Is the Minimum Bet Strategy a Game Theory Exploit?

Discussion in 'Blackjack Tournament Strategy' started by Monkeysystem, Jul 12, 2018 at 9:13 PM.

  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.
    johnr, george, MrPill and 1 other person like this.
  2. Dakota

    Dakota 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.
    johnr, george and KenSmith like this.
  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.
    george and johnr like this.
  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).
    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.
    george likes this.

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