21+3 tourney

Discussion in 'Other Games Tournament Strategy' started by S. Yama, Apr 13, 2009.

  1. S. Yama

    S. Yama Active Member

    About a month ago on Wong’s site bj21.com a poster asked about 21+3 tourney:
    “I saw a new twist on a blackjack tournament yesterday. It had a 21+3 side bet that was not limited by your blackjack wager. This was a 20 round tournament, with a $20 buy in, $1,000 in tournament chips and a $500 max bet on either bet. I ignored the side bet until the last hand. At that point the other three players left all had more chips than I had. I bet $10 on the BJ wager and $130 on the side bet. On that hand everybody hit the side bet except me. The ploppies seemed to love the format. I realized that it gave much more emphasis to pure luck.”

    My response was:
    XX (a valuable bj21 contributor) is right and used very nice analogy that any additional rule can be yet another arrow in a skilled player’s quiver.
    However, some new rules “naturally” make less experienced player play more aggressively, which is the right way of playing for them.
    Even if you were the best player in the world, your competition would reduce your edge by taking turns with big bets, so you would have to rely on pure luck to catch up with them. Your opponents would be best served by making bets with regular bj bets that have a lower casino edge instead of bets on 21+3 side bet, but the difference is not that detrimental. The worse situation would be if they staggered betting two at a time using 4-5 step progression, and if two players won their bets others would try to best highest score. Because of 9 to 1 payouts proper 4-step progression on 21+3 side bet is not 1/15 1/7 1/3 and the rest, but more like 21%, 23%, 26%, and 30% of the original bankroll. This of course is not a good way of playing but it would be toughest for you to compete against, as you would have in majority of cases two players with one and half to tripled bankrolls.
    Of course most players think that their skills are much better than average, though a median player represents below average ability.
    Some gimmick rules help skilled players more than the other, but that will depend on how most of other tournament players utilize them. Though, on practical level, it is always only the ones that play against you on your table.
    In your example, you most likely should have made an effort to become BR1 or BR2 one round before the last, but that depended on who you played against, their bankrolls and your betting position.

    And here is my teaser for you.
    21+3 side bet pays 9 to 1 on a straight, flush or three of a kind. 10 to 500 betting limits on either/each bj or side bet. BR1 has over 3000 and bets minimum, two players advance.

    ..................bankroll........main bet.......side bet

    case 1:

    case 2:
  2. TXtourplayer

    TXtourplayer Executive Member

    Off the top of my head I'd bet:

    500 on the main bet and 60 on the side bet. Hope that all the above lose their side bets.
    If I win my main bet would give me 1,000 + my left behind 40 = 1,040. which would cover BR3 DD win with side bet loss by 10.

    I'd still need to win my side bet should BR4 win a DD though, they could get to 1,180, best I could get to would be 1,040 without hiting my side bet as well.

    I tried to do this as fast as could as if I was actually at the table playing so I may be way off.
  3. tgun

    tgun Member


    I tried doing this even faster than Tex!

    you case #1 bj bet= 350 +3 bet= 80 keep 300 for 2nd low and 2nd high

    you case #2 bj bet= 290 +3 bet= 10 keep 300 for 2nd low and chance to swing table

    I give up! Thinking fast is not my forte!

  4. London Colin

    London Colin Top Member


    Can bets be multiples of 5, or must they be multiples of the minimum bet (10)?

    [Deleted some nonsense here that was based on dodgy arithmetic.:eek:]
    Last edited: Apr 15, 2009
  5. London Colin

    London Colin Top Member

    There's less difference than I thought between the 10 and 5-chip bet multiples. I thought it made a crucial difference in case 2, but I miscalculated.

    I'm still not entirely sure about my answer. But here goes anyway ....

    If you work under the assumption that side bets will be lost, some possible outcomes are -

              Main Bet Result
         Lose  Push  Win  BJ   DD
    BR2  580   590   600  605  610
    BR3  280   530   780  905  1030
    BR4  290   590   890  1040 1180

    If bets must be multiples of 10, then -

    Case 1 (730)
    Main bet: 80
    Side bet: 20

    A bet of 60 gives the high and low against BR3 and completely locks out BR2. The BR2 lockout holds for any bet up to 110. That would then mean we have something close to a two-player game against BR4, who we must hope doesn't win the hand.

