# Roulette wheel "even money" bets **URL:** \ **Category:** In My Humble Opinion\ **Created:** [October 18, 2018, 7:23pm UTC](https://boards.straightdope.com/t/roulette-wheel-even-money-bets/823166 "2018-10-18T19:23:55Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![Lare](https://avatars.discourse-cdn.com/v4/letter/l/53a042/32.png) [@Lare](https://boards.straightdope.com/u/Lare)\ **Post date:** [October 19, 2018, 12:32am UTC](https://boards.straightdope.com/t/roulette-wheel-even-money-bets/823166/21 "2018-10-19T00:32:48Z")
I will therefore plan to bet on 19-36 if I can come to an agreement with **begbert2** or **SpoilerVirgin** to split our winnings. ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [October 19, 2018, 12:46am UTC](https://boards.straightdope.com/t/roulette-wheel-even-money-bets/823166/22 "2018-10-19T00:46:06Z")
> [@DCnDC](#): > > No. It’s entirely a pointless exercise in selecting between equal choices. Pointless? Then isn’t it in the wrong forum? ---
**Author:** ![Riemann](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/riemann/32/3133_2.png) [@Riemann](https://boards.straightdope.com/u/Riemann)\ **Post date:** [October 19, 2018, 12:49am UTC](https://boards.straightdope.com/t/roulette-wheel-even-money-bets/823166/23 "2018-10-19T00:49:21Z")
> [@Exapno\_Mapcase](#): > > Pointless? Then isn’t it in the wrong forum? Great Debates? ---
**Author:** ![ftg](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ftg/32/2801_2.png) [@ftg](https://boards.straightdope.com/u/ftg)\ **Post date:** [October 19, 2018, 1:10pm UTC](https://boards.straightdope.com/t/roulette-wheel-even-money-bets/823166/24 "2018-10-19T13:10:36Z")
> [@markn\_1](#): > > I’d put the chip on red and then put $25,000 of my own money on black. Then I can’t lose! Mwah ha ha ha! > Whaddya mean “zero”? 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? ---
**Author:** ![Cheesesteak](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cheesesteak/32/3694_2.png) [@Cheesesteak](https://boards.straightdope.com/u/Cheesesteak)\ **Post date:** [October 19, 2018, 1:41pm UTC](https://boards.straightdope.com/t/roulette-wheel-even-money-bets/823166/25 "2018-10-19T13:41:10Z")
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. ---
**Author:** ![RTFirefly](https://avatars.discourse-cdn.com/v4/letter/r/c77e96/32.png) [@RTFirefly](https://boards.straightdope.com/u/RTFirefly)\ **Post date:** [October 19, 2018, 2:05pm UTC](https://boards.straightdope.com/t/roulette-wheel-even-money-bets/823166/26 "2018-10-19T14:05:50Z")
> [@ftg](#): > > 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? 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. ---
**Author:** ![Spiderman](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/spiderman/32/230_2.png) [@Spiderman](https://boards.straightdope.com/u/Spiderman)\ **Post date:** [October 19, 2018, 3:39pm UTC](https://boards.straightdope.com/t/roulette-wheel-even-money-bets/823166/27 "2018-10-19T15:39:18Z")
> [@DCnDC](#): > > What do you bet? Nothing. I immediately cash out, spend $15,000 on hookers & blow & _still_ come home with a nice profit! 🆒 ---
**Author:** ![Peter\_Morris](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/peter_morris/32/359_2.png) [@Peter\_Morris](https://boards.straightdope.com/u/Peter_Morris)\ **Post date:** [October 19, 2018, 4:31pm UTC](https://boards.straightdope.com/t/roulette-wheel-even-money-bets/823166/28 "2018-10-19T16:31:11Z")
Let me give you a word of advice. Always bet on black. ---
**Author:** ![begbert2](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/begbert2/32/3357_2.png) [@begbert2](https://boards.straightdope.com/u/begbert2)\ **Post date:** [October 19, 2018, 5:23pm UTC](https://boards.straightdope.com/t/roulette-wheel-even-money-bets/823166/29 "2018-10-19T17:23:59Z")
> [@Lare](#): > > I will therefore plan to bet on 19-36 if I can come to an agreement with **begbert2** or **SpoilerVirgin** to split our winnings. 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. ---
**Author:** ![Lare](https://avatars.discourse-cdn.com/v4/letter/l/53a042/32.png) [@Lare](https://boards.straightdope.com/u/Lare)\ **Post date:** [October 19, 2018, 5:28pm UTC](https://boards.straightdope.com/t/roulette-wheel-even-money-bets/823166/30 "2018-10-19T17:28:03Z")
Ok, I’ll throw in a couple tacos. ---
