5 Card Trick Bonus

I appreciate a lot of you are US based so can't make use of this offer, but from a maths/Blackjack geek perspective some of you may find it as interesting as I do.

I've come across a promotion with a UK online casino in which the player is awarded an instant £25 cash prize (no wagering requirements) every time they get 5 cards and win the hand. The minimum bet for the table is £5, and if the player is betting table minimum they still qualify for the full £25 prize.

The game is live Blackjack (dealt slowly by a dealer in front of a camera, usually an Eastern European woman caked in makeup), with a house edge of 0.7%. At the lowest tier of the site membership there is £1 cashback for every £1000 wagered on Blackjack, effectively making the house edge 0.6%.

I haven't delved into the maths fully but I'm pretty sure this is an EV+ offer simply by playing Basic Strategy betting £5 a hand and hitting the £25 wins every once in a while.

To boost the EV basic strategy could be altered. The wizard has a handy altered basic strategy chart for any games with a 5 card charlie rule, however I don't think the strategy would be identical as the conditions are different here.

With a 5 card charlie, if the player gets 5 cards without busting and the dealer doesn't get Blackjack, the player has won their stake x 2. With this offer, the player can get 5 cards without busting and still lose, without the dealer getting Blackjack. Also, the payout is bigger; if the player wins with 5 cards they get their stake back x 7 (the original stake, the win from the base bet, and the £25 from the promotion).

Card counting online games is usually a fruitless endeavour with the 8 or more decks and the limited penetration, however I think it could be used in this case to identify times when the chance of getting 5 cards unbusted is much higher. For instance I could bet £5 on 1 hand, but when the true count drops below -2 then spread out to more hands. An ace side count would also be useful, as when the count is low but the number of aces remaining is disproportionately high I could really go for it and spread out across as many boxes as possible.

Any thoughts?

I'm guessing if the bonus is a fixed $25 then you're better off playing $5 unless, by counting etc., you've got a +EV situation ignoring the bonus. They may be many situations where you hit 4-card hands and 3-card soft totals of 18 (except against 7). I'd also guess you hit most 3-card 12s, so it may be better to hit not double (say) 9 vs 3.

Interesting. It sounds off the cuff that if you bet $5 per hand and occasionally win and extra $25 which is a huge bonus even if it happens just once every 100 hands, the game would be extremely +EV. If I am misguessing and this situation will come up far less than 1 in a hundred then you need to know the denominator. But even if it is 1 in 250 it may be enough to turn the game to +EV.

I guess one of the smarter math guys can make a guess as to how much the bonus is worth, it might not be exact because you would need to change basic strategy..... you are definitely hitting a 4 card 12 against a 6 as an example....

Is this "no peek" European BJ?

Without any basic strategy changes: You should get a 5-card hand about 2% of the time . Such hands will tend to be evenly distributed between 17-21 and will have a win rate vs dealer in teh ballpark of 40%. So, roughly, this bonus is worth an average of $0.20 on a $5 wager without any strategy changes. (please forgive the U.S. currency units.) That's approximately a 4% EV bump to player.

However, as charliepatrick says, there are some changes to basic strategy to allow you to win this bonus more frequently.
1. Hitting any 4-card hand that is <18 and some 4-card 18s.
2. Hitting all 3 card 12s vs 4-6 and 3-card 13s vs 2-6.
3. Standing on most/all 5 card hands totalling 16 or less.
4. Not doubling on some soft hands (and some hard hands) that you would normally double on.
5. Not splitting A-A and instead hitting it in some situations.
6. Hitting (not splitting) 2-2 or 3-3 in some situations. (Or vice versa - splitting some pairs that you would normally hit, lol.)

So, this is a lucrative bonus. Played optimally and with minimum table stakes, I imagine that player will have >5% advantage on the house.

I could do a more precise infinite deck calculation but I think that some forumites have better tools than me and can do this calc more efficiently than I can.

I ran a Markov chain to see how many hands would go to 5+ cards and win and it was 0.00604, or about 1 in 165.

So that would be a 3% bump to EV (5 unit bonus every 165 hands).