    But rather than pick any bet in the range 60-110, we can use the leeway to add a side bet. We have 50 spare chips, half of which could go on the side bet, and half on the main bet, so that if (or more likely when) the side bet loses, we are no worse off than if we had just bet 60. That would mean a main bet of 85 and a side bet of 25, but since the bets must be multiples of 10, that becomes 80 and 20.

    Lose the side bet and win the main: -20 + 80 = +60 = 790
    Win side bet + lose main bet = 180 - 80 = +100 = 840 (covering same outcomes as main bet win)
    Win both : 180 + 80 = +260 = 990 (also covering BR4 win and BR3 BJ)
    Win side bet + double main bet = 180 + 160 = +340 = 1070 (also covering BR4 BJ and BR3 DD)

    Case 2 (600)
    Main bet: 500
    Side bet: none

    We can no longer lock out BR2. So I think we probably should take the high. We can't cover BR4's DD with a single bet, so we may have to double down. A side bet of 10 would give the possibility of making a total of 1190 without doubling, but if lost then doubling for the remaining 90 would only achieve a total of 1180, tieing with a BR4 DD.

    If the total were 605, rather than 600, then you could have -
    Main bet: 490
    Side bet: 10

    This makes it possible to reach 1185 or 1190.

    If bets can be multiples of 5, then -

    Case 1 (730)
    Main bet: 85
    Side bet: 30

    55 is now enough to give the high against BR3, and 115 locks out BR2. The range 55-115 is now 60 spare chips, so 30 can be shared between the main and side bets, making 85 and 30.

    The coverage then becomes -

    Lose the side bet and win the main: -30 + 85 = +55 = 785
    Win side bet + lose main bet = 270 - 85 = +185 = 915 (covering BR4 win and BR3 BJ)
    Win both : 270 + 85 = +355 = 1085 (also covering BR4 BJ and BR3 DD)
    Win side bet + double main bet = 270 + 170 = +440 = 1170 (which is not enough to cover anything further)

    Case 2 (600)
    No change.
  6. S. Yama

    S. Yama Active Member

    let the fun begin

    Sure, Colin, min 5 or even 1 would be fine. I am curious what you came up with.

    There are many approaches to try to come up with good bets.
    Before we attempt any of them we need to realize that, unlike in regular blackjack game, there is almost no correlation for +3 side bet. That means that if I hit a winning combination then the chance for other player(s) is the same as if I have not won my side bet. Also, there is no important correlation by winning or losing regular bj hands effecting the side bet.

    Because the payout on the side bet is 9 to 1 and casino has to have an edge we safely can assume that winning combination happens less than 10% of the time (actually it does occur only 8.7%). That is a smaller chance than swinging even one player.

    Our first approach should be to try to advance if we win the main (regular) blackjack bet.
    If any of our opponents wins his or her side bet it moves them to at least 1790, even if main bet is lost, or more. We can’t beat that with our regular bj bet, so our first and immediate goal is to beat the highest winning reg. bj bet by our opponents and assuming that they lose side bet.
    BR3 would have the highest score of 890, so both Rick and tgun got their bets correct.
    Rick would bet at least 310 (to 360 to be able to spilt) with no side bet. Tgun would bet 350 on bj and 80 on side bet, which nets 270 if side is lost, which would get him to “magic” score of 900. This bet, however, offers additional benefits: if the main bet is lost but the side bet won it would still moved us to over 900.

    But, as Ken says, there is always a better bet, so, can you find a bet that would put us ahead of everybody else when:
    1. Everybody wins main bet but loses the side bets,
    2. Everybody wins both, the side bet and the main bet
    3. Everybody wins the side bet and loses the main bet
    4. Maybe there is even a bet that covers points 1 and 3

    S. Yama
  7. S. Yama

    S. Yama Active Member

    Nice post

    Very nice, elaborate, and detailed post Colin!

    I made mine before I’d read your response.
    At first glance, I see that for your bets both BR3 and BR4 (both) have to lose both bets, and you have to win main bet, or you have to be the only player to hit the side bet. Winning main bet while others win or lose it has a grater potential. (I may as well miss something, lol)
    I will look into details later tomorrow.

