Zcore13
Joined: Nov 30, 2009
• Posts: 3521
July 23rd, 2010 at 11:44:50 AM permalink
The \$150 bet doesn't allow you to get paid the full 3-1 on suited blackjacks. Aren't you shorting yourself a little. Play 2 hands at \$100 each instead of 1 hand of \$150+?
I am an employee of a Casino. All the personal opinions I post are my own and do not represent the opinions of the Casino or Tribe that I work for.
rudeboyoi
Joined: Mar 28, 2010
• Posts: 2001
July 23rd, 2010 at 8:34:03 PM permalink
Quote: teddys

I also tend to think it is higher. The Wizard's page says 2-1 blackjack is an off-the-top 2.27% advantage. That's a given. Then in addition to that for every suited BJ you will get an extra payout of another bet. Rudeboyoi, I'm not saying your math is wrong, but just an additional .30% advantage for that seems low.

teddy, thats okay. i wasnt sure if my math was correct either. the wizards rules variations are relative to a given set of rules. i cant be sure about my math since these rules are different. i can just give educated guesses and can describe to you the process i take.
weaselman
Joined: Jul 11, 2010
• Posts: 2349
July 24th, 2010 at 9:26:58 AM permalink
So, I wanted to show a more transparent way of arriving to the answer that referring to a magical program, but got stumbled upon a mysterious mistake that I cannot figure out. Maybe, someone can look at this with a fresh eye and spot it?
So, I break the total expectation into two separate values - when you have blackjack, and when you don't:
E = p*e1 + (1-p)*e2
where p is the probability of having blackjack.
Now, we can say that e1 = (1-p)*S, where S is the payout rate (if the dealer does not have blackjack, you get S, otherwise you get 0). (this is assuming infinite decks, but the difference compared to 6 or 8 decks is really small, definitely, not worth the added complication).
From this, it is easy to tell how changes in blackjack payout affect the overall outcome:
E' = p*(1-p)*S' + (1-p)*e2 = E + p*(1-p)*(S'-S)

Basically, if the payout rate changes by D=S'-S, then the expectation changes by p(1-p)*D.
For example, if blackjack pays 2 to 1 as opposed to 3 to 2, that's a change of 0.5, so the change in expectation should be p(1-p)*0.5.
The p - probability of getting blackjack is 1/13*4/13 = 4/169, so the expected change in value is:
0.5*(4*165)/169^2

Now, this is where the mystery begins. The value above is about 1.16% - way lower than Wizard's 2.27%.
I would think that, perhaps, Wizard is mistaken (yeah, it can happen to even the best of us, and my respect of authority is almost non-existent compared to that of formulas), or that the figure in his table means something else ... but my own program I mentioned earlier (the one that just computes the expectation of each hand) gives the same answer as the Wizard's table to the seventh digit, even though it does not agree with Wizard on some other details (like the values of split hands). So, it seems pretty obvious that both Wizard and the program should be correct in this case, and my formula above must be wrong, but however I look at it, I just don't see the error.
"When two people always agree one of them is unnecessary"
FleaStiff
Joined: Oct 19, 2009
• Posts: 14374
July 24th, 2010 at 9:45:28 AM permalink
Quote: Zcore13

It's as real as it gets. Bucky's Casino in Prescott, AZ. 8am-9am, 3pm-4pm and 9pm-10pm Mon-Thurs for players with a players card.

Sounds like Bucky knows what he is doing. Any sort of "special" that is applicable to the "Get 'em in early hours" and the "Keep 'em there late hours" but only those narrow time periods is certainly going to be viewed by Bucky as being special. No way he is going to put up with all the hassles and complaints and disputes unless he thinks there is money involved in this. Is it a good a deal as might be thought? Beats me. Even with my shoes off, I couldn't solve the math puzzle but no casino would go thru the rigamarole unless it really meant something!
FleaStiff
Joined: Oct 19, 2009
• Posts: 14374
July 24th, 2010 at 9:51:54 AM permalink
Now this is a different question than what is the value to a sharpie who happens to live in or near Prescott, AZ?