**Author:** ![begbert2](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/begbert2/32/3357_2.png) [@begbert2](https://boards.straightdope.com/u/begbert2)\ **Post date:** [October 19, 2018, 5:33pm UTC](https://boards.straightdope.com/t/roulette-wheel-even-money-bets/823166/31 "2018-10-19T17:33:55Z")
> [@Lare](#): > > 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. ---
**Author:** ![glee](https://avatars.discourse-cdn.com/v4/letter/g/b5a626/32.png) [@glee](https://boards.straightdope.com/u/glee)\ **Post date:** [October 19, 2018, 6:24pm UTC](https://boards.straightdope.com/t/roulette-wheel-even-money-bets/823166/32 "2018-10-19T18:24:22Z")
> [@Spiderman](#): > > Nothing. I immediately cash out, spend $15,000 on hookers & blow & _still_ come home with a nice profit! 🆒 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! ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [October 19, 2018, 6:29pm UTC](https://boards.straightdope.com/t/roulette-wheel-even-money-bets/823166/33 "2018-10-19T18:29:39Z")
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. > [@RTFirefly](#): > > 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. 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. ---
**Author:** ![DCnDC](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dcndc/32/2842_2.png) [@DCnDC](https://boards.straightdope.com/u/DCnDC)\ **Post date:** [October 19, 2018, 7:08pm UTC](https://boards.straightdope.com/t/roulette-wheel-even-money-bets/823166/34 "2018-10-19T19:08:06Z")
> [@septimus](#): > > 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. 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. . ---
**Author:** ![thelurkinghorror](https://avatars.discourse-cdn.com/v4/letter/t/7c8e57/32.png) [@thelurkinghorror](https://boards.straightdope.com/u/thelurkinghorror)\ **Post date:** [October 19, 2018, 7:47pm UTC](https://boards.straightdope.com/t/roulette-wheel-even-money-bets/823166/35 "2018-10-19T19:47:46Z")
> [@Peter\_Morris](#): > > Let me give you a word of advice. Always bet on black. 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. ---
**Author:** ![Riemann](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/riemann/32/3133_2.png) [@Riemann](https://boards.straightdope.com/u/Riemann)\ **Post date:** [October 19, 2018, 7:49pm UTC](https://boards.straightdope.com/t/roulette-wheel-even-money-bets/823166/36 "2018-10-19T19:49:52Z")
> [@thelurkinghorror](#): > > 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. Yup, we clearly need advice from someone who _got away with_ tax evasion. ---
**Author:** ![ftg](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ftg/32/2801_2.png) [@ftg](https://boards.straightdope.com/u/ftg)\ **Post date:** [October 19, 2018, 8:00pm UTC](https://boards.straightdope.com/t/roulette-wheel-even-money-bets/823166/37 "2018-10-19T20:00:52Z")
> [@RTFirefly](#): > > You’re not off by that much. You need to bet $2778 (I’m gonna stick with dollar amounts) on the 0/00 'row … 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. ---
**Author:** ![Shodan](https://avatars.discourse-cdn.com/v4/letter/s/9f8e36/32.png) [@Shodan](https://boards.straightdope.com/u/Shodan)\ **Post date:** [October 19, 2018, 8:10pm UTC](https://boards.straightdope.com/t/roulette-wheel-even-money-bets/823166/38 "2018-10-19T20:10:31Z")
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 ---
**Author:** ![RTFirefly](https://avatars.discourse-cdn.com/v4/letter/r/c77e96/32.png) [@RTFirefly](https://boards.straightdope.com/u/RTFirefly)\ **Post date:** [October 20, 2018, 10:49am UTC](https://boards.straightdope.com/t/roulette-wheel-even-money-bets/823166/39 "2018-10-20T10:49:48Z")
> [@septimus](#): > > 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._ 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+0.8_A)]\*(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. ---
**Author:** ![RTFirefly](https://avatars.discourse-cdn.com/v4/letter/r/c77e96/32.png) [@RTFirefly](https://boards.straightdope.com/u/RTFirefly)\ **Post date:** [October 20, 2018, 12:33pm UTC](https://boards.straightdope.com/t/roulette-wheel-even-money-bets/823166/40 "2018-10-20T12:33:00Z")
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. [Previous page](https://boards.straightdope.com/t/roulette-wheel-even-money-bets/823166.md?page=1) [Next page](https://boards.straightdope.com/t/roulette-wheel-even-money-bets/823166.md?page=3)