Ridiculous

[euklid314]

But the stakes are not ELO but the final position within the match. Your opponents ELO do not matter at all.

If you play against 3 weaker (in ELO) opponents it is predetermined that you can gain almost no ELO and lose a lot. Still your goal is to play optimally such that you optimize your chances of winning the match.

If you fold hands that you should have taken then you will lose ELO (in a probabilistic sense).

[Jol_]

Let me give another example.

You're a high-ELO player joining a 4-player table, each having 100 chips. 3 players just shove all-in pre-flop with their random hands in front of you and you're in big blind holding pocket KK. Knowing that KK performs mediocre in multi-way pot, you estimate that your chance of winning the whole pot is around 60%.

If you call and win (60% chance), you'll receive +6 ELO points.
If you call and lose (40% chance), you'll get 2nd place together with 2 other players and get -16 ELO penalty.
If you fold, you'll at least get a 2nd place ahead of 2 other players and get a -2 ELO penalty.

What is the optimal play here?

Chip EV
You expect to get 400 * 60% of chips = 240 chips, a +140 increase from your original 100 chips. So the optimal play is a call here.

ELO EV
If you call, you expect to have (+6) * 60% + (-16) * 40% = -2.8 ELO points.
If you fold, the worst case is that you receive a -2 ELO penalty.
In this case, the optimal play is to fold your KK here to at least secure the 2nd place. And this also implies that lower-ELO players should in general over-bet / over-shove a lot against higher ELO players as higher-ELO players need to over-fold against elimination pressure.

Sorry for over-complicating things but what I'd like to point out is that chip EV does not directly translate into ELO EV. This echoes with what a couple previous replies - a tournament-styled poker game in BGA coupled with ELO rating with assymetrical payout do affects players' risk/reward dynamics and playstyle. Once a table is started, a higher "risk premium" is assigned to a high-ELO player as it is more costly for them to get eliminated first due to a bad beat.

And of course, all the above does not matter if ELO rating does not matter for you and you only care about winning the first place.

[Jol_]

BTW my above bulls**t is not a made-up concept or anything . In real-life tournaments there are also a lot of extreme spots like this (spots that you even need to fold AA preflop), but these spots tend to be only prominent in certain phases called "bubbles".

Here in BGA we have a more extreme manifestation. As soon as a high-ELO player joins the game he has an inherently higher "risk premium" and should make very cautious decisions when betting/making calls. A lower-ELO player, knowing the tendancy that the other player overfolds, could exploit by over-betting and over-shoving. Though as he makes progress towards higher ELO, this "loose aggressive" play would no longer work.

[euklid314]

I do not have the exact numbers but my point is that all you said is independent of the ELO distribution.

If your example (all 3 opponents go all in immediately against your KK) happens against 3 opponents of equal ELO to you then you will receive, say
+17 ELO points if you call and win
-5 ELO points if you call and lose
guaranteed +9 ELO point if you fold

And if you play against 3 stronger opponents the numbers might be:
+20 ELO points if you call and win
-2 ELO points if you call and lose
guaranteed +12 ELO point if you fold

I did not check the numbers but the relative difference in ELO will always be approx. the same X, X-22, X-8.

Thus you should always fold KK in such situations if you want to optimize ELO - independent of your opponents strength. A guaranteed 2nd place has always the same value.

[Jol_]

The ELO distribution affects your range / "breakeven threshold" which you can accept an all-in. It may not affect KK this particular hand but it deffo moves the threshold.

It is not different from real-life tournaments, where we also cannot simply ignore the payout structure. The pay jump affects "risk premium" which we need to incorporate in every decision we make.

The only thing different here in BGA is that the payout structure, being the ELO points, acts unequally against different players from the start of the game.

[Edit] Removing description on AA as it adds to confusion.

[euklid314]

Now you are calculating a new value.

If I remain with your original "ELO EV", it gave a loss of 0.8 ELO points for taking (-2.8 ELO) vs. folding (-2 ELO).

In my examples you also have the same loss of 0.8 ELO points:
(+17)*60%+(-5)*40%=+8.2 ELO vs guaranteed +9.
(+20)*60%+(-2)*40%=+11.2 ELO vs guaranteed +12.

True, a loss of 0.8 ELO points might be relatively more important if the stakes are in the range -2.8 to -2, but in absolute values it is always a 0.8 loss.

