Cover Double with Double or Cover Two Swings?

gronbog said:
Betting 9000 to match BR2 finishes first with the highest percentage, but all of the results are extremely close.
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I'm surprised the first two (9000 and 6675) are quite so close in the sim. (67.5526% and 67.4138%).

Isn't the only difference between them the fact that 9000 covers a BR2 natural without the need to double down?

If that's the case, then I think the difference in BR1's success rate ought to be given by -

prob(BR2 natural) * (prob(BR1 no win, without doubling) - prob(BR1 no win, with forced double))

- which is approximately 4.7% * (0.56 - 0.67) = -0.5%

[The only other difference that I can see between the bets is that 6675 would allow splitting to three hands. Maybe that is worth more than you might think.]
 
There is another benefit of 9000 bet vs. 6,675, BR1 bj automatically covers BR2 winning dd, without having to double,
worth about quarter percent.
The benefits of 6,675 are from splitting to three hands, but probably more often to win a"rescue" double down as a third bet to:
a) winnign two bets and push one if BR2 wins double
b) end up winning one bet if BR2 wins one
c) net push if BR3 gets bj or wins (and BR2 loses of pushes)
d) net push if BR2 pushes

S. Yama
 
For S. Yama - sim results for BR1 betting 13,400. As expected, the best option yet, were it to be allowed.

Code: 
Player 1:
    Finishes 1: 25,554,562/389,267,493 = 6.5648%    Standard Error: 0.001255%
    Finishes 2: 62,668,514/389,267,493 = 16.0991%    Standard Error: 0.001863%
    Ties for 2: 8,500,127/389,267,493 = 2.1836%    Standard Error: 0.000741%
    Finishes 3: 292,544,290/389,267,493 = 75.1525%    Standard Error: 0.002190%
  Reaches goal: 25,554,562/389,267,493 = 6.5648%    Standard Error: 0.001255%
Player 2:
    Finishes 1: 84,176,768/389,267,493 = 21.6244%    Standard Error: 0.002087%
    Finishes 2: 232,260,893/389,267,493 = 59.6661%    Standard Error: 0.002486%
    Ties for 2: 8,500,127/389,267,493 = 2.1836%    Standard Error: 0.000741%
    Finishes 3: 64,329,705/389,267,493 = 16.5258%    Standard Error: 0.001882%
  Reaches goal: 84,176,768/389,267,493 = 21.6244%    Standard Error: 0.002087%
Player 3:
    Finishes 1: 279,536,163/389,267,493 = 71.8108%    Standard Error: 0.002280%
    Finishes 2: 85,837,959/389,267,493 = 22.0512%    Standard Error: 0.002101%
    Finishes 3: 23,893,371/389,267,493 = 6.1380%    Standard Error: 0.001217%
  Reaches goal: 279,536,163/389,267,493 = 71.8108%    Standard Error: 0.002280%
 
gronbog said:
For S. Yama - sim results for BR1 betting 13,400. As expected, the best option yet, were it to be allowed.

Code: 
Player 1:
    Finishes 1: 25,554,562/389,267,493 = 6.5648%    Standard Error: 0.001255%
    Finishes 2: 62,668,514/389,267,493 = 16.0991%    Standard Error: 0.001863%
    Ties for 2: 8,500,127/389,267,493 = 2.1836%    Standard Error: 0.000741%
    Finishes 3: 292,544,290/389,267,493 = 75.1525%    Standard Error: 0.002190%
  Reaches goal: 25,554,562/389,267,493 = 6.5648%    Standard Error: 0.001255%
Player 2:
    Finishes 1: 84,176,768/389,267,493 = 21.6244%    Standard Error: 0.002087%
    Finishes 2: 232,260,893/389,267,493 = 59.6661%    Standard Error: 0.002486%
    Ties for 2: 8,500,127/389,267,493 = 2.1836%    Standard Error: 0.000741%
    Finishes 3: 64,329,705/389,267,493 = 16.5258%    Standard Error: 0.001882%
  Reaches goal: 84,176,768/389,267,493 = 21.6244%    Standard Error: 0.002087%
Player 3:
    Finishes 1: 279,536,163/389,267,493 = 71.8108%    Standard Error: 0.002280%
    Finishes 2: 85,837,959/389,267,493 = 22.0512%    Standard Error: 0.002101%
    Finishes 3: 23,893,371/389,267,493 = 6.1380%    Standard Error: 0.001217%
  Reaches goal: 279,536,163/389,267,493 = 71.8108%    Standard Error: 0.002280%
Click to expand...


