Avoiding certain Splits and Doubles and its positive impact on comps

Good question. Let's first make some assumptions. For the rules, let's assume six decks, dealer stands on soft 17, and double after a split is allowed. Let's say the casino assumes a house edge of 0.75% in blackjack, and comps back 40% of theoretical loss. I get the 0.75% from my game comparison, and the 40% is more or less a standard policy at casinos with a liberal comp policy. So, if you value comps equally to cash, then you are getting 0.0075 × 0.4 = 0.3% back for all initial bets. Players are not supposed to get rated on doubles and splits, although some floormen don't know this. If doubles are splits are not rated, then your question is moot, so let's assume doubles and splits are rated.

So, the question is whether there is any situation where the expected value of splitting is less than 0.3% than the next best alternative. The closest hand is 3,3 against a 2 (corrected). From my blackjack appendix 9, we get the following expected values:

Stand -0.292445
Hit -0.142183
Double -0.563298
Split -0.133356

So splitting if favored by 0.008827. That is much larger than the 0.003 comp reward, so the player should still split.

To summarize, my answer is that comps are not generous enough to ever deviate from basic strategy. Perhaps there is some other set of rules where the value of splitting on some hand is less than 0.3%, but value of this trick would be worth pennies, even if there were such a situation.

Quote: Wizard

If doubles are splits are not rated, then your question is moot, so let's assume doubles and splits are rated.

To summarize, my answer is that comps are not generous enough to ever deviate from basic strategy. Perhaps there is some other set of rules where the value of splitting on some hand is less than 0.3%, but value of this trick would be worth pennies, even if there were such a situation.

Wizard, you say above that if doubles and splits are not rated my question is moot, don’t you mean that if they are rated my question is moot? The rest of your response seemed to imply that you understood that and may have just mistyped.

Other then that you have answered my question perfectly! But I guess that’s why you are the Wizard. I think I may have had my decimal places off by a bit in my conclusion that there was an advantage to not splitting. I guess that’s why you shouldn't send a CPA to do an actuaries work. Accountants get confused at anything more then two decimal places.

Another quick note. You say "The closest hand is 2,2 against a 3" The numbers that you gave are for 3,3 against a 2, which I believe is actually the closest hand. This is why everyone's work should be checked by an auditor :)

Sorry I misread your question. You can see I answered it at 2:49 AM.

To keep it simple, let's ignore comps and loss rebates. Is the cost of making a bad double or split sometimes smaller than the house edge of the game itself? In most cases, yes. Let's look at this example:

6 decks
Dealer stands on soft 17
Player has A,7
Dealer has 2

Here are the EV figures from my blackjack appendix 9.

Stand = 0.124001
Hit = 0.063289
Double = 0.12098

So, doubling would be an error costing 0.003021.

If your goal is to minimize the ratio of expected loss to total money bet, which is a good goal, then you should double if the element of risk in blackjack is greater than 0.003021. It will be greater than that if either double after split, surrender, or re-splitting aces is not allowed.

You could make this same point in any game that involves raising. For example, in Three Card Poker if you want to minimize the expected loss per hand, then the optimal strategy is to raise on Q64 or better. However, if your goal is to minimize the expected loss per total amount bet, then the optimal strategy is to raise on Q62 or better.

This begs the question of why do gambling writers like me base strategy on minimizing the expected loss per original bet, rather than the total amount bet? It is mainly out of tradition. That is how the blackjack basic strategy was created, and everybody has kept that methodology out of habit and simplicity. Other benefits of playing strategies based on minimizing the expected loss to the original wager is the variance and expected loss per hour are less, due to smaller average total bets.

I would like to add my 2c worth... if you are going to make any exception to the 8-8 rule, just the 10's only. Play according to strategy otherwise. JMH2c