Blackjack Promo - Is This EV+?
Get BJ two times in a row
Win a hand with 5 cards or more
Win 4 hands in a row
Recieve a hand with 777
Get 3 Aces or more in a hand
The deck is 8 shoes with 0.71% house edge (no DAS, no re-splitting, dealer peeks on A not 10, 3:2).
The prizes are these:
1 completed objective - Nothing
2 completed objectives - 25
3 completed objectives - 50
4 completed objectives - 100
5 completed objectives - 500
Min bet is 5.
Is there any positive expectation in any of it? Should all 5 be aimed at or stop somewhere in the middle?
Without doing the maths, I'd strongly suggest that this is not +EVQuote: Sm0keyHi folks. There is a casino promotion running that gives you points for clearing different objectives:
Get BJ two times in a row
Win a hand with 5 cards or more
Win 4 hands in a row
Recieve a hand with 777
Get 3 Aces or more in a hand
The deck is 8 shoes with 0.71% house edge (no DAS, no re-splitting, dealer peeks on A not 10, 3:2).
The prizes are these:
1 completed objective - Nothing
2 completed objectives - 25
3 completed objectives - 50
4 completed objectives - 100
5 completed objectives - 500
Min bet is 5.
Is there any positive expectation in any of it? Should all 5 be aimed at or stop somewhere in the middle?
Each of those objectives is pretty improbable... Rather a lot really. and the scale of rewards for achieving them is truly abysmal to see 5 completed objectives in a session would probably take wayyy over 24 hours of continual play, each hand grinding down your bankroll relentlessly.
Also, it sounds like an online game with those rules. Do you trust the casino... And do they have any stupid wagering requirements on the bonus wins? That would be serious insult to injury.
I'll agree with one thing (intuitively) the 500 is the prize to aspire to. But the amount of play to reach that goal would be massive and I'd be confident that you will have wasted 500 of bankroll way before getting there.Quote: Sm0keyNo there are no wagering requirements and yes i trust them. The jump from 4 to 5 completed looks like one of those progressive jackpot/royal flush video poker type of things so i was thinking maybe it's value as long as you keep playing until you finish.
It hardly matters, but is it 500 + all the other lower tiers collected along the way, or just 500?
2 obj - 704
3 obj - 1,408
4 obj - 2,816
5 obj - 14,084
If the cycle is less than that for that number of objectives, assuming you're playing 5E hands (my American computer doesn't do Euro symbols*), then it's going to be +EV.
Hitting 2 BJ's in a row is about 1 in 446. (1/((4/13)*(1/13)*2))^2
Not sure about winning with 5 cards or more....although in my experience, that's going to be pretty low....probably the easiest one on there. Not sure about three Aces nor 777. Side question (not that it'd help me), does it need to be exactly 777? What if you get 7-2-7-7?
Winning 4 hands in a row, excluding pushes, should be about 0.48^4 = 1 in 18.83.
You should, at bear minimum, have +EV if you just go for the "win 4-in-a-row" and "win a 5+ card hand" and collect the 25E bonus. Not sure about the others. I'd bet each of those objectives is going to be +EV. As far as if it's worth it and the time spent on it, that's for you personally to decide.
What is a cycle and how do i know if it's less or more?
It has to be 777 as i understand it.
What do you approximate my EV at for 2 completed objectives? I want to maximize my value irrespective of time spent.
Quote: Sm0key
What do you approximate my EV at for 2 completed objectives? I want to maximize my value irrespective of time spent.
I believe hitting two of the objectives and quitting would be +EV. Winning four hands in a row is very common. Winning a hand with five cards is not hard if that is the objective and you abandon basic strategy.
I would play basic strategy until I won four in a row and then adjust strategy to get a five card winner. I have no idea how to do the math but it definitely seems positive to me.
Quote: DRichI believe hitting two of the objectives and quitting would be +EV. Winning four hands in a row is very common. Winning a hand with five cards is not hard if that is the objective and you abandon basic strategy.
I would play basic strategy until I won four in a row and then adjust strategy to get a five card winner. I have no idea how to do the math but it definitely seems positive to me.
How would you go about getting a 5 card win?
Follow BS with the five card Charlie rules.Quote: Sm0keyHow would you go about getting a 5 card win?
