Peculiar hybrid format: Any strategy tips?

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Thanks to S. Yama for privately and politely pointing out that my mehodology is incorrect here. Since there is correlation due to all of the players playing against the same dealer up-card, one cannot simply multiply the probability of a single player succesfully doubling/splitting/swinging against itself to obtain the result for more than one player. As a result, the calculations in this post are not correct.

Probability caclulations can be complex, which is why I prefer to obtain my results via simulation. In fact, I think I'll do just that
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Assuming that you can split unlike tens, then the probability that a single player will NOT be successful on his double/split is 1 - 0.1205 = 0.8795. The probability that none of the other 5 players will be successful (assuming they all try -- i.e. worst case) is 0.8795 ^ 5 = 0.5262.

Similarly, the probability of an individual NOT swinging you is about 0.88, so the probability that no one will swing you is about 0.5277.

Seems like a pretty close call, however the numbers for doubling/splitting assume optimal strategy, so perhaps give the nod to not covering the doubles (i.e. bet low).

Now, if you know that only 4 players will attempt the double/split then the probability that none of the other 4 will be successful rises to 0.5983 (i.e. bet small)

Also, if you cannot split unlike 10s, then the probability that all 5 will be unsuccessful in doubling/splitting rises, so you would favour betting small.

These calculations assume that doubling/splitting or a blackjack would be of no help to you should you bet small.

 

I'm back

Yeah, I was aware of the correlation issue. That's why I phrased it as a rhetorical question; I didn't expect anyone to have the patience to work it out. (Plus, with the pay structure as I described it, going all-out to retain BR1 doesn't seem the best way to maximise EV in any case.)


On to what actually happened....

 

The bad luck continued

I didn't make the final table. In fact, I finished dead last, even being beaten by a player who didn't show up and had a min bet deducted on each hand!

As it turned out, the rules did in fact allow DOA, after all. That, plus the fact that there was one fewer player meant that I wasn't quite sure what goal to go for.

In the end I chose to min bet for most of the first round and then reassess things after the scores were posted on the leaderboard (or during the round if everyone at my table disappeared off into a big lead).

The latter seemed to be slightly the case towards the end, so I made one raised bet of 400 on the final hand (viewing it as the first of a two-step, 400,1000 progression) which I lost.

When the scores were posted it was clear I would need to win a few max bets, so I set about making max bets on every hand in the second round. My 5000 chips lasted exactly 5 hands; the dealer beat me every time!

For round three, I estimated I would need to win about 10 max bets. This time I made a little progress and briefly dared to hope that it might be possible, but then I fell back and eventually, running out of both hands and chips, went out with a losing double-down.

The scores were as follows -

Qualifying:

Code:

Round 1  Round 2  Round 3  Total
6300     9250     5100     20650
6750     6000     7100     19850
6700     6800     6300     19800
8700     3500     6800     19000
6900     5500     5800     18200
7650     5200     4700     17550 

4350     6900     2950     14200
5500     4000     4600     14100
6400     2400     3600     12400
5400     3200     3300     11900
4200     6300     0        10500
7000     3050     0        10050
4900     4800     200      9900
5400     4400     0        9800
2900     2900     2900     8700
6700     0        0        6700
4950     0        0        4950
4700     0        0        4700  (me)

Final Table:

Code:

Round 1  Round 2  Round 3  Total
6950     3800     6650     17400
7050     50       10100    17200
4250     6000     4000     14250
4800     4800     950      10550
5850     2700     1550     10100
1000     4900     2850     8750

 

But the good news is...

It was all a lot of fun. (It's been a while since I last left a party at 6am!)

The blackjack tournament was a side event within a poker tour - http://www.unibetopen.com. This was actually their second bj tournament; there was one held at the previous tour stop in Riga in December, but I found out about it too late.

They say they plan to hold blackjack and also roulette tournaments at most future events, but that won't be possible at the next event in Paris, because it is being held in a poker room, not a casino.

So the next chance should be London in August.

 

Sorry to hear that luck was not on your side. It is an unfortunate side effect of leveraging variance by betting max that it goes both ways and that the optimal strategy for reaching a goal beyond a max bet is also the optimal strategy for busting out :sad:

This is unfortunate, but should not have mattered that much for the preliminary sessions since, for basic strategy, it only deprives you of the soft double downs.

