To Cover, Or Not to Cover (the double downs) PART DEUX

Loved the discussion on the original thread so I'd like to pose my own situation with a little twist (which actually happened to me yesterday and I've been wracking my brain since).

Betting range 100 to 2000. BJ pays 3:2. No surrender allowed. Last hand, one advances.

Villan 1: Bankroll 4,000 bet 2000
Villan 2: Bankroll 5,300 bet 800
Me: Bankroll 5,250 bet ?

What would you bet and why?

 

Will have time to think of it in a few days..
but a 10 seconds bet is 600.

S. Yama

 

My 30 second answer is 1400. If everyone wins you win. If everyone one doubles you can be ahead also if everyone wins.

 

I'm now waiting to see what others are going to say, but S.Yama with 600 appears to be going for the low, while still being in a position for a possible double if needed. Is Tucson last to play?

 

Yes RanDom,
Players bet and play in the order listed so Tucson (I) was the last to play. Thanks for the considering and looking forward to your responses.
m

 

Jumping in late here, but I'm just back from vacation. Only one advances here, so you either go for the high or the low. My 1 minute answer, with 2 opponents in play, is to go for the high. You can do this with a bet of 900. You can't cover Villain1's double outright because of the 2,000 limit, but with a bet of 1,400 or more you can cover his double with a double of your own while only giving up a 1/2 swing to him. With a bet of 1900, you beat Villain1's double with a blackjack with no additional risk. In the heat of battle, I think I would bet the max -- 2,000 -- just in case my arithmetic was flakey.

As a general rule of thumb, when going for the high, once you've decided on a bet that gives up everything there is to give, an easy max bet will automatically cover any additional and possible high situations.

 

1900 would have been my 20 seconds response too because a blackjack of yours covers a double down win from BR3

 

Bet options for tucson could be characterize into two categories:
A. High bet, range of 1300 to 2000 (more than the lead over BR3), and
B. Low bet, range of 100 to 700 (low to all players)

A.) High bet.
The higher the bet the more options become available for BR2 to exercise, with some negatives increased to a smaller degree.
Bet of 1400 covers BR2’s double by winning a doubled bet,
bet of 1700 covers BR1’s double,
bet of 1800 covers BR3’s blackjack,
bets of 1900 and 2000 cover BR3 winning a double bet by BR2’s blackjack.
bets of 1800 or more have one drawback – BR2 can not split to three hands;
winning at least one (or two) net bets without being able to split to three hands has less benefits than improvements by betting of 1900 or 2000).
Optimal bet: 1900 - 2000

B.) Low bet.
Winning bet of 100 covers BR1’s push (and BR3’s push),
bet of 600 covers BR1’s win by BR2’s blackjack, and losing full double or split retains the low to BR3’s push and BR1 losing a full double,
bet of 700 - doubling covers BR1’s blackjack but losing full double (splits) brings BR2’s bankroll below BR3’s push.
Optimal bet: 600 or 700 (close call)

The exact numbers could be achieved by a simulation, I wish we knew someone who has the expertise doing it .

S. Yama

 

Let’s try to see dynamics of different plays and try to estimate the outcomes.

A) BR2’s “high bet” of 2000
B) BR2’s “low bet” of 600
A.) BR2’s bet of 600
Play in order of action

BR3.
When both BR1 and BR2 bet low, BR3 have to play to win while BR1 pushes and BR2 doesn’t get bj or wins doubled bet. The best option for BR3, however is to win a doubled bet and have lock on both opponents.
BR3 playing to win a double bet (or getting a blackjack) succeeds just under 35% (depending on skills for playing splits). This number can be slightly improved by right choosing to play for half and full swings to both opponents.

BR1.
BR1 has to play to correlate to BR2 assuming BR3 doesn’t win his double.
BR1 wins about 20% of the hands when BR3 wins his double, that leaves him with about 25% of wins when BR3 doesn’t wins the double. Some of these hands have to be won as a double to protect against BR3’s not winning dd and BR2 winning his double (or having a bj). BR1 advances also when he pushes and neither of BR2 or BR3 wins.

BR2 (tucson).
BR3 and BR1 can’t win dd, if he has a single “winning” bet we need to win a doubled bet;
if BR1 has single “winning” bet (and BR3 has a “bad” dd) BR2 has to win doubled bet.
BR2 has to play to at least 17 and hit to one point higher than BR1 and the same score as BR3; BR2 has to double if BR3 has a losing double and BR1 stands on a “winning” hand.

So, BR3 advances 35% plus, by doubling or swings;
BR1 advances 3-4% when he pushes and others don’t win, and about 25% when BR3 doesn’t win double, but we have to deduct from his wins cases when BR2 wins doubles.
That leaves BR2’s chances at about 45%.

The other way of looking at BR2’s chances would be to check BlueLight table, where we can find that one specific player’s (BR3) push or loss and the second player (BR1) loss, plus as above but the second player push and our win gives 37% chance of advancing.
This number can be significantly improved because of BR3’s lower chance of winning (doubles almost everything) and our play to hit to a better score than the opponents, and winning doubles when BR1 has a winning hand.

S. Yama

 

B.) BR2’s bet of 2000
Play in order of action

BR3
His chances are significantly reduced compared to both of his opponents betting low.
Now, his bj is covered by BR2’s single win and his winning of double is covered by BR2’s double, and of course he doesn’t have the low even if he pushes. Still his best chances are by doubling and the totlal advancement could be in 15%-20% range.

BR1
He has low to both opponents, but no high to BR2 or BR3’s winning double.
For basic strategy players, neither BR1 nor BR2 win their hands 42% of the times. But with BR2 and BR3 battling it out with forced doubles, plus BR1’s win when BR3 wins only a single bet and BR2 doesn’t win, his total chances grow to upper 40-ish %.

