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Improving to flush, straight or full house

The approximate odds improving to flush, straight or full house by drawing one card is shown in Table 9.

It can be seen that an opponent drawing one card and hoping to fill a straight flush, flush, straight or full hous never has a better chance than just over 2 to 1 against. Indeed, unless he holds four cards which could make a straight flush (once in about 500 hands) then his chances of improvement are never better than over 4 to 1 against (not counting an improvement to one pair).
Table 9 also reveals that holding four cards to a flush, you have only a little worse than a 4 to 1 against chance of completing a flush with the draw. No skilled poker player would think of drawing two cards when holding three of the same suit, hoping to fill in a flush. The odds are about 23 to 1. The odds are about the same of filling to a straight when holding three cards in sequence – it is simply not worth attempting.

TABLE 9: Probability of improving certain hands by drawing one card
Four-card hand held		Improved final hand	Odds against
Double-ended straight flush (i.e. you could add a card to either end)		Straight flush Flush Straight Any of above	22.6 to 1 5.8 to 1 6.8 to 1 2.1 to 1
Straight flush with single end or gap in middle (i.e. there is only one value card you can add)		Straight flush Flush Straight Any of above	46 to 1 4.9 to 1 14.7 to 1 2.9 to 1
Four-card flush		Flush	4.2 to 1
Double-ended straight (i.e. you could add a card to either end)		Straight	4.9 to 1
Straight with single end or gap in middle (i.e. there is only one value card you can add)		Straight	10.8 to 1
Two pairs		Full house	10.8 to 1

The odds opposed to the pot

Players should have an idea of the odds against improving a hand at the draw so that they don’t bet more than their ‘expectation’. The expectation is the amount a gambler stands to win multiplied by his probability of winning it.