Were you unsuccessful in finding anyone who had an idea of what the goal should be?

I feel (and have felt) your pain :sad:

 

Did you get a read on any common strategies used by folks in either round? That combined with the rule update and the actual advancing threshold from this past weekend can help us to estimate a better goal and aggression level for you for next time.

 

Prague

Prague – what a great city, the mix of medieval, belle époque, and everything in between wonderful architecture. The whole city use to be breathing art and freshness at every corner you turn wandering its magnificent streets - especially if one appreciates their famous beer. And the memories...

As a teenager I used to be part of a small group of black marketers. We would go on about ten days long trips starting in (East) Germany or Poland and stuffing valises with American jeans and electronics.
Then, we would travel on steam powered trains to Russia to trade/sell it for gold, jewelry and caviar.
Next stop Romania and Bulgaria, where we would unload part of the merchandise that was not found (we had to hide it in various ways) and confiscated crossing border or used as bribes for customs officers. There we had bought big shaggy fur coats. One or two days of relaxing on the beaches of Black Sea (usually in Constanca). Officially a person could cross the border with only one fur coat in the luggage but there was no limits how you were dressed. So, we were wearing, each of us, up to four fur coats, even it the heat of the summer, dripping sweat and barely fitting into doorways.
On our way to Budapest in winter times we would stop for some skiing near Brasov, then we would get coffee beans in Hungary and end up in Prague getting pounds of peanuts. Yes, lol, peanuts! Czechoslovakia was the only country that had some international trade agreements and had been importing peanuts. All communist block was so screwed up that the shortages of almost everything caused incredible inbalances; A pound of peanuts was worth about two days of wages in all other countries
In the end, we would profit ,each of us, ten to fifteen times the original investment– an equivalent of a averege yearly salery.
It was our tradition to celebrate the end of the trip in one of many Prague’s great pubs, located in a full of history, cool, stone cellars. Upon sitting at the old wooden pub’s bench, within less than a minute, a waiter would bang the mug of cool delicious brewski in front of you, causing it to foam over its rims, and mark one check on the beer coaster. When you had less than an inch of beer left in the mug it would be replaced with a new one, no need to ask for, second check on the beer coaster. And third mark, and fourth...

Colin,
I hope you enjoyed your trip, and got just the right amount of marks on the beer coaster, lol.
I was able to visit Prague a couple years ago, still wonderful city but it was a little too crowded and too touristy. Or maybe I just couldn’t see with the eyes of an adolescent.

S. Yama

 

hybrid tourney

Colin,
You’ve got great and detailed analysis from gronbog, so I will somewhat repeat it in my comments, but I am throwing in a few numbers.

The key in your effectiveness was to estimate the goal score. It seems to me that the results were quite normal, with slightly higher scores in the first round and lower in the next two.
The best approach is almost always to bet max from the very beginning and stopping a bit higher than the goal, which if you’re successful allows you to drift down with consequent minimum bets.
The drawback of posting your own high score from the first round is the psychological effect of raising the overall scores, propping others to bet more aggressively. That is worse with max bet being low relative to the starting bankroll. With no max bets, or ½ to whole original brl as max bet, it may be helpful because players will overestimate the goal and keep betting (hopefully losing) when they already had enough to pass you.
Betting contrary to players on your table would apply only if one of the big bettors would turn out to be the one that pushes you exactly one place down from advancing, minus the chance that he wins and passes you by the same, exactly one spot – slimmer than slim chance.
Time (right to make a possibly winning bet) is of essence. So, always bet max from the beginning. The only (minimal) exception is when you have plenty of rounds and the goal is low, so you can benefit from defensive splits for which you may bet half of your bankroll.

In your Prague tournament if you guessed you goals right and tried to win total of 3K (three max bets) in the first round of 21 hands you would had 50% chance of making it and you would bust out about 1/3 of the times. The rest of the results would leave you below the goal and not busted out, about .5% at the extreme ends to 1.5% for most of the middle for every half max bet interval between 0 and 8K (half max caused by blackjacks).

Sitting out a hand (betting minimum) with the goal to win three max bets cost more than 1% of total chances to reach the goal per hand if you get to play 15 hands, and ¾ of 1% for a round with 21 hands.

