Is the Minimum Bet Strategy a Game Theory Exploit?

Discussion in 'Blackjack Tournament Strategy' started by Monkeysystem, Jul 12, 2018.

  1. Monkeysystem

    Monkeysystem Top Member Staff Member

    I’ll start with some definitions.

    By the “minimum bet strategy” I mean betting the minimum bet in the early and middle hands of a tournament round, until there are five or ten hands remaining to be played. When you decide to bet more, you make big bets in hopes of catching the chip leader(s) or make correlation bets to protect a lead if you have it.

    By “game theory exploit” I mean a deviation from a Game Theory Optimal (GTO) strategy in order to improve your expectation against an opponent who is not playing in a GTO manner. Since exploitative strategies are in themselves a deviation from GTO strategy, they are vulnerable to counter-exploitation.

    GTO strategy is a strategy that mathematically cannot be exploited. Two players A and B each using GTO strategy will play to a tie. If player A deviates from GTO strategy and player B continues using GTO strategy, player B will win. In this case player B can then deviate from GTO strategy in order to improve his mathematical expectation in the game over what he would win if he continued using GTO strategy. However, in doing so player B incurs the risk that player A will adjust with a counter-exploit and “turn the tables” on player B.

    What does all this mean to the minimum bet strategy?

    Back in the low-hanging fruit days of blackjack tournaments, the advice of the good players was to bet the minimum bet until the last five to ten hands of a tournament round. This had several purposes:

    - Minimize the losses due to the inherent house advantage in blackjack. If all of your opponents are betting more than you, chances are that you will be ahead of most of your opponents when the critical last few hands come up. You can then make big bets in hopes of catching any chip leaders ahead of you. This minimizes the number of bets you must win in order to finish ahead of your opponents.

    - Eliminate the risk of busting out early. You can only win if you’re still in the game at the end. Also, your absolute loss limit compared with the essentially limitless amount you and your opponents can win makes lost chips more valuable than won chips, in terms of the cash buy-in and prize payouts.

    - Most opponents did not effectively manage their bankrolls. Many of your opponents busted themselves out with their huge bets. If they got way ahead of you, they kept betting big until their bankroll came back down to yours or they even busted out entirely.

    When I started playing blackjack tournaments in 2004 I noticed that a number of local regulars in my favorite venue were making medium sized bets in the early and middle hands and then correlating their opponents if they took the lead. These regs were frequent visitors to the final table. When I played against them they seldom busted out for me. When they took the lead they throttled back their bet size to make it almost impossible to lose all those chips back.

    Time and time again employing the minimum bet strategy I found myself making a maximum bet somewhere near the end of rounds, hoping to catch up. Sometimes it worked. Usually it didn’t. It usually didn’t work because these regs knew that in the critical last hands they could protect their lead by betting around half the maximum.

    In other words, these regs had learned through experience how to manage their bankrolls in a blackjack tournament.

    Since my first tournament in 2004 these regs have only gotten better at managing their bankrolls. They have also gotten better at basic strategy deviations on the last hand such as hard doubling. Couple this with the tendency on the part of casinos over the years to simplify the format of blackjack tournaments, and the game has gotten harder to beat.

    Since the minimum bet strategy is meant to exploit bad bankroll management, and if our opponents are managing their bankrolls effectively, that means the minimum bet strategy is being counter-exploited by these players.

    Sure, the minimum bet strategy accounts for the mathematical house advantage of blackjack.* It also accounts for the absolute loss limit versus unlimited win limit effect of the cash value of our tournament chips.

    However, there are other mathematical factors in blackjack that the minimum bet strategy does little to account for:
    - Variance. You are likely at some point in a round to have more chips than you started with.
    - Correlation of players’ results. You are most likely to have the same outcome in a hand as an opponent.

    The minimum bet strategy does not take variance and correlation into account until you have decided to make your move. And by then your opponents have begun to correlate your catch-up attempts.

    So if bad bankroll management is not there for you to exploit with the minimum bet strategy and is being counter-exploited, what strategy can you use in the early and middle hands?

