How much would you bet on a fair bet?

There is so much talk about craps odds and such lately, I wondered, how much would you bet on a truly fair bet?

Very few exist. Somebody is probably not going to offer you a fair coin flip unless they are a degenerate gambler. Casinos offer no fair bets, except the odds bets in craps (in conjunction with pass line), double up feature in VP (need to make regular VP bet first), and certain VP games with optimal strategy. BetFair offers some zero house edge games with very low limits.

The Santa Ana Star casino near Albuquerque, N.M. offers a free buy on the 4 and 10, and a fair field bet (triple on 12 and 2). As far as I know, their maximums are reasonable for a brick-and-mortar casino.

If you had the opportunity to make a fair bet multiple times, how would you play?

"How" I would play the wager would, of course, depend on "whether" I would play. If I didn't find the wager entertaining, I likely wouldn't play it longer than it took to learn that I wasn't entertained. I doubt I would ever play coin flips. If I did find some even-wager game entertaining, I would probably wager an amount designed to maximize my entertainment. Based on what I know of myself, that is likely to be closer to a table minimum than a maximum, but I wouldn't spend much time playing $0.01 at a time if that were offered (yeah, right). Even my wife plays the penny slots for more like $0.50 - 0.75 per spin.

Same way as with low -EV bets, except I'd not be worried about playing too long.

didnt vote, my choice would be the size bet I am generally comfortable with, that's $20 to $50 or so. I would be greatly pleased to know there is no HE, but that's not advantage play, so how can you get too excited?

At that New Mex casino, I can picture myself making pass line bets too, at least some. I almost know I would. Why would I do that? Can't answer.

PS: having seen quite a bit of excitement when boxcars get rolled a lot on a field bet that pays triple on that bet, I wonder how crazy it sometimes gets at some of those new mex tables.

How about this question: How much would you bet if you had an advantageous bet but could only bet it once?

Suppose there is a promotion where a bet on one dozen (12 numbers) in single zero roulette pays 3:1 instead of 2:1, for a return of 129.7%. You can bet an unlimited amount on this one dozen but can do it only once. How much would you be willing to bet?

A) $10
B) $100
C) $1000
D) $10000
E) All the money at my disposal
F) All the money at my disposal plus I would loan/borrow all the money I can get to make the bet
G) Wouldn't participate

I would go for option C) as it would be the optimal for me from the risk/reward standpoint.

For a +EV bet, the proper solution is to calculate it via expected utility.
Without going into exact numbers, if for instance your wealth is now $15,000 and you bet $5,000, you'll either have $10,000 (2/3) or $30,000 (1/3). If your your utility function is for instance u=1/ln(W/100), then your quality of life metric is now 2,993. After betting, it will be either 2,171 or 5,260. The average is 3,200, making a $5,000 bet of slightly positive expected utility.

C) $1000

10k is too life-changing, would have to hedge it or just stick to the 1k.

the next question is, would there be a hedging formula that would make sense?

Quote: Jufo81

How about this question: How much would you bet if you had an advantageous bet but could only bet it once?

Suppose there is a promotion where a bet on one dozen (12 numbers) in single zero roulette pays 3:1 instead of 2:1, for a return of 129.7%. You can bet an unlimited amount on this one dozen but can do it only once. How much would you be willing to bet?

A) $10
B) $100
C) $1000
D) $10000
E) All the money at my disposal
F) All the money at my disposal plus I would loan/borrow all the money I can get to make the bet
G) Wouldn't participate

I would go for option C) as it would be the optimal for me from the risk/reward standpoint.

Can I make other bets at the same time? Two units on 0/00, nine units on first dozen, twelve on second dozen, twelve on third dozen. 35 units spent, guaranteed return of 36 units. If this is an option, I choose F.

More practically, and to answer the original question, when I play craps I'm really playing for the variance to be in my favor. In the case of betting Don't, this is essentially hoping that the distribution of 7's is greater than 1/6 and (very imporant!) not bunched together. Having zero-vig bets doesn't really change this in the short run, meaning one individual session. I say this from experience having played at the Santa Ana Star.

I think Santa Ana pays 16:1 and 31:1 (or maybe 33:1 to be consistent, although I recall the felt saying 31:1) on hop bets as well, including horn/C&E type bets, although in the latter case there may be a minimum.

Quote: 7outlineaway

Can I make other bets at the same time? Two units on 0/00, nine units on first dozen, twelve on second dozen, twelve on third dozen. 35 units spent, guaranteed return of 36 units. If this is an option, I choose F.

Obviously my idea was that you couldn't. With my question I wanted to know how much people are willing to risk on a one-shot advantage play where the chances to lose the bet are high.

Quote: Jufo81

Obviously my idea was that you couldn't.

If it truly was obvious I wouldn't have asked.

Quote: 7outlineaway

If it truly was obvious I wouldn't have asked.

Ok, sorry, it was only obvious to me :)

I am wondering if anyone would choose options E) or F). After all the expected profit is highest with those choices.

Quote: Jufo81

Ok, sorry, it was only obvious to me :)

I am wondering if anyone would choose options E) or F). After all the expected profit is highest with those choices.

In that case, probably choice B ($100), and only if I were up at least that much from other play at that casino (ie, playing with the house's money). Shouldn't matter statistically, but my marginal utility changes whether it's $100 I didn't have before versus my last $100.

If I don't have the ability to spread risk, either through multiple trials or multiple bets during the same trial, I become much more risk-averse, and I think most others are the same way.

Rampart Casino in Summerlin, Las Vegas permits 100X odds up to $5000. It's a four diamond hotel. To the best of my knowledge, this bet is the maximum bet in the world with the smallest house edge.

The even money bets at the Santa Ana casino in New Mexico have far more restricted maximums, and they will ask you to leave if you sat there and played nothing else all day.

Quote: Jufo81

How about this question: How much would you bet if you had an advantageous bet but could only bet it once?

Suppose there is a promotion where a bet on one dozen (12 numbers) in single zero roulette pays 3:1 instead of 2:1, for a return of 129.7%. You can bet an unlimited amount on this one dozen but can do it only once. How much would you be willing to bet?

A) $10
B) $100
C) $1000
D) $10000
E) All the money at my disposal
F) All the money at my disposal plus I would loan/borrow all the money I can get to make the bet
G) Wouldn't participate

I would go for option C) as it would be the optimal for me from the risk/reward standpoint.

E or F provided I had 3 partners. 2 with the same amount of money on the other 2 dozens and the other covering enough on the zero to break even on the 3 other bets. Considering there is no limitations on players at the game this would not be a difficult bet to win and even bankrupt the casino. The other answers made me chuckle.