This is a decent but ballpark estimate since:

1) No adjustments to basic strategy
2) Did not account for splits/doubles . Overcounted 5+ hands so this probably cancels #1 more or less
3) Used infinite deck
4) Assumed all 5 card hands are vs dealer upcard >6. Only about 1 in 1000 hands go to > 4 cards when basic strategy says not to hit stiff hands (dealer upcard <7). Dealer upcard of 2/3 vs 12 would be immaterial

As with most Blackjack variations, simulation is probably the only way to get a precise number.

Quote: gordonm888

Is this "no peek" European BJ?

Without any basic strategy changes: You should get a 5-card hand about 2% of the time . Such hands will tend to be evenly distributed between 17-21 and will have a win rate vs dealer in teh ballpark of 40%. So, roughly, this bonus is worth an average of $0.20 on a $5 wager without any strategy changes. (please forgive the U.S. currency units.) That's approximately a 4% EV bump to player.

However, as charliepatrick says, there are some changes to basic strategy to allow you to win this bonus more frequently.
1. Hitting any 4-card hand that is <18 and some 4-card 18s.
2. Hitting all 3 card 12s vs 4-6 and 3-card 13s vs 2-6.
3. Standing on most/all 5 card hands totalling 16 or less.
4. Not doubling on some soft hands (and some hard hands) that you would normally double on.
5. Not splitting A-A and instead hitting it in some situations.
6. Hitting (not splitting) 2-2 or 3-3 in some situations. (Or vice versa - splitting some pairs that you would normally hit, lol.)

So, this is a lucrative bonus. Played optimally and with minimum table stakes, I imagine that player will have >5% advantage on the house.

I could do a more precise infinite deck calculation but I think that some forumites have better tools than me and can do this calc more efficiently than I can.

Thanks for that Gordon. Yes it's no hole card. Specifically the rules are:
8 decks.
No resplits.
Only 1 card to split aces.
DAS allowed.
Dealer stands on soft 17.
No surrender.
If the dealer is showing a 10-value card and gets blackjack, any money the player has placed on a double they get back.

I'm thinking that when the count is +1 or higher I can increase my bet size by spreading £5 a box across several boxes, rather than increasing the amount wagered on just 1 box. That way I also increase the chance of hitting a 5 card hand.

Without being able to calculate a precise basic strategy I will be following the kinds of rules you have suggested. I'd be very surprised if on proper examination any of them turned out to be incorrect plays. By altering BS in this way the expected loss on my base bet will increase, but not to the point that it makes the offer negative EV.

I usually don't do offers online unless I am 100% sure of the maths in advance. However with this one being uncapped and likely being one of the few online offers that other UK advantage players won't touch I'm definitely going to milk it.

Thanks Ace that's really interesting. As you suggest, the offer is definitely EV+ before making any adjustments for BS changes. With some of the more obvious changes being made the EV should be higher, though how much higher I don't know.

Quote: blackjacklad

...I'm thinking that when the count is +1 or higher I can increase my bet size by spreading £5 a box across several boxes, rather than increasing the amount wagered on just 1 box. That way I also increase the chance of hitting a 5 card hand....

The higher the TC gets the less likely you are to draw out a 5 card hand. You should ignore counting, unless you want to count and spread to more hands when the TC goes negative, then some will argue you're card eating all the bad counts, etc, etc, etc.

You need to quantify the amount of the promotion. I saw above ~3%. If the game is -.7% off the top, then you have approximately till TC -4 before the added hand -EV over-weighs the positive EV return from the hand due to the promotion.

i.e.

TC < -3 = 1 hand, or sit out
TC = -2 = 2 hands
TC = -1 = 2 hands
TC = 0 = 2 hands
TC >= +1 = 1 hand

Some finer simulations/etc could tell you whether or not to play more than one hand in slightly positive territory.

Quote: Ace

I ran a Markov chain to see how many hands would go to 5+ cards and win and it was 0.00604, or about 1 in 165....

I ran a very quick simulation using UK rules (i.e. allows resplits). The normal House Edge came out at 0.52% and 248269 out of 39.7m hands (1m shoes) used 5 cards or more and won. This comes out at 1 hand in 160 so corresponds with your figure.

