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By Monkeysystem

Monkeysystem has been playing advantage blackjack recreationally for many years.  Early in his career he used High-low and AOII, and then simplified things, switching to Knockout a few years ago and getting better results.  He started playing tournaments in 2004 and has cashed in several. In this article he presents a new strategy Ė the use of Nash equilibriums - for maximizing your expectation in tournaments in which the bets in the final hand are secret. Excerpts are taken from Ken Smithís article in the March 2009 Blackjack Insider, "Read Those Rules."

In the March, 2009 edition of Blackjack Insider, Ken Smith gave a scenario for the final hand of a blackjack tournament at Harrahís New Orleans in which the players had a secret bet. The Ultimate Blackjack Tour format includes a secret bet that can be used once in a tournament round. Secret bets have been around for a while, and they continue to be included in the formats of some blackjack tournaments. Casinos incorporating this format may be seeking to make their blackjack tournaments a little more like poker. Or, they may just be trying to make their game fairer, because secret bets eliminate last-hand position as a major factor in playersí chances of success in the tournament. For the serious player, itís worthwhile to study strategy in this format.

As previously stated, secret bets eliminate the advantage of having late position on the final hand, and eliminate the disadvantage of early position. The late position advantage stems from knowing the opponentís betting decision and then reacting to it in the way that maximizes your probability of advancing. In a two-player match-up, all the player in early position can do is mitigate his disadvantage by leaving the lucky late position opponent the least attractive possible choices of strategy. With secret bets, neither player knows what his opponent will have bet. They wouldnít even need to take turns betting; they could both write down their bets on paper and hand them to the dealer at the same time. The chip leader has the advantage and the chaser is at a disadvantage, but there is no effect of position on either playerís chances (unless the player in late position has discerned a tell that indicates what his opponent may have done.)

Donít worry ... Iíll distill the fairly complex analysis that follows into a Tools You Can Use section at the end of this article.

Letís use a classic two-player heads up situation for our analysis of the problems players typically face when there is a secret bet. One player has a chip lead of ľ of a maximum bet: weíll call him "Leader." The other is behind: weíll call him "Chaser." Letís also assume for now that neither player has discerned any tells or betting patterns that indicate a preference for one style of play.

Both players seek to maximize their probability of success. The goals for Leader are prioritized as follows:

1. High-Low correlation, meaning Leader advances if both players get the same result on the hand, whether itís winning (the high) or losing (the low.) His probability of advancing is about 70%.

2. Getting the low. His probability is about 56%.

3. Getting the high. This reduces the game to a 50-50 coin flip and is the least desirable outcome for Leader.

The goals for Chaser are the reverse of Leaderís, and his percentages are 100% minus Leaderís in each scenario:

1. Getting the low. His probability is a 50-50 coin flip.

2. Getting the high. His probability is 44%.

3. Getting the high-low correlation. Chaserís probability of winning in this scenario is reduced to 30% and is his least desirable outcome.

A typical analysis of each playerís thought process in determining his secret bet size could go something like this...

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