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Implied Odds and Calling on a Draw in No Limit Cash Games
I was playing a No-Limit Hold’em cash game the other day on the internet, and was being berated by another player after I took almost his entire stack of chips.
It was a $100 capped buy-in, $0.50/$1 blinds game. I was in late position with the A-Q of spades, and a stack of about $150. He'd raised to $4 from second position, and got one caller. I called and everyone else folded.
The flop came 10-7-4 with two spades. He bet the size of the pot ($13.50), and the second player folded.
When I asked some other players what they would do in this situation, I got a number of dodgy responses to what is essentially an incomplete question. Many of these answers said that I was getting pot odds of 2-1, but I needed odds of nearly 4-1 to call. However, it's not possible to give a good comprehensive answer to the problem without knowing how many chips are in your opponent's stack. Anyway, here's what I did:
Because my opponent had me covered (had more money than me) I called. The turn came with a blank, let’s say an offsuit deuce. He bet the size of the pot again ($40.50), and I called. At this point there was $121.50 in the pot and I had about $92 left. On the last card, the beautiful king of spades fell. My opponent put me all in for $92, I called, showed him the nuts, and doubled up. He showed a pair of kings and started berating me for my bad play - complaining that I had terrible pot odds to call on the flop, and that I should have folded.
This kind of problem is all about odds, but not just pot odds, implied odds too. It is implied odds that the other player neglected to consider. This is quite a common mistake amongst new no-limit players, particularly those that have moved up from limit games.
On the flop I have a flush draw, and will make my flush on the turn 21% of the time (I'm disregarding the overcards I was holding to illustrate a point). My opponent is betting the size of the pot, which is $13.50, laying me exactly 2-1. So the decision on the flop is a clear fold according to pot odds.
My implied odds on the flop, however, are superb. My opponent has more chips than I do and has shown his affinity for betting the size of the pot. Let’s assume a couple of things: First, that my opponent will bet the size of the pot or thereabouts on the turn and the river (if you've been observing your opponents well, you should know whether they have this tendency or whether they will vary their bet), and second, that I will fold on the river if I don't improve to a flush (it'd just be silly to call otherwise, unless I improved to two pair or something). Lastly, I'm ignoring the money that's already in the pot before the flop because I'll lose that if I fold anyway, and it no longer belongs to me but to the pot.
63% of the time, I'll miss the flush and lose money. I'll lose $13.50 from my call on the flop and $40.50 from my call on the turn, or $54.
37% of the time, I'll hit the flush on the turn or river and double up (I'll win $146).
The end result of this is:
(.63 x -54) + (.37 x 146) = $20
This means that this particular sequence of calling on the flop and turn wins at least $20 on average, which means that it is profitable. In the case where I do hit my flush, I have won $146 for a $13.50 investment on the flop (nearly 11-1 implied odds). It gets better - the calculation above doesn't take account of the times when I make my flush on the turn (21% of the time) and doesn't take account of the times when I improve to something else good which wins, like three of a kind or top two pair, or the times when my opponent checks or folds.
Now let’s change something slightly. Instead of my opponent having me covered, let’s say he has only $75 at the start of the hand. Now, he bets the pot on the flop, leaving him with $57.50. He bets the pot on the turn ($40.50) leaving him with $17. And he'll go all in on the river for $17.
63% of the time, I'll miss and lose $54 ($13.50 on the flop and $40.50 on the turn).
37% of the time, I'll hit my flush and win $75 (his entire stack).
The end result of this is:
(.63 x -54) + (.37 x 75) = -$6.27
Now the play loses me $6.27 on average, making it unprofitable! And all because your opponent's stack wasn't big enough to pay you off if you did hit. So how do you work out how big your opponent's stack needs to be in order for you to call? It's simple really. Just work out how much you'll lose if you don't make your flush. In this case, I'll lose $54 the times I miss, and I miss 63% of the time, about 1.7 times as often as I hit. So my opponent must be able (and inclined) to dump 1.7 times $54 ($91.80) over to me when I hit my flush for it to be a breakeven play to call. Note that I must have at least $91.80 in my stack for this to be possible (since I can't win more than I invest).
Notice the breakeven point for the call is about 7 times the flop bet. Therefore, provided you've evaluated the situation correctly, you should call (with a flush draw) when you and your opponent have more than this.
This kind of play has a substantial amount of fluctuation to it, as does no-limit poker in general when played aggressively. Calling on the flop with nothing but a flush draw might not be the best play in a tournament, since in such a situation you often choose the play with a lower variance over the play with the higher expected value. In cash games, sometimes the situation will call for a raise instead. However, if you evaluate the situation correctly, calling with a draw in no-limit cash games can make you a lot of money!