    Is there a betting strategy for the early and middle hands that takes into account all of the mathematical factors of blackjack – house advantage, loss limit, variance, and correlation of player outcomes?

    *Most blackjack tournaments these days pay 2:1 on blackjacks, meaning the players actually have the mathematical advantage.
  2. Dakota

    Dakota Top Member

    A very nice analysis, Monkeysystem. Thank you.

    I generally don't like 2:1 blackjack payouts because it's a case of every player has equal advantage... but some are more equal than others. For example, big bettors, early on before coming back down or busting out (if at all), will have a slight advantage over more conservative bettors. And, in my case, my application of "going with the flow" in early to mid-session hands means betting 50%-75% of the bet amounts which I'm following (and not 100%). Another slight negative effect of 2:1 payouts.

    Thanks again for your thoughts on minimum bet strategy and your personal experiences.
  3. gronbog

    gronbog Top Member

    For me, every bet has a purpose. As such, the minimum bet is a waiting bet. I use it at the beginning of the round while evaluating the other players and waiting to see how the table develops. However, I do not believe in waiting for a pre-determined number of rounds to elapse before making more strategic bets.

    Every situation has a proper strategic bet whether it be early, middle or late in the round. As soon as I recognize the strategy I will need to use to advance, I begin implementing it. That's not to say that I begin increasing my bets right away. Sometimes the strategy I have identified still requires more waiting bets. But in situations where I believe that more strategically sized bets are required, I do not wait. I engage right away.
  4. gronbog

    gronbog Top Member

    I've said this before, but I think it bears repeating. 2:1 blackjacks do create a positive edge for the player in most blackjack games. However, the edge comes from an event which is relatively rare. A blackjack is dealt approximately once every 21 hands. In many tournament rounds, there is a good chance that you will not get one. For perspective, an opportunity to strategically double down occurs much more frequently, allowing you to create the same opportunity for yourself, when needed. Also, similar to the arguments against card-counting during tournament rounds, any small edge in EV which is gained by those betting more than average is completely inconsequential compared to the advantage gained by smart strategic play.

    For this reason, I personally do not alter my strategy for 2:1 blackjack events, nor do I worry too much about the other players benefiting. If anything, it's one less calculation I have to make, since I'm usually already considering the possibility of a double or split by my opponent(s).
    Ternamint, george and johnr like this.
  5. The_Professional

    The_Professional Active Member

    Nice discussion Monkysystem. One caution I would see in your post that the observation you made are comparing the minimum bet approach you take compared to the mid bet approach taken by several players. In other words, you have seen these player go to the final but not all of them, probably only one at a time. If you would compare your results to a given individual you probably will come ahead.
    johnr and george like this.
  6. Ternamint

    Ternamint Member

    I am surprised you would make an observation about the locals that could be selective memory. If they were locals, I assume they were regulars. If they were regulars, I assume they would be in the finals regularly. But as the OP mentioned, they probably weren't all in the finals all the time.

    Furthermore, an early loss by all players would favor the small bettor. As for a big catch up bet, aren't a preponderence of late bets large?

    Maybe the strategy differs with a capped max bet that makes catching up late tougher than with no cap, but I like to see where I stand, as the OP stated, in early going.

    With a mulligan, and the willingess to use it early, I could see medium bet sizing, possibly. I think the depth of the start stacks are a factor too.
    johnr likes this.
  7. Ternamint

    Ternamint Member

    Dakota, I do not underatand what this means. "I generally don't like 2:1 blackjack payouts because it's a case of every player has equal advantage... but some are more equal than others. " If you think 2:1 blackjack could be good, should you actually change your stance on the concept and be the one betting big from hand #1?

    gronbog, is every 21 hands actually "rare" in a tournament? If you have 8 players and 15 hands dealt, won't there be several naturals expected? Doubling can be done on any two, except a natural, so your point is well taken about the opportunity of doubling.

