Buying a double (with tax?)

[ChampangePloppy]

According to a table from the Wizard of Oz website, the expected return of doubling down against a dealers 7 when we have 11 is about 46% (it can range from 45-48% depending on the exact composition of the hand).

So say the player is betting $100, and is about to hit 6,5 v a dealer 7. I say "Stop! Can I double that hand because its lucky for me..." (or whatever). The player says ok, but give me 10% of your win. (a freeroll for the player, player does not pay me anything if I lose). Should I still do this?

If I bet $100 with an ER of .46 then every $100 I bet should get me an average of $146 returned to me. With the 10% tax I'm effictively giving the player $4.60 I suppose, which means my new net ER is $141.40.

But since I'm risking $100 of the wager while winning $90 and losing $100 I feel like thats not right. What is the correct way to calculate this situation?
What would the cutoff % be that the player can ask for where we would break even from a EV perspective?

(I am interested in the math on how to get this answer, I need to learn how to think about this situation on the fly, this situation seems somewhat elementary and is making me feel bad about my self).

Thank you for the help

[ChampangePloppy]

So it just hit me, was I not able to figure it out because idk how often I will win the hand?:

so p is probability
w is win l is lose

[pw(90)]-[pl(100)]=net win?

I guess that would make sense?

actually idk at least you can see where my thought process is at

[ChampangePloppy]

Actually wait, there should be a way to know without the probability since I already have my expected return right? I just have to show how the 10% tax reduces this expected return.

I'd need the probability if I was trying to figure out the EV of a play instead? Is expected return not the same as expected value? Ok now I'm just confusing myself I'll just wait for some feedback lol

[Exoter175]

I think you're trying to overlook or over complicate the situation. You basically had it right the first time. If the expected return is .46 of the wager, then there is no reason to calculate anything else, as that's the final calculation of the value. Example, lets say this happens 15 times at the table, or 150 times at the table. Eventually your results will reach the .46 return number over time.

Having said that, I think you're using the wrong numbers to start off with. In order for this to be fair to the original player, you'll have to buy him out of the hand completely, and then give him 10% of the wager. Remember, if he/she wasn't planning to double, you could ultimately have created a difference decision for the player. If the next card out was a 2, then the original player would have likely hit his 13 against the dealer 17, and though he might have busted, he'll never see that scenario play out if you offered to double. If your double doesn't work out, in the example of simply buying the double and giving him 10% of the proceeds, then he actually loses out. The right play, here, would be to offer to buy his hand and do the double as is, with a 10% bonus for a win. In that sense, you're in for $200 for the hand and the double, and he's in for $0. Your win returns $200, you give him $20, and you'll have made $180 on top of the $200 wagered.

[DSchles]

"so p is probability
w is win l is lose
[pw(90)]-[pl(100)]=net win"

Yes, right.

"I guess that would make sense?"

So, all you need to do is change the +46% e.v. into probability of winning or losing the hand. But, you must be careful. The urge is to say win 73% of the time, and lose 27%, so that 73% - 27% = 46%. But that would be wrong, because the +46% doubles the original bet, and you're not doubling. So, the +46% is the net result of having doubled, which you aren't doing. Therefore, the net e.v. for a single bet on the hand is +23%, which means (excluding ties): win 61.5% and lose 38.5%. That's what you have to plug into your equation above.

So, if the original wager is $100, to which you're going to add $100 of your own, your e.v., given the 10% of winnings arrangement, is:
(0.615)(90) - (0.38.5)(100) = 16.85, or $16.85.

When does the bet turn negative? A little algebra (simultaneous equations) leads to pw = 52.63% and pl = 47.37%. This is for the pre-doubled values. The pure edge would be 5.26% and the doubled edge (given in books and tables) would be 10.52%. Higher than that value, you accept the 10% tax. Lower, you don't.

Clear?

Don

[Freightman]

Forget the math - this time. Fuck him. A cold day in hell before I pay a percentage of the win. Max EV is not everything. Principles trump. Not withstanding the principle, what if our purchased double from our ploppy friend produces air. We've now robbed him of his opportunity to hit again.

Notwithstanding, scavenging is an art form - never pay for it.

[Exoter175]

Forget the math - this time. Fuck him. A cold day in hell before I pay a percentage of the win. Max EV is not everything. Principles trump. Not withstanding the principle, what if our purchased double from our ploppy friend produces air. We've now robbed him of his opportunity to hit again.

Notwithstanding, scavenging is an art form - never pay for it.

Slightly inclined to agree with you a little, which is why I said that it would only be right to buy the Original Player out of the hand entirely, while offering the 10% still. The value isn't necessarily in the decision itself, but in the already existing wager waiting for said decision. Offering to double the Original Players' wager, AND giving up 10% of the wager in a wager is robbery in my eyes. Sure, the numbers will workout the same in a tit for tat if you did this twice, but I'd want the whole enchilada, not just the second half of it.

