A TOUGH CHOICE (or is it)

you are tied in chips and must have a 3 hand playoff. after the 2nd hand you are still tied. both bet max bet and have enought to double, triple, etc. the delema, you acting first get a BJ. your options are

tuck for a 21 (opponent does not know you have BJ but no premium payoff)
double down
take the payoff
surrender is not allowed (just kidding)

what would you do

 

Looks like the initial two cards are face down in this case.

I think I would take the payoff for the BJ assuming that it at least 3/2. If it is more, then I would definitely take it. This move forces your opponent to double down or split. Without being able to see your opponent's cards, and not knowing what the dealer's up card is, that gives you about a 70% chance of beating him. This will vary depending on the dealer's up card.

Simply tucking would also probably prompt your opponent to double, but he could tie you simply by winning his hand or he might also have a blackjack, so why not cover those situations?

Doubling down gives up the low and would likely make your opponent less aggressive. The probability of winning your double would be the same as doubling on 11 and I think your chances would be less than 70% (someone here probably has a table with actual number).

As a side note, if you take the payout for the BJ and your opponent also has BJ, he should probably double anyway for a better than 50% chance of beating you.

 

Gronbog is correct that decision weather to tuck the bj or not will be influenced by the dealer’s up-card.

We assume that if we take 3 to 2 payout on the bj our opponent doubles which gives him slightly over 30% chance of beating us.
Statistical approach shows that, without knowing the dealer up-card or the opponent’s two cards (we have to assume he should play basic strategy, and actually be a bit more conservative), he will win double bets about 6% and get bj 4.7%. So, we lose about 11% and the rest of the hands he wins about 1/3 of the times. We both win about 30% of hands, which takes us to second playoff. Half of them we should win (and if the rules are right in the second playoff, in turn, we should be in position of having the last bet, which should make us about 60% favorite). In total our opponent has 11% chance of besting us by bj or winning more than one bet and up to 15% from the second playoff.
Our chance will be in mid 70's%, slightly better than taking bj.

Now, since there is no such a thing as statistical dealer up-card, I will try to estimate, and type about them as I go, chances at the dealer’s up-card 7- first case where player should mimic dealer’s strategy hit to 17. Checking numbers for average casino advantage based on dealer up-card can be helpful. For dealer’s up-card 7 player has advantage 13%. It has to be easier for the opponent to win than against up-cards 8 (player advantage 6%), or dealer up cards 9 or higher- advantage casino, or even up-cards 2 and 3 – 9% and 11% respectively.
There will be approximately the same amount of doubling as average but winnings should be slightly harder to come by. Assuming we lose to double wins and bj about 10% we need to find out our opponent win rate for the rest of the hands (~83% excluding doubles, splits and bj). A quick calc. shows me that that this rate is about 43%. 43% times 83% = 35.7%. Since we win half (or more) of second playoffs our opponent chances are 10% plus 18% =28%. Tucking bj vs. dealer’s 7 seems a better play than taking 3 to 2 payoff.
My guess is that even against dealer’s 6 hiding our bj would be a very close play, and a better one if the second playoff gives us last betting position.

And a quick quiz:
What do you do if the dealer has an Ace and ask for insurance?
My answer is a few lines down.
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I would take insurance for less, in a manner to motivate the opponent to take insurance for more than I did.

S. Yama

 

wrong data similar outcome

Ooops!
I guess I could try to blame it for writing at 4 a.m. after coming back from Vegas and sleeping less than 20 hours in the last four nights but the truth is I just made a simple mistake. When I calculated win rate for hands other than bj and the ones we double against dealer’s up-card seven instead of omitting two-cards totals ten and eleven I took outcomes of all the hands with first cards other than Ten and Ace. My bad, have to re-do it.
...

The other quick way to roughly estimate it would be to look at the game EV for the particular up-card.
In my picked up case of up-card seven the casino has an edge of about 13%.
This perhaps could come from:
winning bj: 4.5% times one and half ~= 7%
winning double plus bet, 6% won, 4% lost ~= 4%
This leaves us with about 90% hands and if we take away 7.5% (just a guess) of pushed hands all other hands are 82%.
To get the remaining 2% edge from won to lost hands ratio it would have to be about 42% vs. 40%.
Coincidentally this is very close to my previous erroneous calculation of 43% vs. 40%.
That leaves me with the same conclusions as in the post above.

Time to get a nap, lol.

S. Yama

 

Tuck BJ

askdick stated "tuck for a 21, opponent does not know you have BJ but no premium payoff), he can verify but "no premium payout" indicates to me it's a pitch game that pays even money for a tucked winning BJ.

 

Tucked Bust?

Interesting form of deception and a reasonable way to handle it. What is typically done for a mistakenly (or purposely) tucked busted hand? I could see doing it on purpose as a way to encourage your opponent act more aggressively than he needs to.

 

thanks for your comments...
this was at rampart in las vegas. it was not my hands, as i was playing in the round but was out. the results was the dealer had a face up, the guy with blackjack took the payoff. 3/2. the other player had a 3,2 doubled down and caught a 2. the dealer turned over a 4 for fourteen and busted with a face. of course the double down beat the blackjack and won the round.

as barry greenstein says..."mathmatics is ludicrious"

if you tuck a busted hand,,,most of the casinos out here would still treat that as a bust and if the second player busted he would still be treated as the winner.