    Would it be better to actually deviate from BS more often and double when circumstances look favorable for a nice (anything that puts you close to BR1 or makes you BR1) chip up?
    " 2:1 blackjacks do create a positive edge for the player in most blackjack games.However, the edge comes from an event which is relatively rare. A blackjack is dealt approximately once every 21 hands. In many tournament rounds, there is a good chance that you will not get one. For perspective, an opportunity to strategically double down occurs much more frequently, allowing you to create the same opportunity for yourself, when needed."
  8. gronbog

    gronbog Top Member

    Ternamint, I mainly mean that the extra EV provided by the 2:1 blackjack is not some fundamental extra edge that will be applied to every hand played. You have to get lucky at some point to benefit from it.

    With regard to basic strategy departures during tournament play, it is my point that using these is much more a benefit to a skilled player than waiting/hoping for a blackjack. This is true regardless of how much is paid on the blackjack.
    Ternamint and johnr like this.
  9. Ternamint

    Ternamint Member

    Thanks gron. I understand your points and agree.

    My curiosities include the merrit of betting more than the min early, especially if you are going with the flow of a number of OPs, in hopes of being the winner of a natural, and also whether it might make sense to mine for more double down opportunities, also in the early going. These topics have likely been discussed in great detail on this site and I can dig up more info, but I would like to know your current thinking.

    Blackjacks will happen even in a short tournament and doubling more aggressively than BS dictates will be possible any time. Mining for these two events is less harmful to a bankroll because the buy in is fixed so how wrong is it to deviate. Tournament strategy as I know it still calls for sticking with BS most of the time.

    If you are dealt A3 and the dealer has a 4 with an OP or two standing on stiffs, the count is slightly negative, it is early in the tournament and a double down win gives you a slight edge, why not double? Does the possibility of taking the lead overcome, or outweigh, the incorrect BS play. With small starting stacks, I might be inclined to be strict but less so if stacks have a bit of cushion.
  10. gronbog

    gronbog Top Member

    To me, strategic departures from basic strategy are made for a specific purpose. The most common departure is doubling when hitting is normally the correct basic strategy play. The main reasons for doubling more often are to take the lead or when trying to catch up to an opponent who is more than a max bet ahead of you. You generally find yourself in these situations later in the round.

    There are many doubles you can make which have a positive expectation even though they are not correct basic strategy. It makes a lot of sense to make these doubles when in the situations mentioned above. They are an opportunity to place a bet at what can sometimes be a large advantage, where most of your initial bets are placed at a slight disadvantage. The closer to the end of the round you are, the more extreme you need to be when making non-basic strategy doubles. The extreme cases often come during the final few hands, where you may find yourself doubling or splitting anything.
    Ternamint likes this.
  11. Ternamint

    Ternamint Member

    "You generally find yourself in these situations later..." I seem to find myself in these situations early in a round at least as often as later. I am betting min while others are betting more than min and sometimes huge.

    I realize that it is good to wait so you know your situation and can plan a specific attack. But, how early is too early for deviating from BS to take a lead? Is it advisable to deviate early in an attempt to take a small lead, such as a single min bet lead? How powerful is a small lead in early play; powerful enough to offset the tiny negative ev play of a strategic early double?
  12. gronbog

    gronbog Top Member

    The thing about gaining a lead is that you also have to maintain it. The later in the round that you gain a lead, the less time your opponent has to overcome it. The extreme example is taking the lead on the final hand, in which case your opponent has no chance at all.

    You should buy Ken Smith's e-books and read what he says about magic numbers. A minimum bet lead early on has very little value.
    Ternamint likes this.
  13. Monkeysystem

    Monkeysystem Top Member Staff Member

    A small lead early on is not much help. However, a big lead can be. This is because your opponents will have to eventually take shots at you and they will often lose. This process culls the herd so that you won't have to get as lucky as you otherwise would in the crucial final hands.

    With a sizeable lead you can make bets that are somewhat smaller than the average when you see opponents start to bet bigger. This takes advantage the mathematical principles of dealer edge, loss limit, and similar outcomes.

    At this point you deviate from BS, to further take advantage of the mathematical principle of similar outcomes. One example is standing on 12 against dealer 2 and 3, to avoid the double bust. Another example is doubling your smaller-than-average bet with A3 against dealer 4. On this last one you're still correlating your opponents' bets while getting more money on the table in a positive EV situation.

