Blackjack with bonus payouts for 5-7 card 21

There is an online casino promotion where in 8-deck Live Blackjack you get extra payouts for hitting 21 with 5-7 cards. The minimum bet is 5€ and the extra payouts are:

5-card 21: 50€
6-card 21: 250€
7-card 21: 1000€

Obviously one should modify basic blackjack strategy to account for these extra payouts. Does anyone have Blackjack simulator which could analyse this game, and it would be interesting to know what the frequencies of the above hits are.

The game rules are: 8 Decks, Peek on Ace, double-down any 2 cards, no DAS, S17, BJ pays 3:2

Quote: Jufo81

EDIT: I didn't find a way to edit the typo in the title. The title should read: Blackjack with bonus payouts for 5-7 card 21

There is an online casino promotion where in 8-deck Live Blackjack you get extra payouts for hitting 21 with 5-7 cards. The minimum bet is 5€ and the extra payouts are:

5-card 21: 50€
6-card 21: 250€
7-card 21: 1000€

Obviously one should modify basic blackjack strategy to account for these extra payouts. Does anyone have a Blackjack simulator which could analyse this game, and it would be interesting to know what the frequencies of the above hits are.

The game rules are: 8 Decks, Peek on Ace, no DAS, BJ pays 3:2

Fixed the title for you, Jufo. Thanks for the heads-up. Do you know if they stand or hit soft 17?

Quote: beachbumbabs

Fixed the title for you, Jufo. Thanks for the heads-up. Do you know if they stand or hit soft 17?

Thanks. I forgot to post that it is S17, and Double any 2 cards, so the house edge is 0.72% and basic strategy is this:

http://www.beatingbonuses.com/bjstrategy.php?decks2=8&h17=stand&doubleon2=any2cards&peek2=ace&surrender2=no&charlie2=no&resplits2=0&bj=3to2&opt2=1&btn2=Generate+Strategy

So the dealer peeks with an Ace up, buy not with an X up? If the X has an Ace downcard, do you lose all, or just one bet?

Does the bonus pay

1. automatically, or
2. not against a dealer BJ, or
3. hand must win to get bonus?

Dog Hand

Quote: DogHand

So the dealer peeks with an Ace up, buy not with an X up? If the X has an Ace downcard, do you lose all, or just one bet?

Correct, the dealer doesn't check for blackjack with Ten upcard, and you will lose everything if he has a blackjack. This is reflected in the basic strategy I posted above.

Quote: DogHand

Does the bonus pay

1. automatically, or
2. not against a dealer BJ, or
3. hand must win to get bonus?

Dog Hand

The rules only say: "collect extra cash prizes for receiving a total score of 21:
With 7 cards = €1000, With 6 cards = €250, With 5 cards = €50"

There is no mention in the rules that the hand needs win to qualify for a bonus payout, so I assume that it's not required to win. But most 21-point hands win anyway so it's not a big concern.

I played some blackjack in free-play mode with the same rules and it didn't take long time to hit some 5-card and 6-card 21s, but of course the base house edge of the game goes up if you hit your hand to 21 aggressively.

There may be some errors, still checking this out

Assuming you are betting the minimum, (5 pounds):

With a 5 or 6 card hand: Hit a hard 20 or lower, stand on hard 21 (obviously)

With a 4 card hand : Stand on hard 20 or higher
Stand on Hard 19 vs 2-9, Hit hard 19 vs T,A
Hit a Hard 18 or lower

With a 3 card hand: Stand on hard 17 or higher
Stand on hard 16 vs 2-6
Hit hard 15 or lower vs 2-6
Hit a Hard 16 or lower vs 7-A

With a 2 card hand Hit a Hard 12 vs 2-6, Play all other hard hands 13-21 per normal strategy
Double on 2 card 10, 11 as per normal strategy, otherwise hit
Do not double 9, always hit

I have not calculated the EVs for soft hand and pairs but here are some guesses:

Stand on blackjack and 2-card soft 20 (A-9) otherwise hit all soft hands. Do not double soft hands.
Do not split A-A pair, always hit
Split 9-9, and 8-8 per normal strategy
Other pairs - I don't know, you are on your own.

Quote: gordonm888

There may be some errors, still checking this out

Assuming you are betting the minimum, (5 pounds):

With a 5 or 6 card hand: Hit a hard 20 or lower, stand on hard 21 (obviously)

With a 4 card hand : Stand on hard 20 or higher
Stand on Hard 19 vs 2-9, Hit hard 19 vs T,A
Hit a Hard 18 or lower

With a 3 card hand: Stand on hard 17 or higher
Stand on hard 16 vs 2-6
Hit hard 15 or lower vs 2-6
Hit a Hard 16 or lower vs 7-A

With a 2 card hand Hit a Hard 12 vs 2-6, Play all other hard hands 13-21 per normal strategy
Double on 2 card 10, 11 as per normal strategy, otherwise hit
Do not double 9, always hit

I have not calculated the EVs for soft hand and pairs but here are some guesses:

Stand on blackjack and 2-card soft 20 (A-9) otherwise hit all soft hands. Do not double soft hands.
Do not split A-A pair, always hit
Split 9-9, and 8-8 per normal strategy
Other pairs - I don't know, you are on your own.

Thanks, I was working on the strategy too but only managed to solve the 4-card hand case so far. Do you have any way of calculating how often the bonus payout hands are being hit with the above strategy?

One modification to the 2 card strategy: Hit a Hard 13 vs 2,3

Quote: Jufo81

Thanks, I was working on the strategy too but only managed to solve the 4-card hand case so far. Do you have any way of calculating how often the bonus payout hands are being hit with the above strategy?

Actually, no, not quickly. If I put another hour or two or so into it I could probably calculate the entire strategy and the player's EV (infinite deck assumptions.)

I think its a pretty safe assumption though that player has an advantage over the house at minimum table stakes.

Quote: gordonm888

<snip>I think its a pretty safe assumption though that player has an advantage over the house at minimum table stakes.

gordonm888,

At first blush, I'd guess a player's edge of 10% when flat-betting a 5€ wager.

Dog Hand