I was sitting at two decent HSNL tables yesterday with the same very good player, and happened to stack him at both tables. At 25/50, he cold 4-bet TT and called my 5-bet shove. I had AA. At 10/20, he 3-bet 98s, I flatted with KK, we got it in on a 876 flop, and I won the flip.
He sounded like he’d had a rough week and was pretty tilted, started telling me I was terrible and trying to get me to play him heads up. As much as I complain about how nobody at 5/10 will play me, the truth is that I am also pretty nitty about only playing heads up against people I think I hae an edge on. I don’t have a ton of experience with this particular player, but he sits waiting for action at 25/50 and seems solid enough, so it’s a good bet that he’s better than I am.
Long story short, he offered me a 5% return on losses to play him. When I declined, he offered 7%. Now, there were some reasons I didn’t want to play him anyway. We didn’t get into terms, but he discussed it with another player, and wanted to play at least 3 tables of 25/50 for at least 1 hour. Although I will take shots when the games are good, I don’t actually have enough money on stars to play those stakes habitually. Plus, in order to focus, I’d probably have to quit most or all of the other games I was playing, some of which were reasonably good.
I’m curious, though, what a 7% return on losses is really worth. Obviously it’s worth nothing if I’m up on the session. If we were equally likely to finish up, then it would be worth a 3.5% edge. But if he is a bit better than I am, then he’s presumably somewhat more likely to finish up on the session, so maybe it’s worth something like 4%?
I guess it could even affect my strategy, as the ideal one for me would produce distribution of outcomes with a few big wins and many small losses. Perhaps it would be correct to play a few more speculative hands, chase a few more draws, etc.
I’m very curious what you math-types think (ie looking to hear from you here, brue). If opportunity cost and online bankroll weren’t issues, how much of an edge would this guy need to make his offer profitable? How, if at all, should my play change as a result of this arrangement?
Your strategy will be extremely complicated because it will vary as a function of time remaining in the game, a variable over which you have partial control, and how much you are ahead/behind.
Incidentally, this is a point that, as far as I can tell, no one has made about the Durr challenge.
Notice also that the further you are ahead, the less value the return of loss guarantee has. What this means is that, if you are worse than he is without the refund, you may want to slow down play when you are ahead.
This could lead to the perverse (compared to normal poker) situation in which you want to continue playing when you are behind and stop playing when you are ahead.
Finally, I expect that online poker room will offer % return HU tables. It is the most straightforward way to reinvigorate play at the highest levels.
Wow, that’s a complicated question…in terms of your strategy, I don’t think playing a higher variance game would help you…if you think about a standard normal (mean 0, variance 1), multiply the negative numbers by .93, I’m almost sure the new mean will not be affected by variance of the distribution (because the % of time you draw a negative number is unaffected by variance).
For a particular hand, obviously it only matters if it’s going to take you from red to black or vice versa. If folding in a certain spot would take you from plus to minus, the return on losses makes folding slightly more attractive, since you are certain to have that subsidized, whereas if you continue, you have losses subsidized but winnings not.
How much of an edge would he need to make 7% return profitable for him? Like what winnings distribution would he need? It would matter a lot how you structured the sessions…the shorter the sessions, the bigger edge he’d need. If you played infinite number of hands under one session, any edge he’d have would still be an edge when he subsidizes your losses, because he wins with probability one, and 93% of some positive number is still a positive number.
-bruechips
Thanks, gang, very interesting stuff. I hadn’t even thought about the length of the match, but that probably is the biggest strategic decision I would have to make.
Just to clarify, I didn’t necessarily mean variance for variance’s sake. But wouldn’t there exist situations where I would make a call/bluff I otherwise wouldn’t? Hypothetically, last hand of the required hour, we’re even thus far, he open shoves 55, shows it, and I have AK. I’m slightly behind, but with the 7% return on losses, it would be a call, no?
I get that time matters insofar as either of us can choose to stop after an hour. But if we were going to play for a pre-agreed, fixed length of time, is it even possible for this deal to swing a thin positive edge for him into a negative one? As you say, over time, an edge x .93 is still an edge.
Thanks for your very interesting comments.
It's definitely possible if you get the 7% refund on every losing session. It's like if you were taxed on your winning sessions but not allowed to deduct your losing sessions….except the opposite.
In the AK example, yes, if the amount you're putting in is really big relative the pot, you might want to gamble more…if there's some insignificant amount in the pot, and you're gambling for a $1k stack AND at this point in the session you are exactly even, you'd lose 930 54%, win 1000 46%, EV=42.2. I think the condition would be something like 2*(1-e)*(stack size/pot size) > 1 (-(1-e)(1-r)s + es > (1-r)p/2, differentiate wrt r) for when you'd want to gamble more as opposed to fold more when you have the return on losses.
-bruechips
This is a straightforward question that completely depends on the number of hands played.
Here are the assumptions:
His win rate is X bb/100 hands + a normally distributed error term with mean 0 and a variance that is a function solely of the number of hands played.
All of those seem reasonable, and it’s an easy equation to solve once you pick a variance.