related comment. You calculation is based on the house edge against players playing proper basic strategy. If all players used proper basic strategy... I can guarantee the casino would no longer offer blackjack. I seem to recall reading somewhere (when I was heavy into blackjack and card counting) that the house earns 2%-3% per hand on average.

Here is an article that discusses "hold" and states that my number above is 5%, but the "hold" is much greater. For your calculation, the 5% number is more appropriate.
http://www.betfirm.com/casinos-hold-in-blackjack/

Now that is interesting. It may be far more realistic than the mathematical edge, as it is based on actual casino experience, and accounts for the variances of human behavior.

So a realistic number, experienced by the casinos, would be closer to:

For a $5 table -- $50 to $75 per hour
For a $10 table -- $100 to $150 per hour
For a $25 table -- $250 to $375 per hour
For a $50 table -- $500 to $750 per hour

and we can assume, since the bets will vary a bit and not all be the minimum, that the real-life numbers will be somewhere in the range of any two of above rows.
 
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Mental Nomad

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Now that is interesting. It may be far more realistic than the mathematical edge, as it is based on actual casino experience, and accounts for the variances of human behavior.

Careful... hold is an entirely different metric and is not an indicator of the house edge. It's easy to calculate based on cash-in/cash-out, but can't even be calculated per table; it's estimated.

If I buy in for $100, and play a $10 bet 100 times, I've wagered $1000, and if there's a house edge of just 1%, I'd expect to lose $10 (on average.) If that average result actually happens, the "hold" would be 10%.... $100 in, $90 out.

But what if I buy in for $100, play one hand at $50, lose, and go cash out? The expected loss at 1% house edge: fifty cents. The hold? 50%.

What if I buy in for $100, play a little, pick up my chips and go to dinner... is it 100% hold? No, because my chips are still good for cash or play later... But when I come back down, if I then play craps... what is the blackjack hold?


On the actual house edge... yeah, it's more than ideal Basic Strategy, but the average player is not a 5%, either - not by a long shot. Most of the decisions where people don't tightly follow Basic don't really make much of a difference. Do you hit or stand on a hard sixteen versus a dealer ten up? Hitting is bettter - but only by a tiny margin. The truth is that hitting and standing BOTH suck, but standing sucks a tiny bit worse.

Conversely, hitting a hard 12 against a dealer 6 up is the wrong move... but it's not horrendous. It's just a little worse.

People are not standing on hard 12 versus a ten up, or hitting hard 16 versus a dealer 6 up. Those would be much more costly errors.

A little digging brought up Griffin's analysis of the average house edge for typical players, after counting their various errors and adding up the actual cost of those errors:

• Based on a basic house advantage on a six-deck game of 0.60 percent (hit soft 17, double after splitting), the average blackjack player will lose 1.43 percent of the original wager, or $1.43 for every $100 wagered.
• Based on a basic house advantage on a high limit six-deck game of 0.28 percent (stand on soft 17, double after splitting, re-split aces, and surrender) the high limit blackjack player will lose 0.96 percent of the original wager, or $0.96 for every $100 wagered.

(Thanks to the Wizard of Odds site for hosting Zender's article from Casino Enterprise Management on this.)
 

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Excellent write up Nomad. Certainly agree "actual" house edge is entirely different than "hold." I noticed in the Zender article that it stated that "common casino wisdom approximated that the players gave back 2%-3%". I knew I got that from somewhere.

This reminds me of going to Vegas one time. I would frequently visit the Gambler's Book Club when I visited. It is/was a hole in the wall bookstore for gambling books. Along the walls, near the ceiling there were large photographs of "famous" gamblers/gaming authors. Doyle Brunson, Phil Helmuth, Johnny Chan, Edward Thorpe, Arnold Snyder etc. I was looking around at the photos, and the manager of the store stated "If you'd like to know who any of those people are, let me know." I knew who they were, because I had read all of their books (or saw them on TV for the poker players). I quickly noticed that the most obscure person on the wall was Peter Griffin and the photo included the manager of the Gambler's Book Club (the guy I was talking to... Howard Schwartz). I said "yeah, whose that guy next to Peter Griffin?" Howard gave a chuckle... "why, that's me."

Not many will really appreciate that story, but I had to tell it... you see, Peter Griffin is pretty obscure unless you are in to older Blackjack analysis. You don't just pick up Theory of Blackjack because you want to improve your game.
 

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Very few people read Thorpe with any interest, either... they take his work and publish their own books! But yeah, I've still got Thorpe's original and Griffin's ToB. Keepers for nostalgia; I have no interest in working at Blackjack.

On the old "common casino wisdom" - I hear they used to rate players on an A/B/C/X basis: A/Basic Strategy, B/Typical, C/Bad player, X/Expert (card counter). It was up to others to calculate the earnings off each, and more importantly, the comp level (because that's what the ratings really were for.) By the time I was flooring (91 or 92), they'd done away with that, and all we tracked was the amount bet, so the comps assumed everyone was average.
 
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