The cash value of that tournament.
Statistically you would reach the goal in the first round half the time. If you busted out in the first round winning 8 max bets in second round of 21 hands happens 10% of the time. The one sixth of “in-between” scores ads a couple percent chances to make the top six scores, and it is almost impossible to win 10 bets in 21 hands. Your total chances of reaching 18K total score should be in mid 50’s %.
Going for the same goal in the finals have the same chances and I would guess should get you first place every third try, second place about 15%, and the rest of the finals you would end up close to the last place.
Total EV a little above $2,000, but fun and adventure with cards, numbers, meeting interesting people and chance to explore new places – Priceless!

Take care,
S. Yama

 

Even though the tournament ended up allowing DOA, I was 1/2 way through the sims for this and thought that the results might be useful anyway.

With DOA we woulde choose to cover an opponent's double/split when betting first, even if it exposed us to a possible win/lose swing. We would do this against even a single opponent. How does this change with double allowed on only 8, 9, 10 and 11?

The answer is that it depends on whether your bet can also cover your opponents' blackjacks and also upon the skill level of your opponents.

The results are summarized in the table below. Each entry in the table represent how many opponents you can have chasing you and still prefer to avoid the swing.

Code:

Avoid Swing Preferred Over Cover Double Threshold
-------------------------------------------------
Skill/Bet | Lose to BJ  Win Covers BJ
-------------------------------------------------
Basic     |     2            4
Optimal   |     -            1
-------------------------------------------------

So, for example if you can bet such that your win covers the black jacks of 4 basic strategy players, you would still take the low to avoid the swing. If your bet would lose to the black jacks of more than 2 players then you would take the high and cover their doubles.

For optimal strategy players chasing you, you would never take the low if you would lose to even a single opponent's blackjack. If your win would cover the blackjack of a single optimal opponent then you should still take the low.

Note that I did not analyse the case where you can lock out your opponents' blackjacks with your low bet. If you could do that then you are more than 1.5 max bets ahead and can cover their doubles without risking a swing.

 

These numbers seem reasonable. My sim of this tournament predicated a 17640.099868 mean advancing threshold, a 50% advancing rate at 17350 and a 60% advancing rate at 18000. The EV for the most successful bot was $1597.18.

 

But I would have thought it would cause the scores to diverge more towards the high and the low ends of the range, as in round three those who need to catch up begin to run out of hands and start to view every hand as a potential opportunity to double down, basic strategy be damned!

Well I probably could have been more diligent in my research, but since the only previous tournament featured twelve players I was unsure how to equate the two.

There were welcome drinks the night before the tournament. I didn't learn too much there, partly because I was yelling at the top of my voice to be heard over the music.

I spoke to the person who finished 2nd last time. He said he thought the winning score had been around 17000, I think. (There was a language barrier, as well as the music to overcome.)

Thanks.

 

Most people seemed to favour smallish bets of 200, 300, or 400, most of the time. I saw very few max or min bets, except towards the end of the final round at the final table. (Though I'm sure there will have been a few which I missed.)

I don't think many people gave much thought to setting a target, or how best to shoot for that target.

I missed much of the play at the final table, but it looked like the winner deserved his success. On the final hand, he acted after BR1 who had (I think) only bet the min. He had the good sense to ask for (and get) a chip count, and thought about things for a good length of time before betting the max.

I'm not certain if he was actually able to work out that this could give him the win; the circumstances were pretty difficult (including the tournament director reciting the payouts while he was trying to think!). But he went for it and ultimately won by 200 chips.

 

Thanks for your comments, S. Yama. You paint a vivid picture of your teenage years!

I think perhaps you are right that Prague may have become a little too touristy, but I only had a short time to look around. Next time, I will have to book a longer stay.

I did strongly consider betting the max from the beginning. Based on Gronbog's numbers, I initially thought of setting a target of 17500, then when I learned of the rule change to DOA, I thought of making it 18500.

I may well have made the wrong choice, but my logic was that the goal did seem to be quite low (though uncertain), and that a total of 63 hands is quite a lot.

That, plus the small field, tempted me into sitting out the early hands in order to hopefully get a better idea of what the goal should be.

Indeed. It was definitely a fun trip. It's a shame that the next event, if I should qualify, will be so much closer to home!