Avoiding certain Splits and Doubles and its positive impact on comps

Over in the Wizard of Odds web site under the Ask the Wizard section (Asked the Wizard! No 249) a player asked what is the impact of hitting on 8,8 rather then splitting against 9,10,A. The wizard responded that hitting increases the house edge by 0.019%, or about one bet every 5,300 hands played.

This got me thinking from an overall cash return perspective, wouldn't I be better off hitting the 16, and keep track of all the times I hit a 16 rather then using those theoretical unit to play that many hands at double my normal rate, thus increasing my average level of play.

I guess my real point is that every strategy I have seen doesn't take into account the cash payback associated with comps. You aren’t comped additional on doubles or splits so they should have a slightly lower value.

It is my understanding that initial bet drives the comp calc. So there most be certain double down and split plays that so marginally increase your odds that you are better off just hitting or staying. An added benefit of doing this, especially with something so basic as splitting 8 (and having everyone at the table scream at you) is that the pit boss will assume you don’t know apply basic strategy and potentially assign a higher expected loss rate to you.

To look at it in terms of the numbers
My bet is $25 if I split the 8 it will take me 3,500 occurrences to get a benefit equal that amount. But if I take that same $25 and increase my initial bet I should return $197 in comps over those same 3,500 hands.
$25(bet) * 1.5%( theoretical loss rate)* 15% (comp rate)*3500= $197 in additional comps. You would then have to factor in losing one additional hand so your net benefit would be $197-25 = $172.

expected loss of 1.5% multiplied by comp rate of 15% is 0.23% so any split or double that has a positive impact (as compared to the next best non split/double option) lower then that should actually be just a hit or a stay in terms of total cash return.

I looked at the split opportunities in wizards basic blackjack appendix 9 and counted (using excel) and counted 53 instances where splitting or doubling would be an improvement over the hit/stand option. Of those only instances 21 were enough of an improvement after considering the comp benefit of doubling a later initial bet.

So in the end I guess what I would like top see is a basic strategy table adjusted to eliminate split / double options that improve you winning odds by less then the comp rate on that bet. What do others think about my math and the usefulness of such a table/ strategy?

I doubt that your comp rate is affected by your skill level, especially on the decision making on what to do with splitting 8s on a 9-10-A. You would probably get more comps by just hemming or hawing on your strategy and having less hands/hour dealt to the entire table rather than making strategy changes based on your comp.

And I don't really get what you are saying anyway. Your expected value on every hand is decreased the same on every deal by the comp rate on that bet. And because the comp rate differs at every casino and by denomination played, embarking on such an endeavor would not have any effect either. The correct play is always the best play, no matter what the comps are. The only way this would change is if you knew that the pit gave you a bonus every time you did something against basic strategy.

It's an interesting question, but there are too many variables that you're either not considering or making assumptions about.

For example, where did you get the 15% comp rate or the 1.5% theoretical loss rate?

And how about that $25 bet? Comps are not based upon the bet, but the average bet. If the floorman is doing his job, he will notice the splits and doubles and include that when he rates you.


But most important, NEVER play FOR comps. They are a nice little bonus, but should never be considered when you're making your decision to play, or change your bet.



To quote the Wiz from https://wizardofodds.com/ask-the-wizard/tablegames/, about 1/2 way down he talks about comps. Here is his summary:

Quote:

In my opinion, you should play whatever you would play if there were no comps at all. Then consider comps as icing on the cake.

Boymimbo
I'm not sure that your comp rate is affected by your skill level, but I have heard it suggested that those playing a pure basic strategy and using a card would get comped less then a risk taker. Maybe others can comment on that.

As to your second point, my basic premise is that you are not comped on splits or double downs, because you are generally comped only (or primarily) at your rate of initial bet. So you have risked additional money but not been given credit for it in you comp calc. If the expected return (or improvement) on the split or double is less then the comp rate on that same bet then you shouldn't make it.

I did make the assumption that the comp rate is 15% of theoretical loss, but that is a common assumption. You could always lower that rate to 10% and there would be fewer instances were the comp adjusted strategy varies from basic strategy.

