Game Profitability

I would love some insight on the profitability of this game I found. I can’t figure out how to plug the details into my software as I’m extremely technologically challenged so I was hoping somebody could help.

I recently found a game that paid a pretty hefty bonus on 6 deck shoes for any 3 of the same card for numbers 3-7. If they were the same color the bonus was even bigger. There was nothing advertising the promo or payouts on the table so I didn’t get a list, but I hit a few times and noticed it was anywhere from 5x to 10x my bet depending on the colors and card number. 3 red 7s was an automatic $1,000 regardless of the bet size. 10x was a game changer with my higher bets on the table.

The downside was this casino was tiny with only a couple open tables at a time that were always packed regardless of what time I went. Meaning I pretty much had to sit and play through all negative counts and the rounds were often slow. I could tell the dealers were trained to cut 1.5 decks, but they would cut closer to 2 decks to be on the safe side at least 75% of the time. The biggest downside was the dealer took no hole card and a dealer blackjack won all bets.

The rules were ideal: double any first 2, double after split, re-split aces and outside of having a pit boss parked at my hip on two sessions, nobody ever said a word to me about my play or my bet variations so I got several hours in while I was there. I made some good money during most sessions, but most of it was attributed to the bonuses I managed to hit so I’m wondering if maybe I just got lucky.

Can somebody help me determine if the bonuses do in fact make this a profitable game despite 6 decks with typically only 70% penetration, no hole card w/ dealer BJ taking all, full tables, and no Wonging due to the limited availability? Keeping in mind the bet variations didn’t seem to bother any casino personnel. Normally I wouldn’t have the patience to sit through these conditions so I don’t want to unless those bonuses do in fact make this game substantially more profitable.

Thank you.

A player’s hand of three deuces will not get paid the bonus. Is this right? This doesn’t make sense. 

Three of the same card in a row in the player hand? Can other cards be in between? Is it paid on splits and doubles? And what are the exact payouts? We can't tell you the house or player edge without an exact pay table.

Is it the initial two players cards and dealer up card that compose the 3 cards that are evaluated for the bonus?

I apologize I thought I would receive an email if I received a reply.

I think it’s safe to assume the bonus pays 7 to 1 minimum for however much your bet is, including double down (which is mostly relevant when you start 5/5).

The bonus is strictly based on the players 3 card hand. If you split the bonus is still in play, but for each individual new hand. The bonus is strictly for cards 3-7 so three deuces does not pay and anything over 7 is just a bust.

EX: You have 6-6 against a dealer ten so hitting a third 6 pays the bonus and ends the hand. If you double 5-5 against a 9 then the bonus pay includes the double if you get a third 5.

This is not hard to estimate. The probability of a 7-7-7 hand is 1/(13x13x13), so the probability of all bonus is just five times of this. So, the bonus adds a player advantage of 7x5 / (13x13x13) = 1.6%. 
 

You also may double 5-5 vs. 2 or 3-9. This part will add another advantage of 7x (8/13)/ (13 x 13 x 13) =0.2%. 

For the six-deck shoe, the top number is 1.41%. But what you fail to realize is that a good percentage of that number goes away because of the foolish plays you would make by not splitting, in an effort to get the bonus. So, the edge is much less.

See BJA3, pp. 30-31.

Don