with the rules as shown below for Delaware

Park Casino

Number of decks of cards used: 6

Dealer stands on a soft 17:

Player can double after a split: yes

Player can double on: any first two cards

Player can resplit to: unlimited hands

Player can resplit aces: 4 times

Player can hit split aces: no

Player loses only original bet against dealer BJ: yes

Late surrender allowed: yes

Blackjack pays: 3 to 2

customer cannot split 10's

and using a continuous shuffler

Optimal results: ?

Realistic results: ?

unlimited splits is off the chart

the .285 is on the chart you mean

there is now advantage to the player

on the unlimited splits and the

spliting of aces 4 X

Say you're alone at the table, and the dealer has just had you cut a new shoe.

Say your first card is an X and the dealer's first card is a Y. The odds that your second card is an X are ((6*4)-1)/((52*6)-2)=23/310. So there's a 7.5% chance that you'll pair your first card. You'll only want to split a fraction of those paired combinations, but I have ignored that for this example. I have also ignored the fact that even during the times you'll want to split, splitting is only marginally beneficial.

The odds of getting a 3rd X are ((6*4)-2)/((52*6)-3)=22/309, and the odds of getting a 4th paired card are ((6*4)-3)/((52*6)-4)=21/308. The odds of getting a hand to split 3 times into 4 hands are 23/310*22/309*21/308=.036%, or 1:2750 hands.

The odds of getting 5 matched cards are .00036*((6*4)-4)/((52*6)-5)=.00036*(20/307)=.00234% or 1:42600, and the odds of 6 matched cards are .0000234*((6*4)-5)/((52*6)-6)=.0000234*(19/306)=.000145% or 1:688000.

So having the right to split to 5 hands instead of 4 will only affect your play 1 in 42500 hands (1 in 14 hands when you already have 4 matched cards.)

The rarity of the times that you'll have 5 cards to split is what made me say that the infinite splitting would only help you a tiny bit.

they us a continuos shuffler and player cannot split 10's

Quote:rdw4potusI can try to walk through an example. (someone should check my math...)

https://wizardofvegas.com/forum/gambling/blackjack/2036-probability-of-split-hands-infinite-deck/

This is from ininite decks and only to 4 hands:

1 hand = 12/13

2 hands = 144/2197

3 hands = 3456/371293

4 hands = 769/371293

Or 1 in 482 hands can be split into 4 hands.

Quote:PlayBJIs this for the aces 3 hands for a total of 4 what about the unlimited splits what do i do there and how does the continuous shuffler effect the house advantage.

A continuous shuffler lowers the house edge. Only 1 in 6277 hand will end up as aces split to 4 hands. The differance in HE from spliting to 4 hands and unlimmited spliting is very small (less than .01% is my guess). Overall I get a house edge of 0.26197%

Thanks for the reply with all the rules in place at Delaware Park you get .26197% HE I am way off

6 deck +0.54

double down on any cards -0.24

double down after spliting pairs -0.14

late surrender -0.06

re - split aces -0.06

total 0.04

Quote:PlayBJHi Miplet,

Thanks for the reply with all the rules in place at Delaware Park you get .26197% HE I am way off

6 deck +0.54

double down on any cards -0.24

double down after spliting pairs -0.14

late surrender -0.06

re - split aces -0.06

draw to split aces -0.14

total -0.10

I don't understand what you're doing here. How are you getting those adjustments, and why are you starting from 0? Are you sure there's no native house advantage before you start adjusting?

Also, your original set of rule stipulations said that hitting split aces was not allowed. Can you actually draw to split aces in the game at Delaware Park? That would lower the HA quite a bit from the .26197% to .08432%.

No.Quote:PlayBJwith a house edge of .26197 and a customer using perfect basic strategy

Maybe.Quote:card counting

you probably should have started a new thread, there are always folks who stop following certain threads, myself included.

I'm the wrong person to ask, but I suspect at least a minimal player advantage should obtain when the count is favorable. Even the simple ace-five card count can give player advantage up to .57% according to the WoO page below, depending on how good the count is at the time.

https://wizardofodds.com/blackjack/wizardcount.html

Quote:wrxrobFor the record, I played in Delaware Park recently, and they did not offer surrender. At least, the dealer shook his head as if he had never heard of surrender.

Using one of the magnificent tools available at WoO site, it appears the house edge goes from 0.28507% to 0.35767%, realistic window, with no surrender allowed. I input the info from the first post of this thread, changing the surrender bit.

It sure would be nice to be able to nail these things down.

I also am quite curious as to what the minimums are at the tables these days, esp at Harrington.

Here's another vote/request for that info. At the end of my September trip, I will be passing through Delaware, and I have to decide whether to add a day to visit the three casinos. If they are operating like other new eastern-time-zone casinos, where folks were claiming they have crowded tables with minimums of $100 or $200, I will pass on the opportunity.Quote:odiousgambitI also am quite curious as to what the minimums are at the tables these days, esp at Harrington.