Damned if You Do ...

gronbog

gronbog

Top Member
I had this situation come up in a tournament I was in last weekend:

4 hands remaining, 3 players remaining, 1 advances
$100 min, no max, no surrender
Secret bet on final hand

The play was in this order with the button moving on each hand:

BR1: ~39,000, betting small now, but not afraid to bet big, cards: 19
BR2: ~38,000, betting small now, but not afraid to bet big, cards: 18
Me: 18,800, all-in, cards: hard 16
Dealer: 10

I should add that BR1 and BR2 both bet small enough that winning my bet on this hand would not put me in the lead even in both BR1 and BR2 lose. I would still have some work to do. I should also add that I did not know the true count, but you can factor that in if you like.

Considering the entire situation, how would you have played my hand and why? I'll weigh in with my own thoughts later.
 
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As I see, you was going to have advantage on the last hand betting last, but you had to catch up starting with this hand. Dealer had a 10 value card ?

Without knowing the true count, I would stand since right now I need a win not a push. But if the true count were negative, I believe I would hit.
 
Play

You did not mention the dealer's hand, was it 10?
I think essentially, it really does not matter much if you hit or stand under these conditions. True count is irrelevant in this case. The chance of winning 16 in - or + counts is too close to be of any appreciable value. Winning by the dealer busting or by you hitting will double your bank roll. Because the two other players have small bets, nothing will happen to their bank rolls, win or lose. So, you flip a coin and either hit or stand. Personally, not knowing the count, I will hit just for the slight benefit of winning while the one or both other players losing.
 
First of all, let me start by saying that I did not have some clever reason up my sleeve to be discovered for either hitting or standing when I posted this. It really is a damned if you do, damned if you don't kind of situation and I was interested in how others might approach it.

Three approaches have been touched on in the responses: play according to the count, play to win the hand (stand), and play for a possible swing (hit). Another approach would be to play to stay alive (i.e. not lose) which would also warrant hitting.

These approaches all focus on a goal for current hand, however, the real goal here is to get into position to play the final hand. There are 4 hands remaining and winning one hand out of the next 3 while not losing is really what is required. The secret bet on the final hand takes away much of any positional advantage I might have by acting last, but it is still essential that I be in a position by then, otherwise I risk being locked out.

By playing to win (standing) with 16 vs 10, I either succeed or fail right away. The percentages are 23.02% and 76.98% respectively.

By playing to stay alive (hitting) with 16 vs 10, there is a 20.01% chance of succeeding right away by winning plus another 5.90% chance of staying alive by pushing. The latter outcome would leave us in roughly the same situation but with only 3 hands remaining. This hand would also be played using the stay alive strategy and, if we pushed again, we would then use the play to win strategy. The question is, whether this approach of staying alive is more likely to succeed than playing to succeed right away

Let's find out ...

The stay alive strategy (http://gronbog.org/results/blackjac...one/generated/complete/0.0/p1.X/strategy.html) has a 43.39% chance of winning and 8.74% chance of pushing in general.
The play to win strategy (http://gronbog.org/results/blackjac...one/generated/complete/1.0/p1.X/strategy.html) has a 43.81% chance of winning and a 7.78% chance of pushing in general.
In either case, if we lose, we're done.

Armed with these numbers, the chance of success for the multihand strategy of 'stay alive' + 'stay alive' + 'play to win' starting with our 16 vs 10 is

0.2001 + 0.0590 x (0.4339 + 0.0874 x (0.4381)) = 0.2280 or 22.80%

This is less than the success rate of 23.02% for playing to win from the outset, but not by much. As the title of the thread says, damned if you do ...

For what it's worth, none of this went through my head at the time, nor could I have done the math at the table even if it had. I simply decided that I had to play to win and I stood. I ended up losing the hand and I was eliminated. After seeing the cards, I saw that, had I hit, I would have had 17 and the dealer would have busted. It was only then that I wondered if I should have played to stay alive by hitting. As always, hindsight is 20/20.
 
Damned indeed

It is always refreshing to find new perspectives on tournament plays, which gronbog’s post and the following answers instigated.
The situation is complex and board members made good arguments. A few of my comments point details that some, most of them actually, have a small practical use, nevertheless, hopefully someone may find them interesting.

Firstly, deck count does make here a difference.
For example, let’s assume that the cards left represent a full deck, except we replace one of the Tens with one Five card (True Count minus 2). Our hero must draw small card (Ace to 5) to not bust, when this happens the dealer finishes his hand, showing Ten up and drawing from cards representing TC minus 1. Hitting 16 pushes 5.97% of the times and wins 22.21% of the times.
If we follow gronbog’s calculations, where the immediate goal is to win one of the three hands, the final chance is 25.03% versus 22.8% hitting, and 23.02% standing using average statistical outcomes.
And positive count reduces chances of success as it pararelly increases chances of player’s bust and dealer’s good hand -twenty.

It is important to notice that the real goal for our player is to go into the last (secret) bet with the best bankroll possible, preferable as BR1.
There are many strategies for secret bets, some relying on the right guessing what the opponents are going to bet. However, some general rules apply.
Going to the last hand as BR1, with a bet that covers BR2 all-in win (and both getting bj), and winning, guarantees him advancement (minus opponents’ blackjack with big bets). Let’s add advancement from most of the pushes, and when opponents go all-in (or almost all-in) and all three players lose.
Secret bet chances for BR1 should be around 45% to 55%.
Conversely, chances of BR2 fall in 25% to 35%, and for BR3 15% to 25% range
This is a significant distinction.

