Advantage to player during this promotion?

If someone were to play Blackjack at a table that had a promotion going that made Blackjacks pay 2-1 and suited blackjacks pay 3-1, how would that change the house advantage? I'm thinking it turns the advantage to the player during this time. The details are below.

6 deck shoe
dealer hits soft 17
double down on any first 2 cards
split up to 3 times (4 total hands)
no hitting split aces
no surrender
player may play 2 hands if they are next to each other

maximum payout at the bonus odds is $300. So a $200+ suited blackjack would pay 3-1 on the first $100 and 3-2 on the remaining amount.

It seems to me it would be wise to play 2 hands at $100 each during this promotion to maximize changes to win if indeed the advantage is to the player during this time.

Any thoughts?

Uh, is this real? If so, you'd better come out with it. I'm not going to say anything more unless you name the casino. That's the established procedure on this board; no secrets.

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.

https://wizardofodds.com/blackjack/rule-variations.html

Blackjacks pay 2 to 1 +2.27%

this is an estimate.

im using one deck for sake of simplicity.

there are 64 different ways to make blackjack. 4acesx16tenvaluedcards

each blackjack paying 2 to 1 is worth 2.27%/64 or .035469%

there are 16 different ways to make suited blackjacks. 4x1acex4tenvaluedcardsofsamesuit.

16 of those blackjacks are worth 1.5 times as much so .035469% x 16 x 1.5 or .85176% collectively.

48 of those blackjacks are worth .035469% or 1.70352% collectively.

adding those two amounts together equals 2.55528%.

depending on whether you can resplit aces or double down after a split, the house edge is anywhere from .54% to .76%.

so all together the player advantage is about 1.80% to 2.00%.

doublepost.

I am getting +2.68% if you can double after split, and +2.54 if you cannot (with infinite decks)

Quote: weaselman

I am getting +2.68% if you can double after split, and +2.54 if you cannot (with infinite decks)

out of curiosity can you explain how u came up with those numbers?

I think the HA on your basic rules is about .65%. The odds of getting a non-suited blackjack are about 3.75%, and the odds of getting a suited blackjack are about 1.25%. If blackjack pushes are ignored, then paying 2:1 on non-suited blackjack is worth about 1.875% to the player (3.75% of the time, you'll get a extra .5 units). Paying 3:1 on suited blackjack is worth about 1.875% more for the player (1.25% of the time, you'll get an extra 1.5 units).

I'm writing this on my cellphone from O'hare airport, and doing the math in my head (and rounding). I may be missing something, but it looks to me like these rules have a player advantage of about 3.1%.

Thank you.

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.

Regardless, it's a 2-3% advantage and the ideal bet is probably as many hands of $150 as they will let you lay out. That way you take advantage of the full $300 payout on regular BJs. Anything greater than that and you have diminishing returns. You'll stand to make ~$260 per hour for every bet you have out depending on the speed of play.

Edit: $150 is the maximum you would ever care to bet. I can't say it's the optimal bet. I'm not sure what that is. It might be a number somewhere in between $100 and $150. If you just play $100, you're also shorting yourself by not getting the full $300 on the regular BJ's which come up a lot more often than the suiteds.

Quote:

out of curiosity can you explain how u came up with those numbers?

Well, nothing fancy really. I wrote a little program, that computes an expectation of every hand with a given set of rules, and then sums up all the hands multipled by the probabilities.
For this particular calculation I set the blackjack payout to 9/4 (3*1/4 + 2*3/4), and everything else according to the rules mentioned in the original post - H17, no surrender, 3 splits etc.

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+?

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.

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.

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!

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?

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 :)

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?

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 ...

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.

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.

I see your point. On the $150 bet, the player actually gets $375 for the suited blackjack ($300 on the first $100 and $75 for the remaining $50) and $300 for any regular blackjack.

So, if suited blackjacks are only 25% of blackjacks, wouldn't the following be correct?


$100 bet and you get 4 blackjacks per hour, you would get three payments of $200 and one payment of $300 = $900 in blackjacks.

$150 bet and you get 4 blackjack per hour, you would get three payments of $300 and one payment of $375 =$1,275 in blackjacks during the hour.

You just have to hope you don't hit a bad streak of cards with the $150 bet because you can run though a bankroll much quicker at $150 than $100.

Quote: rudeboyoi

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.

Actually, unless I screwed up my math again, the expectation of a non-blackjack hand with these rules is about -7.84%.
20 hands * 50 bucks * 7.84% is $78.40, so, in fact, it is somewhat more likely to be more than $75.

And don't forget that that 21st hand might just happen to be a push too ...

Quote: weaselman

Actually, unless I screwed up my math again, the expectation of a non-blackjack hand with these rules is about -7.84%.
20 hands * 50 bucks * 7.84% is $78.40, so, in fact, it is somewhat more likely to be more than $75.

And don't forget that that 21st hand might just happen to be a push too ...

you probably arent adding in splits or doubles.

yeah, I am ...
The overall expectation is about -0.7%. Blackjack part is 1.5*8/169*161/169, that leaves (-7.83%)*161/169 for everything else, including splits and doubles.

