On the button, at a two advance table

I've been mostly absent from strategy discussions here for the last few years, only posting or replying occasionally. I play only 4 or 5 times a year these days, often even less. And this stuff is not at all like riding a bicycle. I feel rusty ever single time I play now!

But, when someone asked me some questions via private message about an example in Wong's book, I decided my replies would do more good posted publicly. And besides, it will be fun to see others chime in with more recent chops!

I think the example is page 97 in CTS. (I actually don't even have a copy now!)
I'll lay out the scenario and my thoughts in separate messages below.

 

The scenario is this:

BR2 (you), bank $500.
BR1, bank $603.
BR3, bank $480.

Wong's advice is to bet $150, or maybe $200 or $250. He says the hope is that BR1 will bet small behind you.
The original question posed to me was, why not bet $15 to take 2nd low?
My reply follows.

 

Betting 15 will almost certainly give you 2nd low and 3rd high, which is a pretty weak spot. You’ve given BR1 a lock by betting small, and you now have a roughly 56% chance of advancing.
But Wong’s recommendation is likely to play out similarly. If you bet his recommended $150, BR1 has a choice between $200 to cover your possible double, or $120 to cover BR3 push. I would prefer $120 in his spot.

Now BR3 could bet just $125 to get 2nd low, 3rd high, but should instead take 1st high with a big bet. I would keep it simple and go all-in with the $480.
If the three people bet $150 / $120 / $480, you again have the same starting outcomes as if you had bet the $15! You are 3rd high, 2nd low!

So, why is $150 better?

With the larger bet you can double down to take back a high. If you bet $15 your eggs are all in one basket with no option to improve your position with a double. That gives you a better shot than 56%.

Now, my personal decision for this example...
As BR2, I prefer a bet of $225 to $250. BR1 might decide to still bet only $120 (holding back $483) and give you first high. That would be your best scenario.

 

Another thing to consider is your assessment of your opponents' playing style/skill. In 2019 many of your opponents will still reflexively bet the max no matter the situation on the last hand.

If BR1 is such a player you could bet 396 for second low. BR1 will bet 500 and then BR3 is likely to take first low with a bet of 375. This gives you the see-saw you want (2nd hi 2nd low).

If BR3 is such a player you could take a double-minus holdback with a bet of 461 (hold back double the lead minus a chip). BR1 is likely to bet 461 and give you 2nd low 2nd high.

If both players are reflexive max bettors then 461 is your bet for the reasons stated above.

In all cases above you need to have confidence in your read on these players because if you're wrong you could end up with 2nd high 3rd low.

 

You don't want to incentivize your opponents to focus on you while ignoring each other. Because that's what will happen if you go all-in. If that happens you'll wind up with 2nd high and 3rd low. You can probably do better than that.

If you bet 15 BR1 can bet the minimum and lock up his rank. You almost never offer an opponent a lock if you can help it. If you bet 15 you'll get 2nd low and 3rd high. Also very bad. The ideal target is 2nd low 2nd high or better.

 

I gave you my reasoning in reply #3.

 

I'll add a few more ideas here.
I'm assuming that bets must be in $5 increments despite BR1's bankroll of $603 (it could be that a $5 BJ pays $8 in this tournament.)

I think we've covered why $15 is inferior to the others. It gives BR1 a free ride, and you are simply betting that BR3 won't win their hand. A bigger bet gives you more options, because BR1 is now in play, and there are numerous ways you can advance even if BR3 wins their hand.

Once you decide to bet more than $15, how much do you bet? You are trailing BR1 by $103, so you need to bet at least $105 to beat a push by BR1.
But bets of $105 to $220 make BR1's job too easy. They can bet up to $120, and they'll have the high and low over you, and they also hold back more than BR3's total bankroll guarding against a BR3 push.

That's how I got to my preferred $225 in this case.

Now if BR1 wants to cover you high and low it will at least make them give up the BR3 push scenario. In general, you want to make BR1's covering of you as expensive as you can. Give them reasons to not do it.

Now in fact, they probably still will bet enough to cover you, and they certainly should.
If you bet $225, BR1 should bet at least $125 and I would advocate BR1 bet $180 (if everyone gets all-in, that's very helpful because he can double as well).
But again, as BR2, with your bet of $225, BR1 may just let you have the high and bet $120 or less after looking at BR3's unbet stack.

So, why don't I like $250?
It's a very common play, splitting the bankroll.
I think BR1 seeing you split your chips makes it more likely that he will do the same, which you don't want him to do.
So I would choose to bet less than $250 for that reason.

Hmm, now that I think more, if you bet $230 instead of $225, now BR1 must bet at least $130 to cover you, and that means BR3 can take first low with a $5 bet!
Back when I played a lot, this would have probably been automatic for me. It's not now!
With a $230 bet, you've really given BR1 something to think about before he covers you on the high.

That's a perfect example of my credo, "There's always a better bet".
I like $230 now. Is there a better bet? Probably.

In the end, this is a typical scenario where all of these bets will be within a small percentage range of each other in success rate.

 

Not sure where I got $603. It might affect a point or two above, but it should be obvious when that is the case.

Also, I just edited a typo in my big reply above, where I said BR3 could get first high if BR1 bets $130. Obviously I meant first low. The mistake is corrected now.