So the bonuses are tiered. I've assumed that you can get multiple occurrences of one of those events and that will still count?Quote: Sm0key@OnceDear The wins do not accumulate no
What is a cycle and how do i know if it's less or more?
It has to be 777 as i understand it.
What do you approximate my EV at for 2 completed objectives? I want to maximize my value irrespective of time spent.
I can't be bothered to calculate the EV. I guessed it doesn't have +EV but maybe it does. Romes seems to figure it does and I wouldn't argue maths with him. I can't see it being of much value though.
Quote: unJonFollow BS with the five card Charlie rules.
Wizard of Odds chart for this assumes that 5 card Charlie is an automatic win. For me it won't be as i can still lose the hand just as usual.
Also splitting is not counted as one but two separate hands but i guess he already accounted for that too?
Quote: OnceDearSo the bonuses are tiered. I've assumed that you can get multiple occurrences of one of those events and that will still count?
I can't be bothered to calculate the EV. I guessed it doesn't have +EV but maybe it does. Romes seems to figure it does and I wouldn't argue maths with him. I can't see it being of much value though.
You can complete more than one objective on a single hand but you can't complete the same objective multiple times and have it count.
Playing single deck yesterday, I held Ace/8 vs 8. Dealer turned over a second 8 and hit a third. The odds of four out of five cards being the same .just be pretty high.
The second most difficult is 3 aces. If you don't make any strategy exceptions, this will take 2300 hands.
To maximize this one, you almost never double soft hands. Hit any soft hand 12 to 17 (so, never split aces). Hit soft 18 except double vs 6 and stand vs 7. Stand soft 19 except double vs 6 and stand vs 10. Stand soft 20+. This will take about 498 hands.
My gut feeling is to go for 4. Start out with the modified ace strategy until you hit it. The remaining 3 will come naturally.
If you go for 5, then I would start out with the modified 7 and A strategies. You could modify your ace strategy just half or a third of the time and still expect to hit it before the 3 7s.
Are there any time limits? If you cash in on one in a day, can you start again?
Quote: billryanDoes 2-7-7-7 count or must it be 7-7-7 alone?
Playing single deck yesterday, I held Ace/8 vs 8. Dealer turned over a second 8 and hit a third. The odds of four out of five cards being the same .just be pretty high.
there was a progressive video BJ game many years ago that paid the progressive if you hit three 7's. The problem was that there was a bug in it and it paid the progressive even if you busted. Once the AP's found this it didn't last very long. I played it for about a week at Sam's Town before they removed it.
Quote: CrystalMathYou will average 2460 hands before getting the 777. Since I assume this is the most difficult and the one that will earn you the top prize, then you need to change your strategy to always hit 77 vs anything.
The second most difficult is 3 aces. If you don't make any strategy exceptions, this will take 2300 hands.
To maximize this one, you almost never double soft hands. Hit any soft hand 12 to 17 (so, never split aces). Hit soft 18 except double vs 6 and stand vs 7. Stand soft 19 except double vs 6 and stand vs 10. Stand soft 20+. This will take about 498 hands.
My gut feeling is to go for 4. Start out with the modified ace strategy until you hit it. The remaining 3 will come naturally.
If you go for 5, then I would start out with the modified 7 and A strategies. You could modify your ace strategy just half or a third of the time and still expect to hit it before the 3 7s.
Are there any time limits? If you cash in on one in a day, can you start again?
Edit: Saw you already approximated the Aces strategy. How about always hitting 77?
Quote: Sm0keyModify 77 by always hitting and modify A by always hitting soft hands? What is the approximation of hitting these two objectives with these changes 1 in X hands?
3 7s is 1 in 2460 with the modified strategy. Normally it is much worse due to splitting or standing most of the time.
3 aces is about 1 in 498 with the modified strategy. You simplified this strategy a little too much. The simplest strategy would be to hit any soft hand 18 or under.
Quote: unJonFollow BS with the five card Charlie rules.
I disagree. The Five Card Charlie strategy assumes you only win the amount of your original bet. In this scenario you can win up to 500 times your original bet.
Perhaps the best strategy is going for the 5 cards win and 4 wins in a row objective until those are completed, and if some of the other objectives happen to come along on the way then it's like a bonus side win.