Quote: charliepatrick

I ran a very quick simulation using UK rules (i.e. allows resplits). The normal House Edge came out at 0.52% and 248269 out of 39.7m hands (1m shoes) used 5 cards or more and won. This comes out at 1 hand in 160 so corresponds with your figure.

Glad to hear that. That’s closer than I expected.

So with a 5 unit bonus per 160 hands, it’s a 3.125 % boost to the player before making any strategy changes. I can only make an educated guess that those changes would add about another 1%.

All this indicates that the player has about a 3.5 % advantage, with an N0 of only about 1300 hands (estimate standard deviation of 1.25). I assume you could easily play 200 hands per hour, so you could be confident of a profit even in the short term.

The only problem is that you can bet only £5 per hand to get the maximum % boost. Despite that, it’s still £35 per hour EV. If I could find this game in Vegas it would pay for my hotel room.

Quote: Romes

You need to quantify the amount of the promotion. I saw above ~3%. If the game is -.7% off the top, then you have approximately till TC -4 before the added hand -EV over-weighs the positive EV return from the hand due to the promotion.

i.e.

TC < -3 = 1 hand, or sit out
TC = -2 = 2 hands
TC = -1 = 2 hands
TC = 0 = 2 hands
TC >= +1 = 1 hand

Some finer simulations/etc could tell you whether or not to play more than one hand in slightly positive territory.

Thanks Romes. Have you run a sim to come to the conclusion that the increased expected loss on the hand grows disproportionately compared to the increased expected gain on the promotion?

On a quick sim the EV seems to get better with positive counts and I agree that at a reasonable negative TC (I got -6 but then the UK rules were a better game to start with HE=0.49% on this sim) it flips negative.

Quick query: is the bonus for a winning hand of precisely 5 cards, or for a winning hand of 5 or more cards?

Dog Hand

The terms state: 'To win, you must be dealt five cards and beat the dealer.' Which doesn't answer your question unfortunately.

Ignoring any possible change in strategy and running a sim looking for 6+ card winners, nearly 90% of the 5+ winners were 5-cards, so it would be about 1 in 180 hands rather than 1 in 160.

After spending some time using this offer the proposition has become somewhat more complicated. I can confirm that the £25 bonus is only awarded with a 5 card hand - 6 card hands don't qualify.

There are two rule variations for the games the offer works on. The standard Live Blackjack, which I've already mentioned. And a game called Unlimited Blackjack, similar to one the wizard did an article on, but with some rule differences. For taking advantage of the promotions they each have pros and cons.

Unlimited Blackjack has 5 boxes, and an unlimited number of players can bet on as many as they like without any individual player having control. They make this possible by having special rules for pairs.

Some pairs give the usual range of options to the player, but without the option to split.
Some pairs have only 2 options - split, or fold and receive 80% of your stake back.

Other than that the rules are fairly standard:

8 decks.
No resplits.
Only 1 card to split aces.
DAS allowed.
Dealer stands on soft 17.
No surrender.
No peek.
If the dealer is showing a 10-value card and gets blackjack, any money the player has placed on a double they get back.

PRO OF UNLIMITED: The normal Blackjack only allows me to bet on 1 box at a time, whereas with Unlimited I can bet on 5 at a time. With the game being dealt painfully slowly, this makes a big difference in the volume I can bet.

PROS OF STANDARD: 1)In the unlimited mode most of the low pairs have to be split or surrendered. Being able to hit my pair of aces or pair of 2's is great for getting the 5 cards I need. Not being able to make these obvious BS changes reduces the number of 5 card hands I get.

2)For 4 hours some evenings there are on average 1 golden cards drawn from each shu dealt. If dealt to me, I get an instant £5 cash bonus. If dealt to the dealer, all players get a £5 cash bonus. The tables don't usually have many players, so this alone probably makes the game EV+. The golden card 'happy hours' aren't applicable on the Unlimited game.

3) I saved the best until last - on the standard game if I get a 5 card hand and a push, the bonus pays out! This error in the system setup doesn't seem to apply on the Unlimited game.

Based on all of this the EV per hand must be higher on the standard game, especially during happy hours. But being able to place 5 x as many bets on the unlimited mode could be enough to outweigh the better terms in the standard game.

If you were in my position, which would you be playing?