Split or not to split. That is the question.

Sooo...my friend just asked me the following question based on his round at the Golden Nugget and it sounds like there was no consensus at the tournament so I'd like to share with all of you. For those who don't know GN rules in this situation is top 2 advance, no DAS, 3:2 BJ, no late surrender.

"I was BR1 going into last hand with 6700 and I was last to
bet on last hand. BR2 had 5600 and bet the max 2k. BR3 had
5500 and also bet max 2k. BR4 had 5200 and also bet max
2k. So, first question is how much do u bet as BR1?

But, here is where it got tricky:

The dealer is only showing a 6

BR4 doubled down and ended up with a hard 12 (so he
now has 4k bet on last hand with a stiff hand of 12

BR3 also doubled down his 2k bet and ended up with a 21

BR2 just stayed with his 19

so, now me BR1 has 2 face cards with a 20 and i had bet
1600. So do u stay or do u also
split?

Either way I am stuck in the middle since BR2 did not double
down and stayed with his 19

I ended up advancing but none of the regular pros could
agree what the correct decision is"

This was my response. Can someone provide expertise/opinions?

"Thanks for the question. This was a fun one to figure out but really hard.

Your odds of dealer busting showing a 6 is 43.8% in which case your advance rate is 56.2% by staying. Dealer making any hand makes you a winner.

Taking into account the odds of you pulling a good card (10-A) vs a bad card (2-8) vs a neutral card (9) which ties BR2 your advancement rate is the following:
2 good cards 17.3%
2 bad cards 14.8%
One good/bad 21.2%
That alone puts you at 53% but doesn't take into account if your "bad" card is a 7 or 8 which would help your situation but the math is driving me crazy. I'm not sure it would make up the 3% difference so I would stay but it's REALLY close."

 

1 minute answers:
Bet 1475 to keep the low over BR4's push if you are allowed to. If you have to bet in units of $100, then bet 1500
Given your bet of 1600, then if you stand then you have BR2 beat. If you split, and play a no-bust strategy, then you have BR4 beat, you you also retake the high. So I would split.

 

Agree completely with Gronbog and Monkey. Correlation is king in such situations.

P.S. GN does require bets in even hundreds unless you're going all-in with an odd amount.
It's a rule that screwed me hard in a past BJT there. No complaints, that's the rules.

 

My strategy generator confirms that splitting and then playing no-bust (i.e. stand on both hands) is the optimal strategy. Here are the success rates for 8 decks, S17, SP3, NDAS.
Split: 66.0%
Stand: 57.6%

For academic interest, since no one would actually consider these plays:
Hit: 22.7%
Double: 7.5%

 

I have seen a player go all in on the last hand betting other than an even hundred. Since I was not at that table I could not complain about that bet being allowed. Unless I missed something, I saw nothing in the printed rules that are available to the players that would allow that kind of bet. The rules only said that all bets except insurance bets must be made in multiples of 100 with a max bet of 2000. If it were to my disadvantage someone were to bet an non multiple of 100 I would call the pit boss over and take out the rules that I always carry with me and point out the betting rule.

Also note that the rules do not say you have to take insurance in multiples of 50. Maybe you could insure an 800 main bet for say 375 or 325?

For infinite deck:
As far as initial bet is concerned I as BR1 would have simply correlated with a bet of 2000. With everybody playing the basic strategy for hitting and standing (but no doubling or splitting) BR1 should advance 82.6%. A bet of 1600 yields 82.5%.

Oddly enough a bet of 1000 yields 87.8%. Probably because of BR1's big lead. If all the other players were close behind with 6600 each then a bet of 2000 would be best.

With the cards and actions of the other players as shown then standing with 10+10 yields a 56.0% chance while splitting and playing not to bust yields 67.1%.

..................................................................BlueLight

 

Bluelight, thanks for the exact combinatorial numbers. I always like get reliable results from other sources and it looks like my quick sim is in the ball park.

 

Maybe I can provide explanation. At GN all bets are in 100s. However, when player goes all in, general rule is to wait until the hand is played and then settle the bet. This is to avoid dealers counting up the chips for the benefit of others. You are correct about insurance. A player can take insurance for less without restrictions.

 

Leftnut did say that going all in with odd amounts is allowed.

 

The player I saw bet 1 or 2 purple chips, a bunch of black chips and 2 green chips; obviously not an allowed bet according to the rules.

 

According to Leftnut, that would be ok if the player was going all in --- see above.

 

I've seen it happen there twice. Maybe those players got away with it but that's my source.

 

Strong work everybody. Makes we wonder how much I've got to learn but I appreciate everybody's mentorship and sharing of knowledge. These simulation programs you refer to have me curious. Any recommendations?

 

It's my own software. Unfortunately not ready for release into the wild yet. I believe that BlueLight also uses his own software.