Edge without the push

Hey guys,

First thread and apologies if I should have done this differently or if the information was readily available elsewhere.

If you exclude pushes (i.e only count resolved) what effect does that have on the house edge?

The reason I ask is for a casino promo I am looking up which has a cash and comp rebate. It only counts resolved bets as turnover.

Game rules are Stand on 17, 8 Decks, Shoe dealt, 9-11 double, split up to three times. Can double down split, can't hit split aces.

Thanks in advance for any help!

Quote: PaulieG

Hey guys,

First thread and apologies if I should have done this differently or if the information was readily available elsewhere.

If you exclude pushes (i.e only count resolved) what effect does that have on the house edge?

The reason I ask is for a casino promo I am looking up which has a cash and comp rebate. It only counts resolved bets as turnover.

Game rules are Stand on 17, 8 Decks, Shoe dealt, 9-11 double, split up to three times. Can double down split, can't hit split aces.

Thanks in advance for any help!

With all due respect, I don't know that you're really pursuing the question the right way...but maybe you are.

I think all you really need to do is to determine the value of the cash and comp rebate and then go from there. The house edge of the game is just the house edge of the game, so the more valid question is whether or not the value of the comps/cash outweighs the house edge of the game.

In other words, just because cash/comps don't get added to your pushed bets doesn't mean the house edge of the base game changes: it doesn't. It doesn't even change your expected loss per hour on the base game.

The rules are a bit different, but with a six-deck game with a couple other minor differences:

https://wizardofodds.com/games/blackjack/appendix/4/

You push about 8.48% of the time.

If you want to play it safe, maybe just call it 9%.

When you have your 9%, then all you want to do is figure that all 91% of your other action counts, so then figure out what you're losing per hour to the game and how the comps/cash compare to that based on you're getting it for 91% of your hands.

Do you know whether doubles/splits add to the cashback, or is it just the base bet? That's very important, too.

Here is the House Edge calculator:

https://wizardofodds.com/games/blackjack/calculator/

You did not include whether or not you can Surrender or whether or not only the original bet is lost to a Dealer Natural, and both of those rules are pretty significant to the House Edge.

Thanks for your reply.

I thought that the house edge was slightly higher for bet resolved than it was for bets made. I am mainly a craps player and this is the case there. I just thought it was the same.

If it isn't this gives me a different question which I will get to later.

In regards to your questions double and splits are added. You cannot surrender and I believe only original bet loses.

I roughly equate this to be around 0.55% maybe a fraction less.

The other question - If you are correct and turnover doesn't effect house edge then I feel I am micalculating the other casino membership that I obtain.

In this program you need 40,000 points to stay a member and you get 1 point for every $400 hand of blackjack including pushes.

Assuming a house rake of 0.55% I have always calculated the cost of the program as ($400*0.55%)(40,000) =$88,000.

Are you saying the true cost is actually less than that as those 9% of pushes come off the total cost?

The way you were calculating it was correct. The 0.55% HE includes pushes.
So the expected loss of 40000 hands is what you had: ($400*0.55%)(40,000) =$88,000

Edit: Now if you want the expected loss of 40000 resolved hands, then it's ($400*0.55%)(40,000)/0.9152 =$96154
The reason being to have 40000 resolved hands you need to play about 43700 hands. 40000/0.9152
Another way to look at it is the house edge excluding pushes is 0.55%/0.9152=0.6%
Pushes kind of "dilute" the house edge which is why it is larger if they are excluded.

out of curiosity, what kind of membership is worth $88K?

Thanks Tyler,

So by your post I feel like the house edge on my initial $300k resolved turnover question is closer to 0.60%. Given the offer was 0.60% in cash and 10% in comps it still sounds like a good way to have a relatively cheap holiday!

I wouldn't say the other membership is worth $88k but that is the cost. The value is probably closer to $50-$60k. However, I use it alot for client dinners and work functions so do find additional value elsewhere!