Help - Blackjack House Edge Calculation

Hi everyone,

I've been playing Grand Theft Auto Online recently and noticed their Blackjack rules were very generous to the player. So generous, in fact, that I'm curious as to whether the player actually has the edge over the house (which could happen since it's a video game without real money).

The rules are as follows:
-4 Decks w/ Continuous Shuffling Machine
-Dealer Stands Soft 17
-Blackjack pays 3:2
-Double down allowed for any two cards
-Double down allowed after splitting
-Only allowed to split once (split to two hands)
-No Surrender
-No Insurance

This would normally give a house edge of around 0.21655%, according to the Wizard's House Edge Calculator (/games/blackjack/calculator/). However, there are a few extra rules that the calculator doesn't take into account.

The first is 7-Card Charlie. That rule only gives the player a +0.01% boost, so it's almost negligible.
The second is that drawing 10s after splitting Aces is considered a Blackjack (still 3:2). According to the Wizard's Rules Variation page (/games/blackjack/rule-variations/), this would give a massive +0.21%* boost to the player, effectively neutralizing the house's edge.
The final rule is that after splitting Aces, you are allowed to Hit, Double Down, or Stand (but not split, due to the no re-split rule). The draw to split Aces is already factored into the House Edge Calculator and gives a +0.19% boost, but does anyone know if the ability to Double Down is included in this +0.19%, or would the player advantage be even higher with all 3 options available?



*A note on the +0.21%:
Before I found the Rules Variation page, I tried to calculate the edge increase myself, but I got a higher number than Mike did. Obviously splitting 10s is a bad idea, so the only reasonable option was to calculate the odds of drawing a 10 after split Aces.

I took the odds of getting Aces to begin with for each of the dealers shown cards (from Appendix 9, /games/blackjack/appendix/9/4ds17r4/), and then the odds of getting 10 after splitting (about 43.1% to draw a 10 on either Ace, and about 9.6% to draw 10s on both). I then used the Dealer Odds table (/games/blackjack/dealer-odds-blackjack-us-rules/) to find the odds of a dealer getting 21 and reduced it from my existing amounts to analyze them separately. Under normal rules, the odds of drawing a single 10 and the dealer having 20 or less go from a win (+1) to a Blackjack (+1.5), and the odds of drawing two 10s go from two wins (+2) two Blackjacks (+3). The odds of drawing a single 10 and the dealer getting a 21 now change from a push (0) to a Blackjack (+1.5), and drawing two 10s with a dealer 21 goes from two pushes (0) to two Blackjacks (+3).

I'm assuming the difference between the original EVs and the BJ EVs should give the increase in player edge of +0.21%, but I came up with +0.238%. With my +0.238%, the game is actually in the player's favor, so I want to make sure there isn't some obvious piece I'm missing in my calculation. I don't think the differences are from deck size (Rules Variation is for 8-deck), but I could be wrong.

Quote: DarkSpartan

... it's a video game without real money ...

Welcome to the forum! I doubt other members will want to crunch the numbers you provided with no money involved. That raises the question of what the web site's product is. The answer that comes to mind is payment for advertising you view while you play. So probably a favorable house edge is given to keep you engaged. It costs them nothing to let you rack up points. Enjoy!