>I don't really get what you are saying anyway.
I'm not quite certain either.
>The correct play is always the best play, no matter what the comps are.
Agreed, though often there is but a teensy weensy difference between the utterly correct play and the slightly individualistic style of play.
>this would change if you knew that the pit gave you a bonus every time you did something against basic strategy.
Comps are based on average bet and time at table as modified by their overall impression of you and any various policies an individual casino might have. Going against Basic Strategy every now and then would have no effect on anything. Tipping might have a subtle effect. Being personable might have a subtle effect. I don't see how slight deviations from Basic Strategy whether whimsical or not would affect anything.

I have a hard time believing that a floor man will be able to adjust for players who split or double less then the average player. I bet you find that average bet really means average initial bet, and maybe it is adjusted up slightly for splits or doubles, but as the norm that has to be done (if done at all) at some normal rate.

Also my idea doesn’t suggest that you play just for comps, it just suggest you should take the comp rate into account when making certain decisions.

Blackjack players split hairs all the time on things like hitting 16 against 10s or not. That decision actually has a lot less impact on you total return then comps do.

Quote: jburgess

I have a hard time believing that a floor man will be able to adjust for players who split or double less then the average player. I bet you find that average bet really means average initial bet, and maybe it is adjusted up slightly for splits or doubles, but as the norm that has to be done (if done at all) at some normal rate.

Also my idea doesn’t suggest that you play just for comps, it just suggest you should take the comp rate into account when making certain decisions.

Blackjack players split hairs all the time on things like hitting 16 against 10s or not. That decision actually has a lot less impact on you total return then comps do.

perhaps if you are betting $25/hand, they rate you at $30/hand to account for splits and doubles. that would be my guess of how they would go about it if they did rate splits and doubles into your average bet.

Quote: rudeboyoi

perhaps if you are betting $25/hand, they rate you at $30/hand to account for splits and doubles. that would be my guess of how they would go about it if they did rate splits and doubles into your average bet.

I agree. So taking a few low advantage splits our doubles out of you normal plays wouldn't decrease your average level of play. But would allow you to play a few additional hands or have a separate block of play were you increase you average bet and are rated higher during that one block

you can start betting $75/hand when you sit down to get comped at a $75 rate when the floorman is first watching you. then drop down to $50/hand. from a distance 2chips looks very similar to 3chips. and if the floorman walks up to you while you have a $50 bet out. bet $100 on the next hand whether its letting your bet ride or doubling your bet after a loss. so lets assume a 20% comp rate for easy calculations. so if youre getting comped at an avg bet of $75/hand while youre mostly playing $50/hand, its as if youre getting a comp rate of 30% a hand. but due to the costs of having to increase your bet on occassion, it probably averages out to about a 25% comp rate. whatever denomination chips you are betting, follow the 3 chip, then 2 chip structure. so $15 and $10 with redbirds or $300 and $200 with blackchips. betting $15/hand is probably going to be more effective at a $5 table than a $10 table.

Quote: jburgess

To look at it in terms of the numbers
My bet is $25 if I split the 8 it will take me 3,500 occurrences to get a benefit equal that amount. But if I take that same $25 and increase my initial bet I should return $197 in comps over those same 3,500 hands.
$25(bet) * 1.5%( theoretical loss rate)* 15% (comp rate)*3500= $197 in additional comps. You would then have to factor in losing one additional hand so your net benefit would be $197-25 = $172.

expected loss of 1.5% multiplied by comp rate of 15% is 0.23% so any split or double that has a positive impact (as compared to the next best non split/double option) lower then that should actually be just a hit or a stay in terms of total cash return.

What are you increasing your initial $25 bet by? 1/3500 of $25? 1/400 of $25 (the rough number of times you get a pair of eights vs. paint or an ace). Or by the full $25 to get the extra $197 in comps? Remember you'll also be losing $25*1%*3500 = $875 in increasing your bet for every hand.

If your doing every so often, you'd have to be rated at that higher rate all the time, which is possible, but not likely.

Comps are a hand back of YOUR expected losses. You can game it so this hand back is higher than it should be, but not by making extra bets that erode perfect play.

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