Great research and numbers. But max bet is 10.000
 
The lowest BR2 can insure for to win the table if BR1 fails to correlate the insurance bet is 1,875.

- If BR2 insures for 1875 or more, BR1 fails to take insurance, and the dealer doesn't have blackjack, BR2 will NOT have enough chips left to double all-in to retake the high.
- If BR2 declines insurance, he WILL have enough chips to double all-in to retake the high.
- If BR2 takes insurance and BR1 insures for enough to cover BR2's insurance bet, BR2 will lose if the dealer turns up a blackjack and cannot double to cover the high if the dealer does not have blackjack.

In other words, BR2 taking insurance is making a tradeoff. He trades off being able to double to cover the high for the chance of inducing a mistake by BR1 (not correlating insurance) AND having the dealer turn a blackjack.

Is this tradeoff worth it?

Acting quickly and apparently carelessly is contagious in blackjack tournaments. So is taking your time and being deliberate.

The complexity and mathematics of this situation would require any human or simian to take his time to avoid miscalculation. However, you need to act quickly so that your opponent is more likely to make the mistake you want.

Generally speaking, is it worth it to risk making a suboptimal play for the sake of acting quickly enough to induce an opponent's mistake in this kind of complex situation? Why or why not?
 
I am not sure I can see the trade off. You said "If BR2 declines insurance, he WILL have enough chips to double all-in to retake the high". Unless, I am missing something, the chance of BR2 taking the high by doubling down is almost non-existent because BR1 will correlate by doubling down on his 10 and in this case maintains both the high and low on everyone. There is much more chance of BR1 not correlating on the insurance bet though, which makes taking insurance for BR2 his only hope.
 
The_Professional said:
I am not sure I can see the trade off. You said "If BR2 declines insurance, he WILL have enough chips to double all-in to retake the high". Unless, I am missing something, the chance of BR2 taking the high by doubling down is almost non-existent because BR1 will correlate by doubling down on his 10 and in this case maintains both the high and low on everyone. There is much more chance of BR1 not correlating on the insurance bet though, which makes taking insurance for BR2 his only hope.
Click to expand...
You didn't miss anything. I should have stated that BR2 will take the high and force BR1 to double down to maintain the correlation.

I'll give some other folks a chance to post before I reply further.
 
We try to avoid situations like the one I faced as BR2 in this situation. But it can't always be helped. I was BR1 on the second-last hand but fell victim to a full swing on that hand.

Salvaging as much as possible from these situations where you are behind and out of position is important to your long-term win rate.

Inducing opponents' mistakes is an important principle in casino tournaments, and in the case of being behind and out of position can offer you the best chance at getting some wins. To induce opponents' mistakes we need to act fast. As stated previously fast, apparently careless action is contagious at the table. This means risking the possibility of making a suboptimal bet size ourselves.

The Professor was correct in stating that in all likelihood BR1 will correlate our double down bet - thus not making the needed mistake. As Gronbog stated earlier, the insurance bet- and doing it quickly - was our best chance of inducing a mistake by BR1.

We all understand the importance of bankroll management in a blackjack tournament. What has gotten much less discussion over the years has been time management. How much accuracy should we trade off for the benefits of acting quickly? Under what situations should we risk this accuracy? Can we break this down mathematically, possibly using game theory and fuzzy logic principles?

In this situation when I saw the dealer give herself the Ace upcard, I immediately recognized that an insurance mistake by BR1 was my best shot at winning this table. The dealer pointed to BR4, then BR3 in rapid succession because she knew they were all-in and couldn't take insurance. Then she pointed to me. I quickly calculated that I needed to overtake BR1 by more than 4,700, which was the chip deficit. I didn't take the time to factor in the difference in our initial bets. I didn't have time to do that accurately. I quickly as possible counted up 2,400 chips and placed them in the insurance circle. I did this so fast that I didn't even realize the possibility that the excess chips lost in a failed insurance bet might make the difference between having enough to double for the high and not having enough. Only after the action was over did I realize that it would've made no difference. To summarize, I risked making my own error in order to induce a bigger one from my opponent.

By the way, BR1 failed to correlate my insurance bet, but then the dealer did not turn a blackjack. So BR1 made the mistake I wanted, but the cards didn't cooperate with me.

Do you agree or disagree with this psychology driven approach to a blackjack tournament problem? Can you come up with some hard math and logic to support your assertion?

I'll share with you the final results of this hand in a later post, which will also bring up another topic important to card players.
 
