I will therefore plan to bet on 19-36 if I can come to an agreement with begbert2 or SpoilerVirgin to split our winnings.
Pointless? Then isn’t it in the wrong forum?
Great Debates?
Close but no stogie.
You put the chip on red, $25k of your own money on black and you put $2941.17647… of your own money on the “row” bet: 0 and 00. It pays 17 to 1.
So the total money involved is $52941.17647 … of which $27941.17647… is your own money.
If the ball lands on red or black, the loss on one cancels the gain on the other. But you are out the $2941.17647… . Still you walk away with $50k.
If the ball lands on 0 or 00, you are out the $50k on red/black but you get 17*$2941.17647… from the row bet. You walk away with $50k.
For an investment of $27941.17647… you end up with $50k for a net gain of $22058.8235. Which actually seems a bit low. Hmm, where did I mess up?
FTG, you are giving up some net gain for the security of never losing. Essentially paying a $2,900 vig to launder the money through the roulette wheel.
You’re not off by that much. You need to bet $2778 (I’m gonna stick with dollar amounts) on the 0/00 ‘row,’ in addition to the $25K each on red and black. So the total investment is $52,778, of which $27,778 was yours, and $25K from your mysterious benefactor.
If the ball lands on red or black, you walk away with $50K. If it lands on 0 or 00, you walk away with $50,004. So you make a likely profit of $22,222 or possibly $22,226.
Anyhow, if you look at just your return on your own part of the investment, it of course seems low. You should recoup 36/38 of the total investment. And 52778*(36/38) = 50000.21.
Nothing. I immediately cash out, spend $15,000 on hookers & blow & still come home with a nice profit! 
Let me give you a word of advice. Always bet on black.
You know what’s weird? I’m actually debating with myself on this. There’s a part of my stupid brain that’s arguing that it’s better to shoot for the $50000 on a (nearly) fifty percent chance, than to take the (nearly) sure $25000.
The fact that the sane part of my brain has so far failed to quash the stupid part tells me it’s a really, really good thing that I don’t let myself gamble.
Ok, I’ll throw in a couple tacos.
My stupid brain is comparing your tacos with an additional $25000. (Which is 50% nonexistent, but my stupid brain doesn’t notice that.)
My stupid brain is really stupid. Its a wonder I take it out of the house.
I’ve been to Las Vegas and wish to thoroughly disagree with the above…
… first spend it all…
… and don’t spend any on blow!
I’m not sure whether OP clarified whether we get to keep the whole $50,000 or just the $25,000 “winnings.” Everyone else seems to assume we get the whole $50,000 when lucky, so I’ll go with that. (Despite that IIRC most or all casino promotions like this — though for much smaller amounts! — work the other way: the coupon is forfeit, win or lose.
Yesterday in the “What’s your (gambling) game of choice?” thread Chronos asserted the casino might prohibit this as money laundering! But let’s set that objection aside. 
As fellow Doper Kelly Criterion should be able to confirm, the placement of $27,778 on the other 18 numbers, while it seems quite logical, isn’t actually optimal!
Kelly will choose A to maximize
18 * log(Bankroll + 50000 - A) + 20 * log(Bankroll + 0.8 * A)
(0.8 is 16 / (38-18) if that helps.)
With Bankroll = $200,000, I find A = $13,158, much less than $27,778. Instead of a certainty of winning exactly $22,222, you’ll win $22,992 on average.
Let’s do some sanity checks on the formula above. Suppose Bankroll = $20,000,000. Now A = $0. Sure: why give away vigorish to the house? It’s not like you need to protect your possible win.
Suppose Bankroll = $40,000, barely enough to place the hedge without temporarily going into debt. Now the optimal A is $23,684. In the ballpark of $27k+ but still showing the unfavorable-odds hedge as not fully favorable.
Correct. If you win, you take it all. Basically it’s a $50,000 coin toss (with a slim but not insignificant possibility of landing on its edge, i.e. 0 or 00) with no personal risk.
If you choose not to bet at all, e.g. Spiderman, a couple of casino goons in ugly suits take the chip back.
.
I do this but I’m beginning to think I shouldn’t take financial advice from a guy who went to prison for tax evasion. And it doesn’t go up to 57.
Yup, we clearly need advice from someone who got away with tax evasion.
I felt like something wasn’t right. Indeed, I forgot to count the bet on 0/00 in the total money you walk away with if one of those come up. So 50k/18 instead of 50k/17.
Guy is sitting at the roulette wheel. He hears a little voice in his ear, “Bet $100 on red!”
The guy looks around, doesn’t see anyone. He shrugs, and puts $100 on red. He wins!
The little voice says, “OK, now put it on 11.” The guy puts it on 11. He wins!
The little voice says, “OK, one more. Put everything on black.” The guy puts everything on black, and loses it all.
The little voice says, “Oh shit.”
Regards,
Shodan
This makes no sense to me.
First of all, the way you find A to maximize that formula is to take the derivative with respect to A and set it to 0, then solve for A.
I’ll let others check me if they want, and I’ll show my work if they come up with different results, but if f(A) is the above formula, then assuming the log is the natural log, and letting B = Bankroll,
f(A) = 18 * log(B + 50000 - A) + 20 * log(B + 0.8 * A)
f’(A)=[18/(B+50,000-A)](-1) + [20/(B+0.8A)]*(0.8)
and setting f’(A)=0 and solving for A, we eventually get A = 400,000/15.2 - B/15.2.
The first fraction, rounded to 2 digits past the decimal point, is 26315.79, so if you have a zero bankroll, A = $26,315.79.
Not sure what the hell that means, since you never said what we DO with A once we’ve solved for it, but it clearly means we should do something with money we don’t have.
ETA: I get the same value of A as you do for a bankroll of $200,000, but I’ll note that the bigger your bankroll, the smaller your A, and once the bankroll is > $400,000, A is negative.
Maybe this makes sense once we know what A represents, so please clue me in.
BTW, if the goal is to maximize your average gain, the way to do that is to put in $0 of your own money, and put the mysterious benefactor’s $25K chip wherever - and you can do that no matter what your bankroll is. Your expected value is $23,684,21.
The disadvantage is that 52.6% of the time, you’ll be walking away with $0. The purpose of putting your own money in is to increase your guaranteed winnings by modestly reducing the expected value of your winnings. I don’t see what’s being maximized.