Originally Posted by mcap View Post
CE varies wildly based on amount of capital available to my understanding than a straightforward 2:1 ratio, however, it’s related proportionately to the risk of ruin. Most AP’s that aren’t meth-head hustlers RoR is going probably going to be inconsequential on utx so much less gain than a 2:1 ratio. We get it though you’re nittier about variance than most, you’re “retired” and have said you won’t play certain games due to variance or pass on smaller edges.

Example being I just looked at a blackjack card counting simulation on cvcx with 0.0 RoR where edge is 1.25%, win rate per 100 hands is $191.46, CE is 149.27 or about 78% of EV. Doubling the bet amounts (same spread, edge, double EV) gives 1.1% RoR, $382.92 EV but $214.16 CE so CE dropped substantially from 78% to 56% (closer to your 2:1) by going from 0.0% RoR to 1.1%. Doubling it again the RoR rises substantially to 10.3%, and even though EV is now $765.84/100 and edge is the same the CE is $90.82, way lower than the original calculation that had only 1/4 the EV. Given that high multiple UTX plays are pretty high edge and inconsequential betting amounts to bankroll even with variance I would think most will be in that high CE range not equivalent to or 1.3:1 or less rather than 2:1.
Here is the question I had in graduate school: Suppose you had a choice of getting $1 million guaranteed or take a coin flip (fair coin) for $0 or $2,000,000, respectively.

There are many ways to answer this question of take the money or go for the toss.

This is graduate school so the focus is on theory. So in one example, we had the ability to buy “insurance”, e.g. give up some unit of our Wealth in the event we take the coin flip.

Btw, this was a question on my final and something I had to deal with on a constant basis in investment during my professional career. The correct answer depends on the individual’s wealth function, e.g. ln(W), the type of the function, etc. How much wealth must be given up as an insurance payment so the individual is indifferent to the two states. Clearly, it depends on the individual’s wealth and shape of the function. If your bank account is at $10,000 that extra $1,000,000 is going to give you a lot of marginal utility. Conversely if you have $50 million next worth, other things being equal, you might be more inclined to take the risk.

So one answer to solving CE is to look at the individual’s utility and solve for insurance payment so you would be indifferent to the coin toss.

Going back to this situation:
- Video Poker has much higher variance than blackjack as a general comment
- UX has a lot more variance than plain vanilla Video Poker
- This question is a lot more complex because it involves path dependency
- there are two guarantees in this problem so CE rears it head twice: 3X on dealt full house, which IF KEPT, creates 12X on the next wager

Based on my training and career experience, I would solve it based on the insurance approach. As a former Blackjack player myself in the old days, I would say using BJ would not be a good example to use as a corollary.

Notwithstanding the aforementioned, Mission146 is a documented liar. He was obviously butthurt that I turned down his private offer to write a story about me. He is clearly trying to troll me with “own my ass” when he cannot get the units right.

In summary, unless you use Isoquants aka indifference curves, wealth functions, it’s really hard to speak to CE, optimization, etc. But, I will say you do see 2:1 ratio a lot in the finance literature back when I was in school. I gave links to finance (not blackjack) sites for a reason.