Just some more thoughts on the importance of speed and its benefits:

It's baked into our language. The word "hustler" has "hustle" as its root word, implying the importance of speed in inducing a mistake from a person. We're all familiar with the term "pulling a fast one," which implies the same thing. Fast talkers and quick change artists rely on the same thing.

In a more legitimate vein, we see that relief pitchers in major league baseball usually act quickly on the mound, in order to deny the hitter a chance to gather his thoughts and communicate with his coaches. Surprise attacks and other troop movements in military campaigns always emphasize speed, in order to sow confusion and disorganization in the enemy. We have speed limits on the roads mainly because drivers can't think and react quickly enough to changing conditions if they are driving too fast.

In the normally cerebral game of blackjack tournaments, speed kills. So you like to induce your opponent into acting too quickly.
 
Often, we don't need hard numbers to make these kinds of decisions. We only need relative values. We're willing to expose ourselves to a 1/2 swing in order to cover a double/split because the 1/2 swing is less likely than our opponent succeeding with a double/split, even before we see the cards. We don't expose ourselves to the same 1/2 swing in order to cover an opponent's potential blackjack, because the blackjack is less likely than the swing. We often know the approximate percentages but after a while, we don't need to. We just need to know that X is more likely than Y.

In this case, out of position and probably needing some kind of swing to advance, regardless of how we bet or how we play our hand, the ~4/13 chance at winning via insurance seems very large to me in comparison to the other options. Large enough to be worth a shot even if it damages our already-weak position if the insurance bet loses. To me, what is given up by taking the insurance seems less than what is being gained, even though I do not have any hard numbers at my fingertips.
 
I have not really seen that acting quick is contagious at the table. People who play more often can have better feeling about this. In this particular case of insurance bet, the pressure actually comes from the dealer who is going round the table quickly with her hand pointed. In general, I found some players like to play fast and others take time in every single hand simple or not. One could argue the opposite could be true in some situations. If someone takes a long time in a play, other players might get impatient, irritated and act quickly.
 
When stuck with early position on a key late hand, I have used speed as a tactic but in quite the opposite direction. By taking the most time I could get away with taking, then making a bet that seems to have no basis in reason (even though it does), I've sowed confusion in the minds of opponents who may have already had a bet size in mind. They might figure that I know how to play very well and took the extra time to consider many options. I've seen them literally sit back in their seats with confusion written all over their faces, and have induced poorly structured bets from them. This is a bad move when dealing with highly experienced players who won't be fooled by anything as mundane as a surrender trap (or similar) but sometimes it does work on the less knowledgeable opponents.
 
The_Professional said:
I have not really seen that acting quick is contagious at the table. People who play more often can have better feeling about this. In this particular case of insurance bet, the pressure actually comes from the dealer who is going round the table quickly with her hand pointed. In general, I found some players like to play fast and others take time in every single hand simple or not. One could argue the opposite could be true in some situations. If someone takes a long time in a play, other players might get impatient, irritated and act quickly.
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The contagion doesn't always spread to others at the table. But in my experience it usually does. I can't remember the last time someone who wasn't a known expert slowed down the game after one or more fast-acting moves by players acting before them on a last hand.

It doesn't have to work every time. Human behavior being what it is, you can never manipulate others with 100% reliability. 2/3 reliability is what you're looking for. A 2/3 estimate can be thought of as a "strong possibility."
 
LeftNut said:
When stuck with early position on a key late hand, I have used speed as a tactic but in quite the opposite direction. By taking the most time I could get away with taking, then making a bet that seems to have no basis in reason (even though it does), I've sowed confusion in the minds of opponents who may have already had a bet size in mind. They might figure that I know how to play very well and took the extra time to consider many options. I've seen them literally sit back in their seats with confusion written all over their faces, and have induced poorly structured bets from them. This is a bad move when dealing with highly experienced players who won't be fooled by anything as mundane as a surrender trap (or similar) but sometimes it does work on the less knowledgeable opponents.
Click to expand...

If you have a solid read on your opponent that there is a strong (2/3) possibility that he'll overthink it and make a mistake that way, this is a great strategy.

The important thing I am driving at here is the psychological game. Making reads like this is a big factor in excellent card play.
 
gronbog said:
Often, we don't need hard numbers to make these kinds of decisions. We only need relative values. We're willing to expose ourselves to a 1/2 swing in order to cover a double/split because the 1/2 swing is less likely than our opponent succeeding with a double/split, even before we see the cards. We don't expose ourselves to the same 1/2 swing in order to cover an opponent's potential blackjack, because the blackjack is less likely than the swing. We often know the approximate percentages but after a while, we don't need to. We just need to know that X is more likely than Y.