[Freightman]

Slightly inclined to agree with you a little, which is why I said that it would only be right to buy the Original Player out of the hand entirely, while offering the 10% still. The value isn't necessarily in the decision itself, but in the already existing wager waiting for said decision. Offering to double the Original Players' wager, AND giving up 10% of the wager in a wager is robbery in my eyes. Sure, the numbers will workout the same in a tit for tat if you did this twice, but I'd want the whole enchilada, not just the second half of it.

It's a zeeish approach to doing business. By the way, I'm inclined to agree with me a lot.

[ChampangePloppy]

Thanks ex175 and FM, at the time I completely missed the fact that by buying only the "double portion" of the bet that I could be hurting the player. This situation actually happened and I hit a 10 so the player and I won $100 and the player high five me and thanked me for doing the double. Who knows what would have happened if I pulled a 2 and lost to a 17 oh man... I didn't even tip the player for letting me buy the double, I foolishly thought it was win win for both of us since I forgot about the possibility of needing to hit again some of the time, it was during a decently high positive count. I remember I had just under my max bet out myself so I was a little excited and almost screamed when I saw the player was not going to double since I felt like it was throwing money away. Rookie mistake.

The 10% thing didn't actually happen but I was curious because my friend did something similar but he tipped out $10. Then I started wondering how an extra expense like that can affect the profitability of a play and where we would need to draw the line. (I think tipping can sort of fall into the same category?)

Thank you DSchles for the detailed response. I just want to make sure I get it now. I guess the first issue is 73-37=46? I typed it into my calculator at least 20 times but I kept getting 36. Although I suspect it was a typo, you wrote the number 73 for wp and 37 for lp twice, and I trust you more than myself so I was trying to see if I'm missing something haha. Please ease my mind that it was a typo. It all makes sense if its typo.

And then the part about doubling, its not a doubled bet because I am only buying the 2nd portion of it correct? The 46% edge is assuming that both the original bet and the double is mine? Since I am only doing the $100, I half the edge. Okay I think I got that. So we are dealing with a 23% edge on MY BET.

EDIT: I actually typed out a lot of stuff but I figured it out right before I hit send so I deleted it. I guess I'll leave the 2 questions I had lingering about the typo and half edge thing anyway just for clarification. Jumping for joy because it clicked!!! Took me a a hour tho, all good!

[DSchles]

Naturally, all I did was answer the original question, which asked for an explanation of the math involved. Naturally, once again, immediately, everyone else began preaching about everything EXCEPT how the math would work. It gets to the point where the predictable NON-answers are actually quite funny. Ask a question and wait to see how long it takes for six people to provide "answers" to everything except what was asked.

Finally, although it doesn't matter in the slightest what I or any of you think about the 10% tax, it's really quite stupid, if it's a take it or leave it proposition that's being offered to you, not to take it. You all claim to be APs, but what you're saying is that, if you were offered a clearly positive-e.v. bet, you'd hold out for a better deal. And when the player said no to you, then what? You'd tell him "not interested"? How dumb is that?

Clearly, none of you spent 10 years on a trading desk, making dozens of decisions a day, as to where you would or wouldn't buy or sell a commodity or do a deal. The "you'll do it my way or it won't get done" approach gets you dick. Otherwise known as cutting off your nose to spite your face.

Don

[DSchles]

"Thank you DSchles for the detailed response. I just want to make sure I get it now. I guess the first issue is 73-37=46? I typed it into my calculator at least 20 times but I kept getting 36. Although I suspect it was a typo, you wrote the number 73 for wp and 37 for lp twice, and I trust you more than myself so I was trying to see if I'm missing something haha. Please ease my mind that it was a typo. It all makes sense if its typo."

Embarrassing mistake. Not like me. I apologize. Doesn't happen often. Of course, the right numbers should have been 73 - 27 = 46. But the rest of the analysis is correct, as nothing that followed was influenced by the typo, which I have corrected.

"And then the part about doubling, it's not a doubled bet because I am only buying the 2nd portion of it correct?"

Correct.

"The 46% edge is assuming that both the original bet and the double is mine?"

Exactly.

"Since I am only doing the $100, I half the edge. Okay I think I got that. So we are dealing with a 23% edge on MY BET."

Yes. Glad it's clear and sorry for the typo. As for the comment about depriving the player of his right to hit the hand more than once by what you were doing, that's all the more reason why a 10% tax wouldn't have been so unreasonable after all.