Quote: Sm0keyBut with those odds it doesn't seem valuable to go for the top prize? ~2460 that's close to 12500 wagered and the expected value should be a large minus that 500 won't account for.
Perhaps the best strategy is going for the 5 cards win and 4 wins in a row objective until those are completed, and if some of the other objectives happen to come along on the way then it's like a bonus side win.
It should cover the losses, but its got high volatility. If you go for the easy ones and get 777 early, then go for all 5.
Quote: CrystalMathIt should cover the losses, but its got high volatility. If you go for the easy ones and get 777 early, then go for all 5.
If i went for the top prize what kind of expected profit would you give it?
Good point. Withdrawn.Quote: DRichI disagree. The Five Card Charlie strategy assumes you only win the amount of your original bet. In this scenario you can win up to 500 times your original bet.
Certainly less than 500 !Quote: Sm0keyIf i went for the top prize what kind of expected profit would you give it?
And all this talk about changing your strategy away from BS, will inevitably mean you are playing into an increased house edge. It's not one I'd attack. But whatever floats your boat. If you do go for it, then please post about how it works out for you.
Quote: Sm0keyIf i went for the top prize what kind of expected profit would you give it?
371 euros
2700 hands
This is playing a modified 7 strategy until you hit 777 and the simple soft hand strategy (stand >=19 otherwise hit) until you hit 3 aces. I didn't make any strategy adjustments for winning a 5 card hand.
Play with modified 7 and A strategy until you get everything but the 7s. If you hit the 7s, it's a bonus.
Average win = 171 euros, average hands = 1156. (edited avg win from 222 to 171)
You have a 1 in 4.3 chance of having a net loss.
Quote: OnceDearCertainly less than 500 !
And all this talk about changing your strategy away from BS, will inevitably mean you are playing into an increased house edge. It's not one I'd attack. But whatever floats your boat. If you do go for it, then please post about how it works out for you.
Yes you're right. I do wonder though on hands like say 20 vs 5 or 6 to split in order to get closer to 4 hands in a row or if it's just better to get it "naturally" with BS. Also perhaps hitting soft hands vs low cards in order to get 5 cards Charlie primarily while 3 Aces are there as a secondary chance too.
Quote: CrystalMathHere's another scenario:
Play with modified 7 and A strategy until you get everything but the 7s. If you hit the 7s, it's a bonus.
Average win = 222 euros, average hands = 1156.
You have a 1 in 100 chance of having a net loss.
That would win me the 100 prize and the fluctuation of wins & losses you figure will have me an expected profit at 222?
If i do net lose what expectation could i have on that amount?
Quote: Sm0keyThat would win me the 100 prize and the fluctuation of wins & losses you figure will have me an expected profit at 222?
If i do net lose what expectation could i have on that amount?
I had to fix my post. I mixed up some units. The expected profit is 171 euros and you have a 1 in 4.29 of a net loss. If you lose, the average loss is 135 euros. If you win, your average win is 266 euros.
Quote: CrystalMathI had to fix my post. I mixed up some units. The expected profit is 171 euros and you have a 1 in 4.29 of a net loss. If you lose, the average loss is 135 euros. If you win, your average win is 266 euros.
I understand the slightly less than 25% of losing 135 but what are those parts about 171 and 266? I use "expected profit" and "average profit" more or less interchangeably.
If you win (so in the 75% world) you are at an average of 266. Overall averaging wins and losses you are at 171.Quote: Sm0keyI understand the slightly less than 25% of losing 135 but what are those parts about 171 and 266? I use "expected profit" and "average profit" more or less interchangeably.
Quote: Sm0keyI understand the slightly less than 25% of losing 135 but what are those parts about 171 and 266? I use "expected profit" and "average profit" more or less interchangeably.
The average profit is 171 euros, which includes winning sessions and losing sessions.
You just asked for the average loss if you lose, and I also added the average win if you win. All combined, 171.
Quote: JoemanDid OP say you get the cash prize at each level, or do you only get the highest level achieved? E.g., does 4 out of 5 get you 25 + 50 + 100 = 175, or just the 100?
You only get the highest level prize you reach so no accumulated wins.
Quote: CrystalMathThe average profit is 171 euros, which includes winning sessions and losing sessions.