    S. Yama
  8. S. Yama

    S. Yama Active Member

    another close decision

    Colin, I have to admit that I made that teaser by first getting some random numbers for BR2 to BR4 (BR1 was supposed to be out of reach) and then giving BR5 (us) a specific bankroll that has one bet combination, using all the money that has a balanced ratio to advance when all players win their main bets and lose side bets, and to advance when all/each win their side bets.
    So, I was thinking (without checking exact chances) of us, betting as BR5, 450 main bet and 280 side bet – that being all-in.

    However your betting scheme is interesting for additional values present when we lose.
    Let’s try to get specific numbers (they won’t be exact, as optimal play requires some deviations from basic strategy, for example BR4 betting after BR3 should hit to score one point better than BR3, or double).

    Let’s list the conditions. With the main bet of 85 and 30 side bet we advance if:

    1. Nobody (3 players) wins the side bet: 76.2% ....and
    2. We win the main bet while BR4 pushes or loses: 14.5%
    3. at the same time BR3 doesn’t win double or gets blackjack: ~90%
    Total chances when we win: 9.9%

    4. We push and both BR3 and BR4 can’t win: 4.8%
    Total chances when we push: 3.7%

    5. We lose and both BR3 and BR4 can’t win: 29.2%
    Total chances when we lose: 22.2%

    6. We win the side bet and lose/push the main bet, covers BR4 single win and BR3 bj
    Total additional chances of about: 1.5%

    7. We win the side bet and win the main bet, covers BR4 bj and BR3 double win
    Total additional chances of about: 1.9%

    Total chances: 39.2%

    I will try to get numbers for the all-in bet in a couple of days, unless somebody beats me to it, or offers a guess. It should be a close play.

    S. Yama
  9. London Colin

    London Colin Top Member

    Makes my head spin

    I hadn't done any probability calculations when I posted my idea; I just went for an interesting scenario that looked like it might be promising.

    Afterwards, I tried to use the tables that BlueLight generously published to work out the probability of advancing, ignoring the side bets completely. (i.e. assume nobody wins the side bet.)

    The answers I arrived at made the big-bet approach look marginally better (approx. 48.1% vs 47.7%). But I missed some BJ and DD conditions, so neither figure is entirely accurate. I do get the impression that the big-bet may be better, though.

    I was about to say that, since the much larger side bet must give more opportunities to win by that route, that adds another reason to prefer your scheme. But my 48.1% figure was based on the assumption that nobody can double past me if I win my main bet; that's not true if I lose a big side bet.

    For the above to be true, I would have to net > 450 if I win my main bet and lose my side bet. (in order to beat BR4's 1180 DD total.)

    That would mean -

    main: 500 (max)
    side: 49 (or 45, 40, or whatever max bet < 50 is allowed)

    When betting big, do the benefits of possibly winning a 280 side bet outweigh the drawbacks of being exposed to a possible DD from BR3 or BR4 (or a BR3 BJ)?
    Last edited: Apr 21, 2009
  10. S. Yama

    S. Yama Active Member

    85 main, 30 side bet

    The highest score if all players win main bet and lose side bet would be 890 by BR4, the highest score for the side bet would be 2780 by BR3. Our bankroll of 730 allows us to make bet of 450 on regular blackjack and 280 side bet, which gives us 900 if the main bet wins and 2800 if the side bets hits. In either case we would advance. We only lose to BR3 if we both hit the side bets but he/she gains to us with the main bet.
    We start with chances for winning the side bet --8.7%, reduced by BR3 gaining on us with the main bet, that gives us 8.0%.
    Of the 91.3% left, at least one of the opponents will hit the side bet 23.8% and we win 43.3% of the times (using the same, very useful, Bluelight’s table), which would give us additional advancement of 30.1%. That creates total chance of advancement 38.1%, only one percent less than Colin’s bet.
    But BR3 and BR4 bjs and doubles further reduce our chance by about 10% --making this bet definitely not as good as bet 85 main and 30 side bet. Good job Colin!

    S. Yama

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