Given some of the discussion lately about making high variance plays:

Assume you've been playing in a lively 1-2 NL game at a place that does not run 24 hours. On the announced, last hand of the night, you are in the BB and a fun, gambooler is on the Button.

It is folded to the Button and he says "Last hand of the night, All-In."

The SB snap folds, and you look down and see 55. As you're sitting there deciding what to do, the Button says "C'mon, let's do it," and flips over AKo.


How large do the stacks have to be before you say "No, thank you," and fold?

50bb? 100bb? 200bb? ...500bb? ...not folding for any amount?


P.S. I formally request that anyone who asks "Why are you posting a big blind on the last hand of the night?" should get a 24 hour temp-ban

Do we block any suits? Call any amount of bbs you have. Way too big of an edge to pass up for anyone playing 1/2.

If the answer is ever "no" you are under-rolled to have the stack in front of you and should have racked up. 55:45 is actually a very big edge and the Kelly fraction of your bankroll to bet on this would be about 1/10. Of course, we didn't get to choose our own bet-size, so we just have to choose whether the utility of calling is greater than the utility of folding. I think calling is probably better with up to about 1/5th of your bankroll at stake if you are strictly concerned with bankroll growth.

There's also some meta-value in gambling with these types of guys.

This is a kelly criterion problem. Just input your edge on the hand and your bankroll.

I assume that this is the rational, "risk of ruin" analysis.

As a psychologist, I'm curious about the point at which some people who are adequately rolled would begin to hesitate about committing stacks for "only" a 55-45 advantage.

As mentioned earlier, if you have a $10k bankroll (lowish end for $1/$2), you should fold if the bet is more than $1k. Between $1k and $800 is a close decision, lower than $800 is a snap-call.

The Kelly Criterion describes the optimal bet size. A bet can be greater than Kelly and still be a worthwhile bet, though. Someone correct me if I'm wrong, but I believe with a $10k roll and a 10% edge, someone should still call a $1200 bet. I am not sure up to what size calling is better than folding.

I always interpreted it as the maximum bet that allows for an acceptable risk of ruin. Any larger and risk of ruin is too large.

Double kelly and not betting are equal iirc. Greater than double you're better off passing.

In this scenario with the info provided, isn't 55 virtually the same as QQ? V has to spike an A or K regardless to beat you. I think most would snap call with QQ so...

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QQ makes straights less likely for AK and more rarely can’t be counterfeit by double paired boards like small PP’s can.

I don’t give loose action to nits or known hit and runners or at the very end of the night when the next guy to double up is going to leave and break the game.

Correct but I think the difference is < 2%. Hero is still a favorite

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You probably want the psychology forum, then. This is a strategy forum, and post #3 nails the strat answer.

Well, your call should have an EV of $20.55 if you call here 100bb deep (55% of 401).But after factoring rake (10% capped at $10-15), you have a barely +EV call. Personally 100 bigs deep im letting it go, i dont think it’s necessary for me to wager my stack for a 3bb EV call, there are plenty of better spot that arent as high variance. If you dont care about variance/want to gamble/have 1000BI that’s fine.

I rarely play >250 bb stacks because I believe that you should feel comfortable with being able to lose all the money in front of you in a single hand. I usually hover around the 100bb - 200bb range.

That being said, I think the 5% edge is too great to pass up as long as it's not a significant portion of your roll. If you do the EV calculation, you get a 10% edge on the money you put into the pot, which is actually pretty nice. So given that this is a one time "flip" and I wouldn't be playing more than 250bbs, I would call.

If we're being pedantic, the best pocket pair (excluding AA/KK ofc) to *flip* against AKo is TT (56.88%), in particular the TT that doesn't block AKo suits.

Depending on the rake structure, this should be a snap it off moment most of the time.

22 with blocking suits should be a fold though, unless you're doing it for your image.

The Kelly criterion is for maximizing expected bankroll over a large number of bet opportunities. It's obv relevant here, but it assumes we're risk neutral over that eventual bankroll. If we're relying on poker income for life expenses, for instance, that's almost certainly not true, and we should pass up large bets that it says are slightly favorable. There's no simple rule to use, because it depends on what our individual utility function over money looks like.

This is basically the definition of "not being rolled for the game." If your bankroll for your game is also being used for living expenses (i.e. you have no backup living expenses). Then you're not rolled for the game.

Agreed, but that's sidestepping OP's question; if we're responsible grinders practicing good bankroll management, obviously at some point as we run our stack up to infinity, we're not properly rolled to be flipping for it with a small edge.

I'm just pointing out that the Kelly criterion assumes a nice theoretical vacuum where ending up with a 50% chance of $1.5X and a 50% chance of $0.5X is just as good as ending up with $X. For large values of X, this is very unlikely to be true.

Kelly criterion is the boring but optimally right answer. OP wants to know how "degen" we are (in quotes because we have a pretty nice edge in this spot).

Given a roll of 30 buy ins or so I'd probably put in 500bb at 2/5, or 300bb if it was 1/2 and I didn't have the option of dropping down and rebuilding. This is assuming my bankroll is in a vacuum.

It's not, though. The Kelly criterion is a useful baseline, but it assumes a linear utility function over wealth (which imposes a log utility over outcomes of individual gambles), and there's absolutely no axiomatic reason for that to be true; it's just mathematically convenient.

I'm not the first person to point this out:

http://archives1.twoplustwo.com/show...6&Main=5463316

Random thought. If it is folded to the button, doesn't that imply there are more A's and K's in the deck? I always wandered how much that skews the odds on a "flip" spot.

No

This.

Utility of wealth is not linear. E.g. losing 4 BI often tilts people more than it makes someone happy to win 4 BI

A lot. This is actually pretty important. We actually know the cards in this example, but our calling range will change based on the position of the initial raise due to card removal. In fact, card removal defines our opening and calling ranges, but perhaps that should be another thread

Answer to the original question: if you are using a Kelley criterion bankroll then OF COURSE you take a flip! The Kelley criterion is defined by coin flips