Hi all,

Looking for your opinion on a one day promotional blackjack bonus here at my local casino in Belgium.

You basically get 3000 for free every time you get two kings on your box, split them and get another king on one of the two hands. That’s it. Seems exploitable to me. Even if you play at the minimum which is 5 euros.

Is this really free money or am I not seeing this correctly? Anyone can do the math on the probability of this happening?

Cheers

It should be +EV. But be prepare it will be rare. To get KKs is 221:1 and to get another K for first is 4%, secondly 4,08%(It changes, because you will see the other players hands). I think this to happen is 2747:1. GL.

Single deck?

for six deck the chance of your first card being a king is 24:288 or 12:1 against. The chance of the second card being a king is 23:288 or 12.52 : 1 against.


I get 1 in 175.76 for the initial pair of kings.


But you should describe the other rules.

The other rules don't matter much. This is a huge edge on a small bet.

Assuming single deck, the probability of getting a pair of kings is 1/13*1/17 = 1/221. The probability of at least one of the split draws being a king is (1/25+24/25*2/49) for an overall probability of 97/270725 ~= 1 in 2791.
We make roughly 1 euro per hand, which is a 20% edge on the minimum $5 bet. Unfortunately tables will likely be full, so you won't get mad hands per hour. At a full table you should get about 50 hands per hour. 50 euros per hour is amazing for most people. I would try to get as many friends to grind with you as you can and split whatever you win (which you hopefully do!)

For 6 decks I get prob 24/312*23/311*22/310 = 0.000404 to get 3 kings in succession. Assuming the bonus only applies to the next card dealt to each of the 2 split hands I get prob approx. 0.000404 + 0.000404x12/13 which is 0.000776. The EV per hand is 0.000776*3000 = 2.33. So obviously get a team to get as many hands per hour to increase return and decrease variance for each team member.

OP did not mention if the king must be the next card dealt for the split hand. EV would be a bit higher if bonus applies to a king hit card.

You can also do a side count of kings and skip the shoe if fewer than 3 remain, which will bump your return a bit. Like the above poster said make the min bet and don't worry about house edge. Fill up as many open bet spots as there are available. I did not calc your bankroll requirements but I susoect you will need about 1000x min bet to be reasonably safe.

The one thing that hasn't been taken into account here is the EV lost on having to split your kings instead of staying on 20. Obviously it's not a lot and is still well worth the gamble when you actually get those 2 kings, just pointing it out to you EV and statistical purists out there trying to calculate the exact edge.