If our player wins his bet when four hands remained to play, then he has two more hands to play trying to become BR1, before the secret bet. Especially, that on third to last hand, BR2 (betting in front of us) is likely to bet minimum trying to preserve “the low”.
This would be an argument for standing on 16 – which gets us, right away, either win or lose.
When we hit and basically trade some of the wins for twice the amount of pushes, win on the following hand gets us close to the opponents but almost certainly places us as BR3. Being BR3 on the next-to-last hand and betting first can and often will be easily correlated by the opponents.
Having two rounds to try to become BR1 for the secret bet (on the first bet BR1 has to not correlate) gives us about 25% to achieve it, while having only one reduces it to about 10%.

Seems like standing is the right play? Not so fast...

Hitting 16 produces a few wins that are half or full swings, but most of the pushes will cause our opponents to lose. Crippling their bankrolls on this hand (even if their bets are relatively small) may be necessary for not falling behind some of the ranges of the gap between the bankrolls, which would hurt our chances on the last bet. This is a situation when we have two attempts to become BR1 after we win hitting 16 or when we win after a push and then attempt to become BR1 on the next-to-last hand and lose. These gap ranges are: less than 50% of an opponent brl, 2/3rd of an opponent brl, and some others, that just could prevent us from advancing with a push or win on the last hand.

Finally, there are not so obvious possible benefits of pushes (point for hitting 16) – blackjacks.
Consider that we won fourth-to-last hand, now we will be most likely betting minimum more than twice the gap to the leader. With the right play by opponents, even if we get a blackjack, they cover it. If we push on the four-to-go hand, or even have a series of pushes, and then bet all-in again, our blackjack very likely will make us a desirable BR1. Small, overall 0.3% probability, nevertheless a chance worth considering when exploring and comparing all details.

S. Yama
 
Not So Secret

S. Yama said:
Secret bet chances for BR1 should be around 45% to 55%.
Conversely, chances of BR2 fall in 25% to 35%, and for BR3 15% to 25% range
This is a significant distinction.
Click to expand...
There is an interesting detail that I neglected to mention regarding the secret bet in this tournament. In some tournaments, the bet remains secret until all of the hands have been played (recall UBT). In this tournament, once all the bets were made, they would then be revealed before the cards were dealt. So the players would know what the bets were while deciding on how to play their hands. How does this change the percentages above?

Another detail, which was not enforced, was that double down cards were supposed to be dealt face down, but no double for less was allowed, unless it was for all of your remaining chips. The implication is that your opponents would know your double amount, but not the resulting hand.
 
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Hit Or Stand

It's a close shave either way, but I believe this is a situation in which a push is as bad as a loss. That's because you are behind and can expect these opponents to start increasing their bets after this hand. If you hit, make a hand, and then push you only have two more hands in which to try to become BR1. If this had been a hand or two earlier I might play as if a push is as good as a win, and hit.

It's usually important to be BR1 on the last hand, but with a secret bet on the last hand it's even more important.

You were correct to go all in on this hand.

Your information about your read on these players' intentions is interesting and important. They're willing to bet big. If they had instead been rocks and you didn't see any indication from their behavior or past experience with them that they might bet big, you could consider playing to survive.
 
Betting and chances

Seeing opponents’ bets and having position helps but it is not a significant difference.

BR1 has relatively simple decision, whether he sees or not the opponents’ bets.
Almost always the best bet is to cover BR2’s all-in win. He or she has to play to win, or push if opponents don’t have higher totals. That’s just a tad more than 48% for basic strategy and minimally less if the opponents draw to a total one point higher than his total. We have to deduct opponents’ blackjacks if they have big enough bankrolls and have bet big. For a total chances of at least 44%.
Also, it may happen that he has the most unbet chips which gives him advancement if all 3 players lose – that’s additional up to 22% for basic strategy (and slightly more if opponents hit more aggressively trying to take away some of BR1 pushes).
So, being BR1, and have secret bet could offer a whopping chance to advance of 66%. Notice that without the betting position and open bets this would never happen, except with real novice players.
A smaller bet that covers BR3 all-in but doesn’t cover BR2, increases chances of winning when all 3 players lose, but reduces advancement from winning the hand and pushes when BR2 bets big to 19%, for total chances of no more than 41%.
Bet that doesn’t cover BR3 all-in but is bigger than the lead over BR3 carries a risk that both opponents may have “high” and “low”, with total chances for advancing that could be as low as only 19%
Bet of pure low brings back BR1 chances to about 41%.

BR2 play depends on the differences between the bankrolls.
The main objective is to have a smaller gap to BR1 than lead over BR3. In this case most likely the best bet is to minimally overcome BR1 push if won. It may work a little better than keeping minimum more than BR3 bankroll and betting the rest, if for some reason BR1 bets just the lead over BR3. The play is to hit one point more than BR1’s hand and at least the same total as BR3. This situation (in all cases except when BR1 has bet less than twice the difference between his and BR2 bankroll) offers pretty good chance of winning the table – (perhaps surprisingly to some) over 37%.
If BR2’s lead over BR3 is less than the gap to BR1 the goal is to make a bet that gives him the low, otherwise interesting option is to bet big enough to cover BR3 all-in and that his blackjack gets him over BR1’s all-in.

For BR3 it is a guessing game. If his opponents give him the low and allow to bet more than the lead they have then his chances of advancing could be as high as 33%. But if he guesses wrong and has no low and no high than it could be reduced to below 11%.

S. Yama
 
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