    Oftentimes you'll lose the lead as multiple opponents take shots at you. But with a plussed-up stack it's more manageable. And the herd will be culled, making it even more manageable.

    The trick is in knowing how much to bet early in the round so that you get the right balance between risk of ruin and big enough lead.
    Ternamint likes this.
  14. Ternamint

    Ternamint Member

    Monkeysystem: are you going to share "the trick" with us of gaining a large early lead? I assume a large lead is defined as half a max bet or more.

    LS and the ability to rebuy would help I think. Using a progression would also seem a possible tool. If it works to gain a small lead, would it not work to stretch a lead?

    If multiple rebuys were available and practical, would you change your approach on the first buy in to an early aggressive attack until you got your "big lead"?
  15. Monkeysystem

    Monkeysystem Top Member Staff Member

    In tables with one advancing I wait for a few hands with minimum bets until I get an idea of what kind of table it will be. If the table is not hyper aggressive I'll bet maybe one-fifth of my stack until I get the lead. It happens the large majority of the time. Sometimes I dig myself into a hole I can't get out of. But usually I am the chip leader going late into the round.

    If you lose the first large bet you will be recalculating one-fifth of your stack before every turn. Then when you take the big lead you will trigger a betting war that makes tracking stacks much more challenging than when everyone is conservative.

    If you fall enough behind and running out of time you have to go to larger fractions or all-in, the whole time tracking opponents' stacks. You have to be very observant to anticipate when the players to your left are about to make their move on you. You have to work hard to track the chip stacks.

    This is not a strategy I would recommend to inexperienced players. Also, I don't believe this is a profitable strategy when two or more advance.
    Ternamint likes this.
  16. gronbog

    gronbog Top Member

    Sometimes at 2 (or more) advance tables, gaining a big lead for first place can earn you a free pass. The other players sometimes tend to focus on BR2 and leave you alone.
    Ternamint and Monkeysystem like this.
  17. Monkeysystem

    Monkeysystem Top Member Staff Member

    I've often wondered if this aggressive strategy might be profitable for two-advance tables, particularly if you have seven players and/or will act early on the last hand. I don't have any numbers or simulations that prove that, however...
    johnr likes this.
  18. Ternamint

    Ternamint Member

    This was a great thread last year! I have more questions.

    In a very fast tournament, in which end-game strategy can start within the first few hands of each round, and only one advances from Round one and then from Round Two, is it better to be that 20% bettor (.20 x stack) from hand 1 or would you still wait a few hands to gauge the table type? What if by waiting, you lose the protection of last to act? Would having a mulligan alter your response?

    In the example I have in mind, it's possible to be last to act on hand 1 and not again until under 5 hands are remaining! This limits the number of chances to surprise the other players from late position. I am leaning toward attacking as soon as the button passes me in this situation and also if the button is already past but less than half way around.

    Another possibility would be that you get the button after half the hands are over. Now there are well under 10 hands. Starting a 20% of stack attack seems a bit late in this case. I am leaning toward starting immediately in this situation as well. You may be acting very early but you are still acting as close post button as possible (assume button is past you by 2 or 3 seats but there are 8 or 9 players). You could pause and restart when you are again last to act, with 4 or 5 hands remaining, but at least you "got some work done" with 5 to 10 hands left in stead of all crammed in to the final 1 to 5 hands.

    These scenarios all assume a mulligan or two are available to each player. Thanks!
    Last edited: Jun 18, 2019
  19. Monkeysystem

    Monkeysystem Top Member Staff Member

    In your tournament it sounds like you are already approaching the endgame at hand 1. In that case you don't have time to see what kind of table will develop. It sounds like you need to go for it right away.
  20. Ternamint

    Ternamint Member

    Clarification on the "early aggression" scenario.

    If LS is available, rather than minimum bet from hand 1, does it make sense to bet twice the minimum. And would this be a good compromise to the 20% sizing when a round only has 12 hands and 6 players?

    Once you are BR1 Wong's chapter on LS states that LS allows the chip leader to bet twice their lead. I don't recall reading that a BR1 SHOULD always bet twice their lead. Should they?

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