Don

[Exoter175]

Thanks ex175 and FM, at the time I completely missed the fact that by buying only the "double portion" of the bet that I could be hurting the player. This situation actually happened and I hit a 10 so the player and I won $100 and the player high five me and thanked me for doing the double. Who knows what would have happened if I pulled a 2 and lost to a 17 oh man... I didn't even tip the player for letting me buy the double, I foolishly thought it was win win for both of us since I forgot about the possibility of needing to hit again some of the time, it was during a decently high positive count. I remember I had just under my max bet out myself so I was a little excited and almost screamed when I saw the player was not going to double since I felt like it was throwing money away. Rookie mistake.

The 10% thing didn't actually happen but I was curious because my friend did something similar but he tipped out $10. Then I started wondering how an extra expense like that can affect the profitability of a play and where we would need to draw the line. (I think tipping can sort of fall into the same category?)

Thank you DSchles for the detailed response. I just want to make sure I get it now. I guess the first issue is 73-37=46? I typed it into my calculator at least 20 times but I kept getting 36. Although I suspect it was a typo, you wrote the number 73 for wp and 37 for lp twice, and I trust you more than myself so I was trying to see if I'm missing something haha. Please ease my mind that it was a typo. It all makes sense if its typo.

And then the part about doubling, its not a doubled bet because I am only buying the 2nd portion of it correct? The 46% edge is assuming that both the original bet and the double is mine? Since I am only doing the $100, I half the edge. Okay I think I got that. So we are dealing with a 23% edge on MY BET.

EDIT: I actually typed out a lot of stuff but I figured it out right before I hit send so I deleted it. I guess I'll leave the 2 questions I had lingering about the typo and half edge thing anyway just for clarification. Jumping for joy because it clicked!!! Took me a a hour tho, all good!

Don has a way of being right about what he's saying, but using the wrong numbers, or coming up with weird ways to come to the same conclusions as others, and when I read his math post I saw the same error you saw, and disagreed with his angle on a few others.

To me, the representation of a +EV value, is that it is the END of the calculation. A +EV of 46% tells me that after I wager 1,000 hands at $100 a piece, I should have made $146,000, or, rather, profited $46,000 over the course of those 1,000 hands. There is, to me and my understanding, no taking into account a win or loss into the +EV% equation, as it is already done.

Lets use his example for a second. He cut out pushes (which is just wrong on all accounts), and said we had a 61.5% win vs. 38.5% lose. If we wagered 1000 hands at $100 a piece, base, for $200 all total, we'd win 615 hands for $200($123k total win), and lose 385 hands for $200($77k total loss), for a total profit of $46,000. Which goes back to our +EV of 46%.

What he had intended to do, was show you a probability that would represent the +EV of 46% and how it functions, and then compare ti to the +EV of 23% for the second portion of the double, compared to the rake of the original player (10%) ONLY in the event of a win, using more tangible numbers, albeit, wrong numbers for this purpose since he is still not accounting fora push. However, he's showing you how to calculate your cut into the equation of the second portion of the double.

What should have been done, is a simulation of a few thousands hands under this scenario, condensed down to 100 hands to give us a true representation of the "real" expectation of wins, losses, and pushes, so that we could apply the simple dollar values here and there, and we have the "real" numbers to the question.


In any case, he's really both wrong and right here, depending on how he frames the argument and how we choose to view it, and I think we could all agree that if a position is being sold like this, it would behoove the buyer to buyout the whole hand and give 10% on the win, rather than just the doubled portion with a 10% tip. Again, the value is in the setup of the hand, 11 vs. 7, rather than the actual play. The win% is strong here in most all common counts, and in theory could increase or decrease in value in relation to the true count.

Also, we aren't dealing with a 23% edge on your bet, since you're giving up 2.3% of that edge to the owner of the spot you're betting on. Your realized edge is 20.7%.

[Exoter175]

Naturally, all I did was answer the original question, which asked for an explanation of the math involved. Naturally, once again, immediately, everyone else began preaching about everything EXCEPT how the math would work. It gets to the point where the predictable NON-answers are actually quite funny. Ask a question and wait to see how long it takes for six people to provide "answers" to everything except what was asked.

Finally, although it doesn't matter in the slightest what I or any of you think about the 10% tax, it's really quite stupid, if it's a take it or leave it proposition that's being offered to you, not to take it. You all claim to be APs, but what you're saying is that, if you were offered a clearly positive-e.v. bet, you'd hold out for a better deal. And when the player said no to you, then what? You'd tell him "not interested"? How dumb is that?

Clearly, none of you spent 10 years on a trading desk, making dozens of decisions a day, as to where you would or wouldn't buy or sell a commodity or do a deal. The "you'll do it my way or it won't get done" approach gets you dick. Otherwise known as cutting off your nose to spite your face.

Don

I hope you're not referring to me, Don.

I simply brought to light that the better deal, and the moral one, would be to buy the player out all together, reducing the player's risk to 0%, while having a decent probability of making $20 for his tax.