Advantage gained by Blackjack rule variation

Question

There are many tables, charts and simulations for standard Blackjack variations and the % change in house edge that each rule introduces, like this one, for example.

I have come across a Blackjack variant which on the face of it seems very generous, but I'm struggling to work out how much it affects the house edge mathematically.

The variation is that instead of the dealer waiting to reveal his second hole card until after the players have taken their turns, it is exposed from the start.

So you can see the dealer's first two cards before you make any decision as to whether you should stand/hit on your own hand, with the exception of taking 'insurance' against a dealer blackjack.

Is this variation as generous as it sounds?

Answer 1

It is extremely valuable. Any time you have a strategy that says to stand on 17, if the dealer shows 17 you know you have to hit and will win $\frac {16}{52}$ of the time (ignoring used cards). You can also stop earlier when the dealer shows 16, for example, hoping he busts. Unfortunately, this is coupled with the player losing ties instead of pushing them, which is a big downer. If I had to guess, the pair of these changes is more favorable to the house than standard, or they wouldn't offer it.

Answer 2

It's hard to say what the exact numbers are without a computer computation. You still have the disadvantage that you have to play first, which means that you have the opportunity of busting first if your hand is lower than the casino's (so that you are forced to hit). On the other hand, if you were behind the casino, and you hit, then your chances of busting are less than the chances of the casino busting if the casino is forced to hit. So you can get into situations where you are behind the casino but the casino is forced to hit and the casino's chance to bust is greater than $50\%$ so you can just stay. Also you know that if you ever go above the casino and the casino has hard $17$ or higher, then you are a guaranteed winner. All of this adds to your edge, and if it didn't give you the upper hand, then some casinos would offer this form of play. I encourage you to write a computer program that simulates each combination of your hand vs. the dealer's hand. (there aren't that many, because the suit doesn't matter). Then simulate what happens when you stop at different score cutoffs based on the dealer's initial hand. And see what the expected winnings are, and take the maximum (for each choice of the dealer's initial hand) for the score-cutoff when to stop taking cards. Then once you statistically determine the best strategy for each choice of dealer's hand, you can focus your simulations just on using the best strategy, and do a lot more simulations using the best strategy, to get a good estimate on your expected winnings per hand. Most casinos use a pretty large multi-deck so in your simulations you can just assume that each card value has probability 1/13 of being dealt, regardless of what's been dealt so far.