[euklid314]

[Edit: It seems that the example I am referring to was deleted by Jol_ I hope that Jol_ can still make sense of my reply.
Game 1 was three equal opponents, +5 for win, 0 for draw, -5 for loss.
Game 2 was three stronger opponents, +7.5 for win, +2.5 for draw, -2.5 for loss.]

Unfortunately, one number is wrong.

In game 1, when you fold you have a guaranteed +5 points (2nd place = 2 wins + 1 loss = 2x5 -1×5). In game 2 you calculated it correctly (2nd place = 2x7.5 - 2.5 = 12.5, guaranteed).

Thus your example is exactly as I described in my post. In game 1 all ELO outcomes are exactly 7.5 worse as in game 2 (because you have stronger opponents in game 2). If your goal is to win the maximum amount (absolute value) of ELO points you have exactly the same take points and decisions to make.

In game 1, a win gives +15, a solo 2nd place gives +5, a shared 2nd=3rd=4th gives -5
In game 2, a win gives +22.5, a solo 2nd place gives +12.5, a shared 2nd=3rd=4th gives +2.5

In both (!) cases, folding KK is *not* an obvious choice because taking is better than folding and comparing with the guaranteed 2nd place.

[Jol_]

Thanks euklid for clarifying haha. Took me some time to understand that X, X-22, X-8 thingy. I was half asleep and made a calculation mistake.

Not sure if it's exactly how ELO number works (hell lot of assumptions we've made ) The 100-ELO floor still screws things up for a bit but I guess there is a reason for that.

[euklid314]

Thanks euklid for clarifying haha. Took me some time to understand that X, X-22, X-8 thingy. I was half asleep and made a calculation mistake.

In order to summarize (and end?) the discussion (where I had begun to doubt my own arguments :

Yes, I fully agree with you, Jol_, that the high (ELO)incentive to not get 4th definitely can change game play and can lead to a more timid game play in the beginning of a match!

But this incentive is the same for all players, i.e. both for high and low ELO players. Often low ELO players don*t care which is one of the reasons they have low ELO.

Meanwhile I am quite sure I am right: Game play is never influenced by relative ELO. Even more is true: If you are in a game with both low and high ELO opponents it does not make any ELO difference if you lose against the ELO favorite and win against the ELO underdog or the other way around (i.e., you got 2nd place in both cases). Only the sum of ELO points of your opponents and your position in the match decides your ELO outcome in the match.

One may interpret my claim as follows. If you play in a game with 3 opponents you will always get the same ELO point differential for getting 1st, 2nd, 3rd, 4th, plus or minus some fixed bonus points if your opponents are on average stronger or weaker than you, respectively. The stakes might be +15, +5, -5, -15 in one game and 22.5, 12.5, 2.5, -7.5 in a different game. You are always playing for X, X-10, X-20, X-30 ELO points (sorry to use that not-well-defined value X again)...

[Jol_]

Still kinda confused about the X+10, X+20 thingy and I've absolutely no idea whether or not the ELO works like this but I kinda get your logic (I guess?)

In game 1, a win gives +15, a solo 2nd place gives +5, a shared 2nd=3rd=4th gives -5
In game 2, a win gives +22.5, a solo 2nd place gives +12.5, a shared 2nd=3rd=4th gives +2.5

IRL if I know the above, I just calculate the all-in equity needed - both of above should give exactly 50% equity, i.e. my hand should at least need 50% equity in a 4-way pot and the call to be positive EV in ELO points. Not sure if ELO is designed to always give the same equity value needed regardless of opponents but your calculation seems so. So even if all opponents are shoving random trash hands, I can only call with top 3% of all hands {99+, AKs} which is a very narrow range.

And you cleared up this - no matter if I'm a 400-ELO / 300-ELO / 200-ELO it doesn't change the 50% needed. So we should maintain same level of aggression across different ELO levels. The only exception comes to 100-ELO - it might change something but I'm too scared now to go through another monstrosity of numbers.

In the meantime if I calculate the chip EV, only 25% equity is needed in order for the all-in call to be positive EV in terms of chips.

The chip EV / ELO EV still feels like a part of the reason some players here may feel the "bad beat" happens far too often. There are tricky spots that have +ve chip EV but -ve ELO EV, and if they stick to chip EV way of thinking, their ELO may underperform.