In this case, out of position and probably needing some kind of swing to advance, regardless of how we bet or how we play our hand, the ~4/13 chance at winning via insurance seems very large to me in comparison to the other options. Large enough to be worth a shot even if it damages our already-weak position if the insurance bet loses. To me, what is given up by taking the insurance seems less than what is being gained, even though I do not have any hard numbers at my fingertips.
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The insurance mistake seems like the most likely type of mistake we can induce.

Is there another mistake BR2 could induce if the deficit were, say, 1,500 instead of 4,700 and we haven't seen the cards yet?

Is there a way we can induce a mistake if we are the chip leader by 1,500 acting first?

Is there a way to give mathematical treatment to the fuzzy logic of human behavior in the context of inducing opponents' mistakes in blackjack tournaments?
 
There a a couple of ways to give mathematical treatment to fuzzy logic.
  1. One is to determine the value of the situation for each possible response by an opponent and then to weight them by their individual probabilities.
  2. Another similar approach would be to simulate the situation with the opponent randomly making each possible response but again weighted by the expected probabilities of each response.
There are probably other ways as well, but these are two that I came up with off the top of my head.
 
gronbog said:
There a a couple of ways to give mathematical treatment to fuzzy logic.
  1. One is to determine the value of the situation for each possible response by an opponent and then to weight them by their individual probabilities.
  2. Another similar approach would be to simulate the situation with the opponent randomly making each possible response but again weighted by the expected probabilities of each response.
There are probably other ways as well, but these are two that I came up with off the top of my head.
Click to expand...

I like using a Bayesian method in which we assign a two-thirds possibility to a human decision that seems like a strong possibility. This is actually very close to a 68% confidence interval that is defined by one standard deviation.

A human decision that seems like a fair possibility can get a one-third possibility. In other words, there's a strong possibility the human opponent will not make the decision, but a fair possibility he will. Sometimes a fair possibility is all you need.

If you have no idea whatsoever, or if you estimate a coin flip, use 50%.

We can then apply these percentages to the hard probabilities that we understand in a card game to obtain reasonable estimates of EV, win rate, etc.
 
Here’ how the hand turned out in real life:


BR4 bankroll 1,000 bet 1,000 cards hard 16, no insurance, hit, bust

BR3 bankroll ~8,500 bet ~8,500 all-in cards hard 20, no insurance, stand

BR2 (me) bankroll 18,000 bet 9,000, cards hard 14, insurance 2,400, double all-in, bust

BR1 bankroll 22,700 bet 10,000, cards 55, no insurance, hit, hit, bust

Dealer Ace, 6, T

BR3 advanced to the final table.



Why did I double all-in? At this point I was hoping for a miracle swing. I didn’t have the chips to cover a win by BR1. If I had been more on the ball I would’ve taken free hits to a total of 18. Who knows? Maybe BR1 might have doubled down mistakenly and gotten stiffed. The way the cards came out it wouldn’t have mattered anyway, but we don’t rabbit hunt here on blackjacktournaments.com.

Earlier in this thread I alluded to one more topic important to card players that I wanted to bring up, that is relevant to this hand. The topic is tilt. Tilt is why I doubled all-in when I didn’t need the extra money in this hand.

The poker coaches define tilt as any state of mind, brought on by any cause, that impairs our thought processes. Tilt doesn’t have to be anger or frustration. It can be boredom, sleepiness, or distraction. It has many causes. The usual causes are anger at another player or frustration with bad luck.

But it can be caused by self-doubt caused by having made a mistake. It can be distraction because of a football game on one of the TV monitors. You might have a headache or a cold that day, taking you off your A-game.

I have to confess I’ve been a bit tilty lately, in my home life and professional life as well as my card games.

Tilt can have disastrous consequences in a blackjack tournament. It can cause you to deviate from a well-considered middle round strategy. If you’re not on your A-game, you might not recognize a situation, such as needing to hit to a total of 18 instead of doubling all-in. Keeping track of all those bankrolls and then doing the arithmetic to calculate a bet in a last hand situation is mental gymnastics for the best of us. If you’re not on your A-game, you simply can’t do mental gymnastics well enough to get an advantage.

How can we get control of tilt? How do we prevent tilt to begin with, both on and off the table? Do you folks have any thoughts on that?
 
Yes, I have heard that tilt is common more among poker players who often waste away their earned hard money on -EV games. I have recently saw several smart skilled players go on a tilt just because they lost some big bets, which was both amazing and sad to watch. In terms of tournaments, some people can easily get irritated than others. I generally do not try to irritate anyone but I have seen people do it.
 
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