BR2
Some interesting plays are in store for him. Lot’s of plays where the dilemma is to hit/stand to play for push/win that gains to BR1, and at least correlates with BR3’s outcome; or double himself to win outright, or have results like one described above.

Either by adding up the numbers for the opponents chances, or checking that BR2 advances when he wins any doubled bet or by a blackjack, some single bet wins, plus pushes when when BR1 loses and BR2 doesn’t win, bring his chances to somewhere just above 40%.

Let’s hope that gronbog, with his generously spared time and dedication, will be kind to validate (or otherwise, lol) some of the ideas,

S. Yama

 

I've been intending to run some sims on this since it was posted, since I was not sure whether going high or low was actually best. My answer represents what I would have done at the table under pressure and I think that those kinds of answers are valuable, but it would also be nice to gather some simulation evidence. My schedule for the next little while is busy, but I'll see what I can get done.

 

OK -- I found some time and have some results for this scenario. Let me first say that it's a close call no matter what you do as BR3 betting/acting last here so tucson, if you chose any one of the bets suggested here, then you didn't make a big mistake.

In order to come up with an anwer, I had to make assumptions about the skill level of the other players. Two levels of skill that are easy to assign are

1. optimal - i.e. the opponent plays his cards perfectly relative to what card held by the other players.
2. basic - i.e. the opponent plays basic strategy.

Now, neither of these extremes is likely in real life but they are benchmark results and it is likely that the actual expected results lie somewhere between the results for these two assumptions. These assumpations are what Wong refers to when he recommends one strategy vs "a tournament expert" as opposed to vs a basic strategy player. It is also possible that one's opponents will play worse than a basic strategy player, either because they try to be too clever and make an error, or because they are ignorant of basic strategy. However, the behaviour of these kinds of players is difficult to quantify in software.

I analysed the case of optimal opponents because we can then say that tucson's results would likely be as good or better than the results obtained with this assumption. I chose the 3 bets that seemed to be the consensus: 2000 (going high), 600 and 700 (going low). And the results are (drumroll ........):

600
===
Player 3:
Finishes 1: 41.87%
Finishes 2: 40.68%
Finishes 3: 17.45%

700
===
Player 3:
Finishes 1: 43.36%
Finishes 2: 36.37%
Finishes 3: 20.27%

2000
====
Player 3:
Finishes 1: 42.68%
Finishes 2: 35.72%
Finishes 3: 21.60%

So a bet of 700 is the winner, but not by much.

Tucson said that this was a final hand and implies that this was not a final table (he says 1 advances), but if it were, then depending on the prize structure, a bet of 600 could have better EV given the superior performance for finishing either first or second at more than 82%. Unless the prestige of winning the tournament is exceedingly important to you, on the final hand of the final table, the overall EV of your decision should be your main concern.

 

Hey gronbog,
Your work is always very much appreciated.
I am glad that my analysis has come very close to your precisely simulated numbers.
This particular tournament always gathers perhaps the most skilled players (with a few exceptions of people residing too far to attend) in US. The frequently employed strategy there is to double down on the last hands, which is quite effective, but sometimes overused. This would tip favoring the low bet even a bit more.
I always emphasize importance of finding “why” a particular strategy should or should not be used –understanding of it allows us to apply it in similar situations.
Finding out “what” is the right bet/strategy in a particular play is right just for that one.
Numbers you generated justify and show the scale of the effects, they prove (or otherwise) the underling theories, which otherwise would be just hypothesis.
Thanks again,
S. Yama

 

Interesting --- which tournament is this?

 

A few clues in the rules as quoted in the original post point strongly towards this being from the semifinal round of one of the Golden Nugget 100K events in LV.

 

Correct-It was the Nov 7-9 Golden Nugget tournament. I have to say that the results of the simulations took me by surprised. I was sort of thinking that in a 3 person race and one advances, going for the high is better but the analysis showed essentially a tie between going for the low or the high.

 

This is an excellent point. In general, going for the high vs going for the low with two contenders is always pretty close, with each being somewhere in the 42% to 43% range. Specific circumstances can swing the decision one way or another. In this case, going for the low with 700 still leaves BR2 with options for doubling vs BR1. This could be what swung things in favour of going low.

 

I just learned about this post with interesting ideas and some stimulation's results.
In a real world I would bet $1,400.
It doesn't cover BR3's Double by BJ, but makes BR1's life more complicated
If BR2 bets $2,000 then BR1 cannot give away Low over to BR2's (even if he would wish so) by doubling.
But if BR2 bets $1,400 and if BR3 is already busted out, then BR1 should protect himself from BR2's winning hand.
Of course, BR1 may double for less, but this is pretty unusual, plus in some cases, including (T,T), BR1 should split for whole $800 and give away Low.
So, by betting $1,400 - BR2 gets first High and likely Low over the opponents.

 

For a bet of 1400, assuming all players play optimally ...

Player 3:
Finishes 1: 40.20%
Finishes 2: 38.42%
Finishes 3: 21.38%

Not as good as 2000 for finishing first.

 

Thank you, gronbog!
I agree.
Sometimes the opponent's mistake gives us much more than a perfect play.
So, my point here is that depending whom we're playing against, we should try to confuse them, in order to benefit from their mistakes.
For example, if you're a Leader, playing against a poor tournament player right before him in the last hand, knowing that he's gonna bet max - you should bet Max.
Of course, Blackjack in NOT a Poker, but it has some elements of it. Knowing particular player's style and watching opponents through the round we can have an idea about their bet/play.
I should say, that thanks to S. Yama, about 10 years ago, I changed my approach from optimal play to the practical real life play, targeting simply RESULT and never felt sorry