tthree
• Posts: 7
Joined: Mar 20, 2011
March 20th, 2011 at 9:14:21 PM permalink
I play at a casino that allows you to split pairs an unlimited number of times(max 4 hands with aces). It allows double after splitting, surrender, dealer stands on all 17 dealt from 8 deck shoe(sometimes you can find a 6 deck shoe). All the house edge calculating programs Ive found dont allow these generous splitting rules to be entered. What is the house edge on this game? Or atleast how much does it shrink the house edge versus a game that can be entered in these calculating programs(name the splitting rules you are comparing it to)? Ive split to 8 hands once(I had 2 double downs, I was splitting eights against the dealers upcard of 5 and the dealer busted so I won all the hands) and the max of 4 hands with aces twice. I want to play the lowest house edge game I can find but without being able to determine this for this game I cant make that determination with any certainty. Thanks to anyone who can help make these determinations.
P90
• Posts: 1703
Joined: Jan 8, 2011
March 20th, 2011 at 11:05:12 PM permalink
Tried this chart? - https://wizardofodds.com/blackjack/rule-variations.html
Or this calculator - http://www.beatingbonuses.com/houseedge.htm

Resplit to 4 hands or more than 4 doesn't have much effect, something like 0.002%.
Surrender after split is a stronger rule. With surrender being worth 0.075%, and splitting ~1/15 of the time, a rough estimate would be ~0.005%.
Six vs eight deck shoe is worth 0.015%.
Can you double on split aces, and/or play out (hit) split aces?
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tthree
• Posts: 7
Joined: Mar 20, 2011
March 21st, 2011 at 6:16:46 AM permalink
P90 thanks for the help. I used the beating the bonuses web calculator which now got a house edge for splitting to 4 hands. Im not sure if it assumed aces split to 4 hands as well. It didnt have a separate parameter for splitting aces as the wizard does(I was already aware of this tool). Splitting past 4 hands obviously has a ever decreasing impact on the house edge; however, Im still interested in a definitive answer. Another detail left out of game rules blackjack pays 3:2. I refuse to play games that dont as I assume everyone else does so I forgot to put it in original post. You can only late surrender or on your 1st 2 cards. Your effect of the resplitting to 4 hands seems to be off a couple degrees of magnitude, perhaps the % sign was added by mistake. Also you get 1 card only on split(or resplit) ace hands. Thanks again I can always use a new resource. Anyone who can get me closer I would appreciate the help.
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P90
• Posts: 1703
Joined: Jan 8, 2011
March 21st, 2011 at 9:02:18 AM permalink
Quote: tthree

Your effect of the resplitting to 4 hands seems to be off a couple degrees of magnitude, perhaps the % sign was added by mistake.

That one is actually at least of correct order of magnitude, it's for difference between 4-hand and infinite resplit. The first resplit (to 3 hands) removes ~0.1% from the house edge, the second resplit (to 4 hands) 0.01-0.02%. The third resplit (to 5 hands) would then be closer to 0.002%, perhaps 0.003%, the fourth and further not worth calculating. Out of 169 possible hands, only 8 are splittable, and even then not against every upcard.
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tthree
• Posts: 7
Joined: Mar 20, 2011
March 21st, 2011 at 3:23:45 PM permalink
Sorry p90 the correct adjustment seems to be halfway between us, we are both of by 1 order of magnitude off(pair splitting limit raised from 3 to 4 hands decreases the house edge by about .02% as calculated by beatingbonuses website). Still hoping to hear about how unlimited splitting adjusts the house edge. Thanks again P90.
Wizard
• Posts: 26619
Joined: Oct 14, 2009
March 21st, 2011 at 3:39:55 PM permalink
I also show that infinite re-splitting, compared to up to four hands, is worth 0.02% to the player.

I might add that if the infinite re-splitting rule included aces the effect would be 0.05%.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
tthree
• Posts: 7
Joined: Mar 20, 2011
March 21st, 2011 at 4:04:31 PM permalink
WHOOPs didnt read your last post before replying. Not sure how this calculation is done so Im not doubting your numbers; however, the beatingbonuses calculator for splitting to 3 versus 4 hands generates as house edges for each as 0.283% and 0.302%. I know enough about statistics to know the intuitive math can lead you down the wrong path, but as I do the basic math allowing for rounding off I get 0.019% plus or minus 0.001%. Explain why my instinct to just take the difference of the 2 values seems to give a different result than you seem to be suggesting. What am I missing. I may not understand what you are saying yet. I was a real math genius in college(20 years ago) finding all the advanced math classes to be childs play except advanced statistics which I aced as best in the class; however, as I stated earlier I often didnt follow the right train of logic when searching for a solution to a problem. Thanks for your patience.
tthree
• Posts: 7
Joined: Mar 20, 2011
March 21st, 2011 at 4:11:30 PM permalink
Thank you Wizard for giving the missing info I requested. Thanks for your partial solution P90.
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