Quote: Zcore13

I see your point. On the $150 bet, the player actually gets $375 for the suited blackjack ($300 on the first $100 and $75 for the remaining $50) and $300 for any regular blackjack.

So, if suited blackjacks are only 25% of blackjacks, wouldn't the following be correct?


$100 bet and you get 4 blackjacks per hour, you would get three payments of $200 and one payment of $300 = $900 in blackjacks.

$150 bet and you get 4 blackjack per hour, you would get three payments of $300 and one payment of $375 =$1,275 in blackjacks during the hour.

You just have to hope you don't hit a bad streak of cards with the $150 bet because you can run though a bankroll much quicker at $150 than $100.

oh if thats how the blackjack actually works. its definitely better betting a $150/hand. i thought a $150 hand would pay $300 total on a suited blackjack. i didnt realize it would pay $375.


suited blackjacks make up 25% of your blackjacks.

if u bet $100 on a square and get a blackjack.

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

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.

$300(.75)+$375(.25) = $318.75

you get $318.75 on average if you get a blackjack betting $150 on a square.

so theres a $93.75 difference getting paid on blackjacks betting $100 or $150 per hand.

which is greater than weasalmans loss of $78.40 betting $50 more per hand in between getting blackjacks.

Whatever happened to this? Any one want to share their experience? Any estimation on casino losses?

It starts again on November 1st and goes through the end of the year. I've already heard from a few people from this forum that they are flying/driving in to play.

I was not able to make the first go round back in the summer. I knew about it but was too busy. My understanding was that there were very few playing it at that time. I knew this time would be more of a zoo and boy was it.

First off thumbs up to Buckys for offering this promotion. It was very nice of them to do so. I also want to thank them for behaving in a civilized manor and treating the players pretty well for the most part. Often casinos can get very nasty with players during promotions like this. There were a handful of players who were not so courteous to the casino. Some of them had moments where they were clearly out of line. Even these players were treated fairly well when the casino would have been justified in being a bit more curt with them.

Opening extra tables during the promotion time was a nice treat. Often casinos will not bring in the extra staff when needed. The raising of the limits to $50 min before the promotion times was a bit greedy but understandable given the situation.

My only real gripe was that players were told during the final session on Thursday that the promotion would continue on Monday. Some of us traveled quite a distance only to find out the promotion was dead when we showed up on Monday.

I have a pretty good idea on the final results for the week after talking with several of the players and at the end of the week there were a handful of players who lost money and travel expenses on top of it. Although I'm pretty sure that overall the players did alright the casino had quite a lucky run.

I'm glad you had fun and yes it was a zoo compared to the first session a few months before. We did not envision the response we got. We normally have 2 or 3 blackjack tables open during a weekday and 2 or 3 green chip players per day. We did not expect 20 black chip players all at once. Because of this we brought in extra dealers and had a lot of overtime so we could open 7 blackjack tables during the promotional times. We did this for two reasons. One, because we knew players came from a long distance to play. But also, because we had so many non-regulars we needed room for our regular players. They are the ones that support us day in and day out. Our business is our regulars.

I am sorry that the promotion had to be canceled. On Thursday when we told people it would continue on Monday, that was the truth at that time. I don't know which of the 20 players you are, but I was there every day with your guys. I was as fair and honest as I could be with all of you. I even took care of some rooms that I probably shouldn't have. If I knew it was going to be canceled I would have told you and I'm pretty high up on the food chain. Did I think there was a chance it would be canceled... yes. But the plan was to run it at least a few weeks before making any decisions.

I hope you had fun while it lasted and made a little money. We'll do something again that will be a nice promotion, but won't alienate our regulars. I hope someday you'll make it back our way. If you do, let me know... your first drink is on me!

Quote: Zcore13

I am sorry that the promotion had to be canceled. On Thursday when we told people it would continue on Monday, that was the truth at that time.

I respect that you treated the players better than some casinos would have, but that doesn't excuse what you guys did. It's dishonest to advertise a promotion and then discontinue it when people actually show up to play it. "That was the truth at the time"? Oh, come ON--it was a statement about the future, specifically, what your casino would do in the future, which equates to a promise. Then you guys broke that promise.

I realize that you're somewhat in the middle here, since you weren't the one who made the decision to kill the promo. But by doing that, the casino sends a message: don't count on us doing what we say--we reserve the right to change our minds. Anyone who drove any distance only to find that the promo had been canceled would probably not return, except maybe at gunpoint. The question is, is the ill will sown by reneging on the promotion worth the money saved? Somehow, I doubt it.

Arizona is a market that has many gaming options (including driving to Vegas). An isolated, captive-audience casino can afford to treat its customers poorly, but one that must compete to survive can't. I gather that the whole point of the promo was to attract players. It did that, and by slamming the door on those players, Bucky's shot itself in the foot.

By the way, did anyone think of limiting the promo payouts to a $25 bet or less, which would have chased away all those nasty black chip bettors (who, I readily agree, were not the targets of the promotion anyway)?

does anyone know if Buckeyes ever got a virtual dealer BJ machine, and which company is the manufacturer if they did? the only decent ones are the ones made by aruze called dealers angels