[StellarWind]

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Another important factor is that the pot is so small that shutting a flush draw out for one street is not all that important. Even if Nate was 75% sure that he was ahead, and that his raise would protect him from a 4th spade, it's still doubtful that it's worth investing another small bet to raise.

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Let's not lose perspective. If Nate is 75% likely to be ahead then this is a tremendous value raise versus three opponents and increasing our winning chances is merely a very nice bonus.

I suspect 75% is a rather high estimate however.

The pot is not so small when you consider implied odds. There are currently 2.5 BB in the pot. This will increase to 3.5 BB after Hero and (assume) one more player call the flop. Hero intends to bet the turn which if called in two spots will increase the pot to 6.5 BB. Toss in 2 BB for a river bet and one caller and we have 8.5 BB. Obviously it could be less but it could easily also be more.

This is going to be a 7-10 BB pot when someone wins it. That's why it's not a big deal to invest an extra 0.5 BB on the flop to improve our chances.

It's also important to realize that "invest" is not synonymous with "spend" or "lose". If everyone were expected to call then we would be getting 3-1 odds on our raise. We would only need to win 25% of the time for our raise to be free and anything beyond 25% is immediate profit.

I think our pot equity at least meets this 25% threshold. I'm not concerned about the high cost of raising because there is no cost. This is a value raise.

The obvious objection is that we may not get three callers. But our likely best hand is so precarious that virtually any fold is more valuable to us than a caller.

Example: we raise, BB folds as he always intended, Daniel would have called one but folds to two, and Ed calls. Our raise cost us 1 SB and we get these benefits:

1. The pot is 1 SB bigger than it would have been (1 from us, 1 from Ed, less 1 that Daniel keeps instead of calling just one). We are the heads-up favorite and a big piece of that extra SB is ours.

2. Our chance to win is substantially increased by Daniel's departure. This is a process that favors weak made hands over nut draws. If Ed is banking on A [img]/images/graemlins/spade.gif[/img] 3 [img]/images/graemlins/heart.gif[/img] then his nut flush and pair draw give him a very good chance to win. But removing Daniel does almost nothing for that winning chance. Almost all the times Daniel would have won will go to us. Ed would be much better served by Daniel staying in the pot and donating money.

Overall in this example we lose less than 1/2 SB of immediate EV and gain a substantial increase in our chance of winning a medium-size final pot. That is a very favorable trade.

This is a classic example of the Fundamental Theorem of Poker breaking down in a 3-way pot. The junky best hand wants Daniel to fold his outs while the flush draw wants Daniel to stay and donate his money. Whether Daniel is making a mistake by calling or folding is beside the point. [Lest anyone get the wrong idea, Sklansky clearly states that his theorem does not always apply multiway.]

Another perspective on checkraising the flop is that from a purely protection view it is by far the best. The pot is as small as it is ever going to be. Ed is still live behind the potential coldcallers and will also be acting last after our threatened follow-up turn bet. If the middlemen won't fold for two bets now, then they can never be made to fold. This checkraise is the biggest bomb at our disposal and if it won't work then our hand is beyond protection.

Remember that any turn protection is inherently only half as good because it only works against one card instead of two.