You just asked for the average loss if you lose, and I also added the average win if you win. All combined, 171.
So after 1156 hands i can conclude whether the 75% win chance or 25% loss chance struck? If my goal was finishing four objectives do i keep going on at this point if i have say three or better ti call it quits at that point and accept the L?
In that case, I think CM's numbers are a little high. I haven't done the math, but if the promotion was they give you 100 for just showing up, and you then played 1156 hands, your expected return would be a little less than 100, certainly less than 171.Quote: Sm0keyYou only get the highest level prize you reach so no accumulated wins.
Like I said, I didn't do the math. I'm sure CM will be happy to correct me if I'm wrong. Perhaps the chance of getting the 500 award makes up for the difference?
Quote: JoemanIn that case, I think CM's numbers are a little high. I haven't done the math, but if the promotion was they give you 100 for just showing up, and you then played 1156 hands, your expected return would be a little less than 100, certainly less than 171.
Like I said, I didn't do the math. I'm sure CM will be happy to correct me if I'm wrong. Perhaps the chance of getting the 500 award makes up for the difference?
No they absolutely don't give you anything for showing up and you play for your own funds.
Quote: JoemanIn that case, I think CM's numbers are a little high. I haven't done the math, but if the promotion was they give you 100 for just showing up, and you then played 1156 hands, your expected return would be a little less than 100, certainly less than 171.
Like I said, I didn't do the math. I'm sure CM will be happy to correct me if I'm wrong. Perhaps the chance of getting the 500 award makes up for the difference?
Yes, you have about a 34% chance of completing the 777 and getting the 500.
Thanks! I stand corrected.Quote: CrystalMathQuote: JoemanIn that case, I think CM's numbers are a little high. I haven't done the math, but if the promotion was they give you 100 for just showing up, and you then played 1156 hands, your expected return would be a little less than 100, certainly less than 171.
Like I said, I didn't do the math. I'm sure CM will be happy to correct me if I'm wrong. Perhaps the chance of getting the 500 award makes up for the difference?
Yes, you have about a 34% chance of completing the 777 and getting the 500.
Quote: Sm0keySo after 1156 hands i can conclude whether the 75% win chance or 25% loss chance struck? If my goal was finishing four objectives do i keep going on at this point if i have say three or better ti call it quits at that point and accept the L?
I'm not sure. It would depend on which 2 you have yet to get and what your regular blackjack winnings are at that point. My gut feeling is that stopping prematurely will cost you some EV. It's also my gut feeling that you'll get the best EV by just shooting for 2 objectives, but continuing for all 5 if you happen to get the 777.
At that point wouldnt it make sense to keep going until you see a back to back BJ while still playing the modified 7-7 and soft hand strategy?Quote: Sm0keyIf i aim at 5 cards win and 4 wins in a row i could finish them off with relative ease but then it's also likely that i won't complete anything else on the way so it will end there.
ETA: My back of the envelope is that chasing the back to back BJ on its own is slightly -EV but with the chance of getting the other two along the way should tip it to +EV.
Quote: Sm0keyYeah i thought aiming for 4 objectives and considering 777 as a bonus seemed better than staying at 2 but now i don't know.
I think it depends on how often you can re-start and what else you have to do with your time.
Quote: CrystalMathI think it depends on how often you can re-start and what else you have to do with your time.
It's daily runs.
Not splitting A-A pair will help achieve two objectives - 5CC and 3 aces. Indeed, any hand with 3 aces has an excellent chance of being 5 cards.
1. Two BJs in a row - no strategy changes are possible. Probability= 0.002185 or 1/457.62 on any two consecutive hands
2. Winning 4 hands in a row. This is the easy one, of course. Once you have won a hand, the odds that the next 3 hands will be a win are about 1 in 10.
3. 777 - Obviously, always hit any 7-7 pair
4. 3 aces in a hand
Hit any hand 17 or lower with 2 aces, including A-A pair
Never Double, always hit S13 -S16
5. 5 card charlie.
Hit any 4 card hand 17 or lower,
Hit any 3 card 12 or 13
Never Split 2-2, 3-3, 4-4, A-A
Never Double, always hit S13 -S16
If you were going to just shoot for two objectives, then you should make the 5 card changes. Without them, it takes 150 hands, vs 50 with the modifications.
