Double Diamond Blackjack

I have included this study to describe how you go about investigating a new Blackjack rule. This game pays extra on a Diamond Blackjack, but less on other BJ's. Also, several other fancy rules are added. The problem with such a game is the huge penalty of reducing the BJ payoff. I've created a Surface Area Chart which displays the difference in winnings between a normal single deck game and a game like Double Diamond (DD). The DD game I used was 6 card charlie, 5 card 2:1, Diamond BJ pays 2:1, Normal Blackjack pays even, but is automatic win, Double on any number of cards even after splits. The chart has all two card hand types on the x-axis, dealer upcard on the y-axis and difference in winnings on the z-axis. The z-axis is winnings on the Diamond game minus winnings on a normal game.

Looking at the chart, the games are equal where the blue and green meet. Green is a slight advantage for DD, red is a serious disadvantage for DD. The green/blue splotchiness is due to the small number of hands run (160,000,000). It indicates that the variance at that number of hands is actually greater than the difference in results between the two games. The solid green with upcard combinations totalling 5, 6, 7 and 8 indicates a very slight gain in using the DD rules. This is due to the gain from double on any number of cards, 6 card charlie, and 5 card 21. The huge slice through the stack shows the loss due to most BJ's paying even money. This is somewhat less at BJ vs. Ace because of the BJ automatic win rule.

The point of the chart is to show the enormous penalty of the BJ rule change versus the very slight gains by the oddball rules.

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