I think it is necessary to factor in the fact that any such casino visitor is going to be playing at his usual house edge for the rest of the time. A retired person would perhaps be able to take advantage of all three hours each day but fatigue, alcohol consumption and other factors play a role as well. Would that retiree be sharp enough to take full advantage of the promotion at 9:00pm if he has been in the casino since before 8:00am? And of course there is the fundamental question: Will the dealers slow down the rate of play during the special promotion periods?
weaselman
Joined: Jul 11, 2010
• Posts: 2349
July 25th, 2010 at 10:28:49 AM permalink
Ok, I figured it out! The error was in my figure for blackjack probability. It should be 8/169, of course, not 4/169.
So, the expectation change due to a change D in blackjack payout is (8*161)*D/169^2.
With D=0.5 (blackjack pays 2 to 1), this is 2.255% - close enough to Wizard's number to let me write-off the difference on the combination of a rounding error and 6 deck vs. infinite decks deviations.
Back to the original post, suited blackjacks is 1/4 of all blackjacks. So, if a suited blackjack pays 3 to 1 and the rest is 2 to one, then the average payout is 3*1/4 + 2+3/4 = 9/4. This is 3/4 more than the 1.5 to 1. So, D in my formula is 9/4, and the total change in the expected value is (8*161*9/4)/169^2 or about 3.38%. The house edge under the standard 1.5 payout and the rules, stated in the original post (H17, no surrender, up to 3 resplits) is about 0.7% (if you can double after split). Subtracting this from 3.38, we get that 2.68% number I mentioned in my first post.
Now it all makes sensse :)
"When two people always agree one of them is unnecessary"
FleaStiff
Joined: Oct 19, 2009
• Posts: 14374
July 25th, 2010 at 11:01:42 AM permalink
Quote: weaselman

Ok, we get that 2.68% number I mentioned.

Well, 2.68 percent Player Advantage is certainly attractive since ANY player advantage is rare. Assuming there is no slowdown in play and assuming that in order to be able to make use of this special one-hour of player advantage, one must already be seated at the blackjack table, I guess its really just what it pretends to be: a special promotion taking place at the stated times in order draw in an early crowd and keep them there late. If you were to do solely the early evening special hour and in order to make use of that needed to arrive at the blackjack pit at least one hour earlier, you would have two hours of play. Let us assume sixty hands at 0.7 percent house advantage and then sixty hands at 2.68 percent player advantage, I guess one just would consider it to be 120 hands at 2.61 player advantage. If so, for two hours of play, a drink or two, ... it would certainly seem worth it. After all, every other casino is at a house advantage.

If its such a good opportunity for the players, I wonder if Bucky will continue this promotion for long?
weaselman
Joined: Jul 11, 2010
• Posts: 2349
July 25th, 2010 at 5:27:28 PM permalink
Quote: FleaStiff

Let us assume sixty hands at 0.7 percent house advantage and then sixty hands at 2.68 percent player advantage, I guess one just would consider it to be 120 hands at 2.61 player advantage.

1.3% actually, but still not bad ...
"When two people always agree one of them is unnecessary"
Zcore13
Joined: Nov 30, 2009
• Posts: 3521
July 26th, 2010 at 10:47:00 AM permalink
Quote: FleaStiff

Well, 2.68 percent Player Advantage is certainly attractive since ANY player advantage is rare. Assuming there is no slowdown in play and assuming that in order to be able to make use of this special one-hour of player advantage, one must already be seated at the blackjack table, I guess its really just what it pretends to be: a special promotion taking place at the stated times in order draw in an early crowd and keep them there late. If you were to do solely the early evening special hour and in order to make use of that needed to arrive at the blackjack pit at least one hour earlier, you would have two hours of play. Let us assume sixty hands at 0.7 percent house advantage and then sixty hands at 2.68 percent player advantage, I guess one just would consider it to be 120 hands at 2.61 player advantage. If so, for two hours of play, a drink or two, ... it would certainly seem worth it. After all, every other casino is at a house advantage.

If its such a good opportunity for the players, I wonder if Bucky will continue this promotion for long?

No special hooks to playing during the times. It's not one specific table only. It's on all tables for all players card members. You don't have to be seated when it starts. If it gets busy, another table is opened.

I think we've now determined a 2.68% house advantage. Now the question still remains... what is the optimal bet? \$100, \$150? Something in between?

Also, If I were playing, I would not play before and after. I would play the promotional sessions only and rest between.
I am an employee of a Casino. All the personal opinions I post are my own and do not represent the opinions of the Casino or Tribe that I work for.
rudeboyoi
Joined: Mar 28, 2010
• Posts: 2001
July 26th, 2010 at 11:12:31 AM permalink
it might be advantageous to just totally disregard the 3:1 on suited blackjack and just play \$150/hand on as many squares as you can in order to maximize your EV.

some quick math.

suited blackjacks make up 25% of your blackjacks.

if u bet \$100 on a square and get a blackjack, unsuited and suited.

\$200(.75)+(\$300)(.25) = \$225

so you get \$225 on average if you get a blackjack betting \$100 on a square.

if u bet \$150 on a square and get a blackjack, suits are irrelevant, you get \$300.

so its hard to imagine betting an additional \$50/hand is going to cost you more than \$75 in between getting blackjacks which is about 1 in 21 hands.