1, 2, 6, deck betting cover costs (revised-long-Pt.1)

From Stanford Wong's BJ21

Posted by ML on 14 Mar 1999, 7:49 am

I have now finished the CVSim simulations for betting cover in single, double, and six deck. Single deck and double deck data has been previously posted.

But I am reposting single and double deck because, after thinking about the data, I think a different method of comparison than comparing by DI^2 will be more helpful in making true comparisons as to the costs of betting cover. Rather than scaling win rates by DI^2 to get an adjusted win rate as I did in the earlier posts, I will be scaling win rates by the ratios of Average Square Result/Advantage of the different types of cover.

For those of you not totally familar with the development of optimal betting theory, the calculation Average Square Result (Some call this variance as it is variance for all practical purposes)/Advantage or Win Rate defines a bankroll which has the "optimal" betting Risk of Ruin of 13+ per cent for a compound game like blackjack with a predetermined range of bets. This calculation is not optimal betting as such which scales all bets "perfectly" to give the player a minimum N0. As Brh has shown, if this bankroll is multiplied by 1.5, Risk of Ruin for all games compared will be almost exactly 5%. So if one takes the ratio of the bankroll for a benchmark game to a game to which the benchmark is being compared and multiply this ratio by the win rate of the game being compared, a fairer comparison will be made than my previous comparison using DI^2.

Further, I think posting the 5% ruin bankroll gives another valid method of comparison so I will be posting these figures for each game. BTW this method of comparison is likely stepping on Don and John's Blackjack Forum article to some extent but I promise Don that, while I got the article file by email from him, I could not read it. I guess it was in Word and neither my wife nor I could not make my computer decipher it.

So the data posted will be.

Win Rate (WR) Per Hand in % Directly from CVSim.

DI Directly from CVSim.

SD per hand Directly from CVSim.

5% Ruin Bankroll (BR) Calculated ((SD^2)/WR)*1.5 in units.

Adjusted Win Rate as described above. (AWR)

Ratio of Adjusted Win Rate to Benchmark Win Rate. (%)

All sims compare heads up play with play with other players because number of rounds have significance on the effects cover betting has. Further, the Single Deck and Double Deck sims have runs resetting the bet immediately after a shuffle to one unit and two units because this also has an effect.

While rules and betting patterns, of course, change depending on the games, certain CVSim settings were used for all sims. The 1994 Wong Hi-Lo was used for betting and strategy. Ill18 less splitting tens, what is called the "Sweet 16" on CVSim was used. A $10 unit bet and 100 hands/hour were used because data could be read directly from the statistics screens. In multiplayer games, seats were rotated so there would be no seat bias.

Double and Six Deck rules were DAll, DAS, S17, no resplit aces, no surrender. Single Deck was DAll, No DAS, H17, no resplit aces, no surrender.

Single Deck penetrations were three to three and five to one. Double Deck penetration was a cut card at 65 cards or 5/8 for one or three players. Six Deck penetration was a cut card at 1.5 decks for one or four players.

Betting was calculated as optimal for the benchmark games to the nearest reasonable unit. For the Single Deck sims, the basic spread was four with 2 at +1 and 4 at +2. Two spread was run for no cover as a comparison and three spread was run for no cover and with no cover except not making a jump of more than one and a bet of two after the shuffle because I have always liked the looks of that method.

A six spread was used for DD with 2 at +1, 4 at +2, and 6 at +3. A ten spread was used for six deck with 2 at +1, 4 at +2, 8 at +3 and 10 at +4. Optimal betting would have said 5 at +2 and 7 at +3 for the benchmark game.

The benchmark game for SD is three to three no cover and for double and six deck the benchmark game is heads up no cover.

I realize my lettering system in the earlier posts was confusing so I am going to a different system, a numbering system. The first number will be number of decks, the second number will be number of players, and the third number will be bet after shuffle. So 131 will be single deck with three to three and a starting bet of one unit. 212 would be double deck heads up with a starting bet of two units. Six deck only starts with one unit so it will be 61 or 64.

The same conventions as my earlier posts will describe the cover used. P means no change in bet after a push, M means only changing one level of betting at a time, L is no lowering after a win, and R is no raise after a loss. Combinations like MR would be parlay, etc.

Some of the data below might look strange. Betting cover works a number of different ways, depending on the type used. Some types like not raising the bet after a loss hurt win rate but at the same time cut variance. Other types like not changing the bet after a push or not lowering after a loss might help win rate but also raise variance. So, a smaller bankroll might be needed to play cover than the benchmark game or win rate might be higher with some cover than the benchmark game, but one can see things balance out with the various adjusted win rates.

I am going to do a number of posts on this topic so I will post this introductory one and put data and comments below.

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