Basic Strat for when BackBetter >> FrontBet

[dacium]

If the back bet is much larger than front bet, when you split the back bet is essentially having the option of playing two hands or one. This changes the BS. I have almost worked out what the BS should be when the front bet is negligable compared to the back bet:

TT - Normal (never split)
99 - Always split except against 8. Play one hand only against 9, T, A.
88 - Always split. Play one hand only against 8, 9, T, A.
77 - Always split. Play one hand against AT987 32.
66 - Always split. Play one hand against AT987 432.
55 - Normal (never split)
44 - Normal (split and play both against 5 and 6)
33 - Always split. Play one hand against AT987 32
22 - Always split. Play one hand against AT987 32
AA - If one card to each ace play one card only against A
(I just found an error in AA so that one might change).

Also I have found that many sites use 'infinite' decks to do the calculations for BS. I don't know how they could possible do the calculations exactally. For example 88 vs T split has so many play cominbations that can happen (because you play 2 hands the number of combinations goes up exponentially with each card) that it took my computer many hours just to compute this one hand mathematically perfectly for 6 deck with no 'infinite' deck or estimations etc. The difference can be significant on hands like 88 vs 8 where 3 out of 24 8's are gone. I found as much as 5% difference on some 'standard' values given by wizardofodds because he uses infinite deck.

 

[MGP]

Also I have found that many sites use 'infinite' decks to do the calculations for BS. I don't know how they could possible do the calculations exactally.

If you fix the strategy post-split then it's not difficult to calculate the EV exactly for finite decks (once you know how that is). Calculating perfect-play splits that take into account all possible future cards and past card for the entire split round can take a long time per split but nobody can or does play that way. The calculations only take a few seconds for the entire strategy including all split hands.

I know that my numbers, Cacarulo's and Keith Collins' are exact for fixed strategies. Ken Smith and T Hopper both have perfect play split programs that can calculate those values. I'm not sure who else has what. The strategies that you see from me or Cacarulo are correct, including the Cacarulo's strategies in BJA3. You're right though that most sites use estimates for splits.

The size of the bet does not alter the strategy if you are maximizing EV so I'm not sure what you're doing. Furthermore, I have yet to come across an example where the EV for splitting 1 hand is greater than the EV for splitting to the max hands when the correct strategy is to split. There may be some very special shoes where this is the case but so far it hasn't been the case for the top-of-the deck strategies.

 

[shadroch]

how about when the correct strategy isn't to split?
Case in point-2,2 vs. Ace.

 

[Sonny]

TT - Normal (never split)
….
88 - Always split. Play one hand only against 8, 9, T, A.
77 - Always split. Play one hand against AT987 32.
66 - Always split. Play one hand against AT987 432.
55 - Normal (never split)
44 - Normal (split and play both against 5 and 6)
33 - Always split. Play one hand against AT987 32
22 - Always split. Play one hand against AT987 32
….

Everything above is correct. There are just a few changes listed below.

99 - Always split except against 8. Play one hand only against 9, T, A.

I think you meant to say “except against 7”, not 8. You will want to split nines against an eight.

AA - If one card to each ace play one card only against A

Always play two hands with an ace.

If you are playing a game that doesn’t allow DAS then the strategy will be slightly different.

-Sonny-

 

[MGP]

Ok - so I found this from the other thread. If I understand the situation this is how it plays out:

1) Small player places $5 front bet and big player places $50 back bet (or whatever numbers you choose)

2) Small player gets a pair and has the choice of splitting. If he splits then:

a) Big player can split with him and add the appropriate amount to his bet, or
b) Big player can keep his original bet on only the first of the original split bets.

In order to get the exact value of being able to split when you want as a Big player while the Small player splits all the way through whenever he splits it would take some reprogramming which is too much hassle. A very close estimate of getting the value of a single hand of a split is to divide the SPL1 EV in half. This gives an approximate value of having your bet ride on only the first hand of a post-split hand. (This is actually exact if the Small player only splits once as well). It's not exact because it doesn't fully take into account the effects of removal of the Small player's post-split cards beyond the first one - but it's very close in most instances.

Doing it that way, then the correct strategy for the small player would be to split whenever the strategy is already to split or if the SPL1 EV / 2 is > the usual strategy EV.

If we assume 6D S17 DAS SPL3, then the suggestions made make sense except the ones that Sonny pointed out and I would also take exception to only playing one hand for any pair in which the original strategy was to split.

For example, If you only split 22 vs 7 or 66 vs 4 once, then you are playing a negative EV hand vs a positive EV hand if you split every possible time. The other times you are playing a lower EV hand if you only split once. I don't know of any instances where the strategy is to split but the EV decreases with subsequent splits so that's why I'd always split all the way if the original strategy was to split.

 

[dacium]

Yeah thats what I figured out basically as well, and i did mean stand on 99 against 7 (i always say this wrong for some reason!?)

Anyway it turns out for 6 deck game the advantage is about 0.2%, that was in a 6 deck DAS split once S17 Double 9-11 game which has a house edge of about 0.6%, reducing it to about 0.4%. Not sure what it would do on single deck games that only have house edge of 0.2% normally etc.

I still think alot of EVs seem to be over stated because of split errors. For example the game above is typically always given as about 0.58% house edge but sims and my calcs both give slightly over 0.62%, perhaps there is a difference in the way we calculate EV (per bet rather than per starting hand return etc) or something else because I can't find any difference in stategy on all the marginal cases (44 split 4, 16 stand 10, 88 hit A etc.)

 

[MGP]

6 deck DAS split once S17 Double 9-11 game which has a house edge of about 0.6%...

I still think alot of EVs seem to be over stated because of split errors. For example the game above is typically always given as about 0.58% house edge but sims and my calcs both give slightly over 0.62%, perhaps there is a difference in the way we calculate EV (per bet rather than per starting hand return etc) or something else because I can't find any difference in stategy on all the marginal cases (44 split 4, 16 stand 10, 88 hit A etc.)

The exact TD EV for this game is -0.555045971857625%

That means if you fix the number of rounds and use a pure TD strategy (i.e. only deviate for splits) then that's the EV.

If you use a cut card then the results will be slightly different (supposedly better for the player actually).

If that's not what you're getting then you have an error in your sims and calcs.

 

[dacium]

I think that 'exact' ev only applies to perfect shuffle after every hand. I got -0.55 for simulating 6 deck CSM with those rules, but -0.62 when simulation 7 player shoe came with 75% penetration.