Blackjack and Game theory

See my Blackjack House Edge Calculator to determine the house edge under 6, possible rule combinations. It is because the chances that the dealer will bust are much higher when he shows a 6. If nothing says the win on a blackjack, then ask. Here are the full rules of the game. Claude Shannon — A Blackjack in the Scientific Pack Claude Shannon was the father of the information age formulating and proving some of the

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Prisoner’s Dilemma

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. I've said this before, but I think it bears repeating.

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: 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.

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. 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. Ternamint , Jul 19, Dakota, I do not underatand what this means. 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?

Ternamint , Jul 22, Ternamint, I mainly mean that the extra EV provided by the 2: You have to get lucky at some point to benefit from it. This is true regardless of how much is paid on the blackjack. 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.

Ternamint , Jul 23, 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.

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? Ternamint , Jul 27, 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. 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. I have tried my best to determine the optimum strategy and return on investment for this game, but the math is too complex for me. There are too many variables involved and when multiple rolls come into play it becomes overwhelming to fully understand.

I only have basic knowledge of statistics and probability. Help is greatly appreciated. In the following I shall treat the continuous version of the game: It reads as follows: From this we draw the following conclusion: An additional drawing would increase the probability of losing.

I would approach this by essentially working backwards. First, you can figure out what the dealer's probabilities are if the bettor outcome is fixed.

Then we can be calculate it recursively like this: By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service , privacy policy and cookie policy , and that your continued use of the website is subject to these policies. Home Questions Tags Users Unanswered. I am attempting to determine two variables in this game: What number the bettor should stay at The expected value given perfect play: The percent return on a bet when using the optimum strategy Here is how the game works: John Smith 46 3.

Christian Blatter k 7 Thanks in advance J. BLAZE 5, 9 26 Actually I've had a thought, If someone was to roll a 0, then surely you can assume that they intend to roll again, thus making the probability difference of the 'absolute impact on busting' between a die and and a die irrelevant Then following what p. This looks to me more like a question instead of an answer, what you could do is ask this as a new separate question and place a hyper-link that leads back to this post. Sign up or log in Sign up using Google.

Game Theory

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